Harmony Its Theory and Practice-prout

^jjjMjffiifjjiJ^in^^..-.- MT 40.P96 1903 .^ ~f2™*" Un'»e«lty Library 3 1924 021 757 285 CORNELL UNIVERSITY LIBRARY Gift of George H. Sabine MUSIC B « Cornell University Library The tlie original of tliis book is in Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924021757285 AUGENER'S EDITION, No. 918a HARMONY ITS THEORY AND PRACTICE BY EBENEZER PROUT THIRTIETH EDITION REVISED AND LARGELY REWRITTEN TWENTY-EIGHTH IMPRESSION AUGENER, LTD. LONDON Boston, Mass.: THE BOSTON MUSIC Augener & Co, CO. Sole Agents for America Copyright, 1903, for all Countries, by L'Allegro. ." MILTON. GILSON COMPANY BOSTON. U. Stanbope ]pres2 H.S."Untwisting all the Chains that Tie The Hidden Soul of Harmony.A. ble servants or Brahms." or. "Bach is wrong. not that the composer is wrong. In other words. If they ask the help of their teacher in their difficulty. It is a significant fact that. at best. works of Beethoven. and the author hopes that it contains sufficient novelty both in plan and in matter to plead a justification for its appearance." No doubt examples of very free part -writing may be found in the works of Bach and Beethoven. several such are noted and explained in the present work. and make his rules conform to the practice of the master. "This is a licence. The inspired composer goes first. . but. even in the most recent developments of the art. or Dvorak breaks some rule given in old text-books there is. they are probably told. practice must precede theory. it is the business of the theorist not to cavil at every novelty. and invents new effects . and the objections made by musicians of the old school to the novel harmonic progressions of Wagner are little more than repetitions of the severe criticisms which in the early years of the present century were launched at the ! ' ' . " The present volume is the outcome of many years' experience in teaching the theory of music. But the principle must surely be wrong which places the rules of an early stage of musical development above the inspirations of genius Haydn. or even of Haydn and Mozart ." or "Beethoven is wrong. a very strong presumption.that the rule needs modifying. So large a number of works on Harmony already exists that the publication of a new treatise on the subject seems to call for explanation. Most intelligent students of harmony have at times been perplexed by their inability to reconcile passages they have found in the works of the great masters with the rules given in the textbooks. but to follow modestly behind. to say the least. replied that ' ' the rules were all his very obedient humand when we find that in our own time AVagner. if not for apology. when asked according to what rule he had introduced a certain harmony. nothing has yet been written by any composer of eminence which a sound theoretical system cannot satisfactorily account for .PREFACE TO THE FIRST EDITION. of this work (§ 42). or Schumann. the fourth and the sixth. Day's derivation of the chords in a key from the tonic. school of composers. that "the system of Scales. but Ouseley' s explanation of the harmonic origin of the minor third is adopted. (§ 44) that by rejecting altogether the eleventh and thirteenth notes of the harmonic series. nor The system of theory propounded in the present volume is founded upon the dictum of Helmholtz. and that all others are wrong. from these harmonics. the chief objection made by the opponents of all scientific derivation of harmony that two of the most important notes of the scale. and will still further change with the progressive development of humanity. therefore. so that even those musicians who may differ most widely from the author's theoretical views may still be disposed to admit the force of practical rules supported by the authority pf Bach. are founded. dominant. While. the author follows Day and Ouseley in taking the harmonic series as the basis of his calculations. It is from this been written. and taking in their place other notes produced among the secondary harmonics. ' which have already changed. Modes. and Harmonic Tissues does not laws. It has been thought desirable to separate as far as possible the practical from the theoretical portions of this work.iv Preface to the First Edition. are much out of tune ^has been fully met. but in ' other respects his system ical basis is extensively modified. No such claim is made for the system herein set forth but it is hoped that it will at least be found to be in^ perfectly consistent with itself. In the vexed question of the minor tonic chord. The consistent with the not upon that. and sufficiently comprehensive to explain the progressions of the advanced modern . and supertonic is adhered to. The latter are therefore printed in smaller type . though in no degree intheoretical system expounded.. he claims the right to make his own selection. on any other abstract system. It will its purely phys- be seen in Chapter II. to omit at least Chapters II. who may take up this work without any previous knowledge of the subject. quoted in Chapter II. telligible. on aesthetic grounds. being entirely abandoned. . point of view that the present volume has rules herein given. but is rest solely upon unalterable natural at least partly also the result of aesthetical principles. and to use only such of them as appear neeful to explain the practice of the great masters. but upon the actual practice of the great masters . and no writer on harmony is justified in saying that his views are the only correct ones. Helmholtz is followed to a considerable extent . — — Truth is many sided . and III. dealing with the Harmonic Series and Key or Tonality. and it will be found advisable for beginners. Beethoven. many exercises are in the form of double chants or hymn tunes. and valuable feature of the volume be found in the illustrative examples. without exceeding reasonable limits to illustrate all the points mentioned. Not the least interesting will. which in their turn must be pre- — — be. these objects. examples might have been found to illustrate every rule laid down in the volume. especially the higher discords the ninths. had want of space not prevented their quotation. from Bach and Handel down to the present day. the chords. it is hoped. of course. and contravened by the daily practice of modern writers. it is hoped that at least no rule of importance has been given without quoting some recognized author in its support. The learner's motto must " One thing at a time. from a musical point of view. and. chiefly. have been altogether omitted. mostly in four- To stimbar rhythm. It is of the utmost importance that students who wish to master the subject should proceed steadily and deliberately. though not exclusively. and others have been greatly modified while the laws affecting . because modern harmony may be said While it has been impossible to begin with Bach and Handel. materially simplified. a proper understanding of the chords of the eleventh will be impossible until the student is quite familiar with the chords of the ninth. discretion of the teacher.Preface to the First Edition. With this object they are. For example. it is believed. The exact point at which the student will do well to return to the omitted portions will depend upon his progress and his general intelligence. and that done thoroughly. and on Harmonizing Melodies. and the student's ingenuity will be usefully exercised in trying to write as melodious an upper part as possible for these little pieces. ceded by the chords of the seventh. many rules now obsolete. until v some considerable progress has been made in the practical part of the volume. and thirteenths ^have been classified. illustrating the various forms of cadence. ulate the pupil's imagination. written in the form of short musical sentences. and must be left to the In the practical part of the work an attempt has been made With a view of effecting to simplify and to codify the laws. It may at all events be positively said that. be harmonized in several different positions . elevenths. It was originally intended to have included in the present work chapters on Cadences. Each bass can. from the works of the greatest masters. conThese have been selected siderably more than 300 in number. Earlier examples are not given. ." In preparing the exercises a special endeavour has been made to render them interesting. with a few exceptions. as far as possible. and to encourage attempts at composition. To his friend. Louis B. however. . which belong rather to practical composition than to harmony in its It is intended to strict sense. /«Kf. . the author was in frequent correspondence on the subject of this work. and to bring it down to date. The author desires to acknowledge the valuable assistance he has received in the preparation of his work. have been reluctantly omitted.vi Preface to the First Edition. to whom he is indebted for a very large number of the illustrative examples. Valuable aid has also been received from the late Rev. London. with whom. has. that these chapters. Prout. first The volume extended to so much larger dimencontemplated. the author must express his thanks for much generous interest and many most useful suggestions. as well as for his kind assistance in revising the proofsheets of the volume. would be unreasonable to expect that the present work will meet with universal approval but it may at least claim to appeal to teachers and students as an honest attempt to simplify ^he study of harmony. in which sions than was at these and similar subjects will be more appropriately dealt with. It . Sir Frederick Ouseley. down to the time of his lamented death. follow the present work by a treatise on Composition. also. Charles W. Pearce. and who has also written many of the exercises. Dr. 1889. first and foremost from his son. Though called a is new edition. he would have been either hopelessly ignorant or incurably conceited had he not become fully aware of its numerous defects and shortcomings. is so largely the result of aesthetic. it would be hardly too much Considerably more than to describe the present as a new book. whether major or minor. but he has thought it best to complete the series of which this forms the first volume before undertaking so serious a task as remodelling this treatise. and thirteenths series of upper partials were far greater than he had realized in first writing the volume. elevenths. rather than of scientific considerations that it is far better for the student It that it should be dealt with from the former point of view. than twelve years since the first edition of Theory and Practice was published and the great success with which the work has met has no less surprised than gratified its author. He has felt that he could best show his appreciation of its generous reception by the musical public by improving it as far as lay in his power.vu PREFACE TO THE SIXTEENTH EDITION. At the same time he must say that. But the modern key. that the reason for the numerous changes made may A be understood. For some years past it has been his intention to do this as soon ^ as the pressure of work allowed. That the acoustical side of the subject has nevertheless an important bearing on harmony he still holds and this matter is dealt with in Appendix B. Further investigation and thought have convinced the author that the practical objections to the derivation of the higher disfrom the natural cords the ninths. half the text rewritten. after so many years' experience in teaching from it. First and foremost among these is the virtual abandonment of the harmonic series as the basis on which the system is founded. is obvious that this change has necessitated an entirely new treatment of the question of the chromatic constituents of a — — . either additional matter. or has been entirely short account of the modifications introduced is necessary. It is now more : Harmony Its . which replaces Chapter II of previous editions. be found much key. and chromatic chords are considered as being borrowed from neighbouring keys. every chord in each exercise is analyzed on the system here taught. however. . does not apply to the Chants and Hymn Tunes. up to and including the chord of the dominant thirteenth.viii Preface to the Sixteenth Edition. and that each branch of the study throws light upon the other. found that pupils who can do the latter with ease are hopelessly The author's own experiat sea when they attempt the former. it is in practice extremely simple. The system adopted. A new feature of the present edition is that. the diatonic. Though the method looks at first sight complex. the Additional Exercises have been incorporated in the volume. ling. special attention is called to the new Key to the Exercises. and the exercises on each chapter have been graduated. Louis B." it will be most useful to consult it after the exercises have been worked. simpler and easier. especially for self-instruction. is that of E. was first propounded by the author's son. The whole of the diatonic material of the key. from the very beginning. in the order of diiiSculty. though with considerable modification. which it has been thought advisable to place by themselves at the end of each chapter. in his Harmonic Analysis. F. the harmonizing of simple melodies is taught simultaIt is often neously with the harmonizing of figured basses. than its predeThe chromatic element is regarded as subordinate to cessor. To avoid the inconvenience arising from the use of two books. to which little work the author acknowledges his obligations for many valuable suggestions. Though the Key should in no case be used as a " cram. In this. ' ' ' ' ' ' ' ' . The new treatment of the subject has involved the rearrangement of a great part of the contents of the volume. as far as and in some This. is dealt with before the chromatic chords are introduced. if systematically pursued from the beginning and the insight into the harmonic structure of a composition which is obtained by its means will be found by the earnest student invaluable. This view it is believed. the harmonization of a melody presents no very great difficulty even to beginners of average ability. practicable. Prout. The plan now adopted will. if the two are taken together. and the analyses written beneath them. This has necessitated the remodel- cases the entire rewriting of the exercises. and more particularly for teachers who may use this book. ence is that. For his guidance. Richter the author has extended the idea of his predecessor by making a difference between inversions and derivatives of chords (See § 252). Another most important addition to analysis of the this volume is the full harmony given throughout. it is believed. ix of. if it smooths over the difficulties in the path of the student. . owing to the multi . chief among which should be named Marx's Composition and Charles Child Spencer's Brief Account of the know — — Church Modes. not without some confidence. that the present edition will be found not only more complete. but far simpler for teaching purposes than the work in its earlier form . sketch for it professes to be nothing more has been compiled from many sources. the author will feel himself well repaid for the year's hard work spent in its preparation. the second has been already spoken The first contains a necessarily brief and incomplete account of the Ecclesiastical Modes. Greenish and Mr. a subject of which most students little or nothing. Of the two Appendices. A. It is hoped. R. ^ London : December^ igoi. The author would acknowledge his obligations to many who have kindly assisted him with advice and suggestions in the preparation of this new edition. but a slight acquaintance with which will be found of great use in aiding their comprehension of much The of the music of the seventeenth and eighteenth centuries. — plicity of detail. He is also indebted to several kind friends for their help in reading the proofs a more than usually laborious task. Orlando Morgan for many useful practical hints. J.Preface to the Sixteenth Edition. From his son he has received much valuable help and he also desires especially to thank his friends Dr. especially as regards the Key. because the passages in question have been replaced in the new edition by others. they will not be found.NOTE. As the other volumes of the series are reprinted. In consequence of the rearrangement of the subject matter in the present Chapters and Sections have been renumbered. In two cases (^§ 423. As there are many references to Harmony in the following volumes of the series. the necessary alterations of references will be made in the text. with the corresponding numbers in the new edition. a table is here given of the Chapters and Sections referred to. edition. 434). both Previous . 21 Minor intervals. 4 Semitone. g The chromatic scale. 14-16 The Resolution of a Dissonance. . 10 Names of the Scales. to find the tonic — CHAPTER III. 5 Enharmonic Diatonic and chromatic semitones. fifths. 8 degrees of the diatonic scale. 40— How mark the 41 — The material of a minor key. 2g —Table of intervals. 26 Inversion of compound intervals. refer in every instance to the sections. octaves. pitch. 87. 93 The best position of harmony. flats. part-writing. voices." 58 Diminished intervals. 18 Compound intervals. —Development of key from 34— The a key. 6 interval. fourths. 25. 88—^The diatonic triads of a major key. 54-S^- 50. ninths. 1 1-13 Consonance and dissonance defined. diatonic diatonic to difference Position sharps. 30. not to the pages CHAPTER Amount Introduction page I of knowledge presupposed. — The numbers I. 86 intervals. to similar chief difficulties of harmony found in the earlier stages. how treated. INi B. 35 — A Chord: major and minor comand chromatic elements mon 36 — Major and minor keys. — 60 intervals. 45 — Tetrachords. go "Doubling" a note. 2 Melody and harmony defined. 24 Inversion of intervals. 20 Perfect and major intervals. 16 Discords. 57 Rules of melodic progression. 23. The General Laws of Part-Writing page 22 A Part defined. sevenths. inter- note. The three primary triads 104-109 Short score. 38—The material of a major key. 92 Close Triad. 97-99 Omission of one note of a chord. — — 61 — The leap of a seventh with one —Large mediate —Leaping an accented 63 — Harmonic progression oblique. 82-84— Overlapping and crossing of 85 —An unprepared discord best approached by contrary motion. 17 How intervals are reckoned. The Diatonjc Triads of the Major Key A Triad. page 13 diatonic in chords. signatures. 94-96. 5 (note) Tone 7 Diatonic scales. CHAPTER IV. 3 Interval defined. 37 — The " primary notes " of a key. and contrary motion. to note. fifths. 28 and diminished — — — — — — — Perfect and imperfect consonances. or Tonality 31-33 its Definition of JCey. enharmonic keys. roots. 81 —Approaching and 79. 62. 44— Other keys than C. i musical sound . 3g. 43 — of the semitones. 22 Augmented — — — —A — — — — — —A — — — — — intervals. 101 best notes to double.XI TABLE OF CONTENTS. "conjunct" and "disjunct motion.—Key. 102 Three rules for part-writing. 8g —The page 34 Diminished Compass of the voices. 52— Table of keytonic. — — — — — — — — m— . 1 10 Open score. 46 — Keys with 47-49 — Keys with 51 — How of any major key. 53 How to find the signature of a key containing more than seven sharps or flats. 80 — The progression from a second leaving the unison by motion. CHAPTER II. similar. The Treatment of the leading note. 64— Four-part harmony 66— Consecutive unisons names of the 65 — Rules of and 67-70^— Consecutive 71—73 — Hidden octaves and 78— Consecutive seconds. 42—The between major and minor keys. 59 Augmented —The parts. ig Different kinds of intervals. 91 and extended position. 27 Consonant and dissonant intervals. and 74—77— Consecutive a unison. 100. 140 Ditto with bass only given. 200-203 Melodies given for harmonization. the number of possiInversion in general. igo Exercises Special exercises for the treatment of second inversions. 13S 137 Licenses permitted in repetitions of a sequence. 178 Its position in the bar. 141 position of chords in a sequence. 191 on a figured bass. 184-187 for quitting a second inversion. 164 marking the roots. I49 —General — principles. 210 Relative major and minor keys. 138— Changing the Directions for working. 208 Melodic minor scale. 118— The choice of Plagal Cadences. 132 Sequence defined. 128. 114— Exercises with bass given. the key. 120-126 harmony: the reason.xii Contents. The Diatonic Triads of the Major Key (Continued). 181 ^Progression of the voices in a cadential J. 220 The CHAPTER — — — — — — — — : — — — — . 163 Figuring ble inversions. 180 The second inversion of the subdominant chord. 146 — step. 174. 189—The best note to double. 134 Length of doubled. 117 define — — The stiiif effect of chords. 113—The position of the first chord. The Minor Key: Its Diatonic Triads and their Inversions fage 80 The Harmonic Minor Scale. 175 5 " of the tonic chord. 130 The intermixing Three-part harmony with one part of primary and secondary triads. 150-152 — for harmonization." 129 notes to double. 213 The augmented triad on the mediant. 177. 205. 194-I99 melody roots. the importance of hearing the music mentally. 144 The leap of a third. 215 The "Dorian sixth": its employment in the subdominant chord. — — this CHAPTER V. The second Second inversions of secondary inversion of the dominant chord. 159. the leap of a fourth. melody harmonized. 161 to show the position of chords when of the first inversion. 188 Rules triads. 160 The first inversion. 179 ^The same chord used non-cadentially. 166-168 Treatment of — — — —How — a series of first inversions. 172 Its incomplete effect. ?-ifa/ sequence. 212 The diatonic triads of the minor key. 219 ^The Dorian sixth in the supertonic chord. 204 The composition of four-bar phrases. 2i8 A modem example of its use. 211 Tonic major and minor keys. 142 —Which — — — — — f^g' 49 — —Harmonizing melodies 145 — Root progressions 147 — Progressions by — — : : How to begin and end. 131 Tonal sequence. CHAPTER VI. 153-158 —Melodies 148. 133 Irregular sequence . 119— A melody harmonized. 173 How to find the root of a chord from the figured Second inversions of primary triads. Sequences The " secondary triads. The Inversions of the Triads of a Major Key page 61 Inversion of a chord defined. 207 The Dorian scale. 165 Which notes to double. 139. 182. I43 Exercises with treble and bass given. Interval of imitation. 214 The diminished triad on the supertonic. 136 pattern. 176 The " cadential bass. 115— Harmonizing a melody with primary triads only. 206 Older forms of scale the Aeolian. 162 Figured Bass. 192 Enlarged meaning of the term " progression of ^Additional rules for root progression. — — — — — — — — — — — — — — — — — — —A — VII. 217." 193 harmonized. 127 Melodies given for harmonization. 112— The connection of the primary triads with one another. 116 The Cadence: Authentic and The position of the cadence. 209 The leading-note of a minor key never written in the signature. 183 Rules for approaching a second inverson. 169-171 The second inversion. choice of chords. 283 — Modulations modulation from a major key from minor keys. 234 Omission of the fifth. 252 inversion and its derivative. 237-239 on ^t first inversion of the tonic chord. 227 Exercises. xiii progression between dominant and submediant in the minor key. 304 Auxiliaty notes defined. 281 — Change of the primary supertonic minor. —False Key Relation page 115 Modulation and Transition defined. 268 Exercises. 273 — Chords common nearly related key keys. 248-250 Omission of 1 Distinction between inversions and the generator in this inversion. 233 Treatment of the third and seventh of Resolution on the tonic the chord. and Anticipations (I) Auxiliary Notes. 308 Auxiliary notes in more than note. 298—The Inverted Cadence. 292 — Modulation by General means of of the dominant seventh. 231 The chord of the dominant: seventh a " fundamental discord " defined. 303. 278 — Figuring the bass 277 — How modulations. 271 — Related major keys. 279 — Immediate and gradual modulation. 297— Harmonization of Chorals the Cadences. 221 The doubling of the submediant. 241 Resolution on the subdominant chord. 274 — Table of nearly keys. 263 Resolution on the second inversion of the submediant chord the only satisfactory position. 229 — — — — — — CHAPTER Vin. 223 How to indicate the roots of the minor seventh of the Icey. 301 — Implied modulations. 302— Chorals CHAPTER Keys to related their signa- tures differ. Tierce de Ficardie. 261 Examples by Handel. 275. 245versions of the chord of the dominant seventh. Unessential Discords Notes. 296 —Exercises. 228 The these chords. 294 Transitional Dominants. 299 —The Interrupted Cadence. 235 Resolution chord. 257 Its resolution on ih^ first inversion of the chord. 300— Position of the harmonize. 230. 3 10 Examples referred to. to effect in to notes. 266 Treatment of the dominant seventh in a full cadence. 306 When a tone and when a semitone from the harmony Chromatic auxiliary notes. 305 How taken and left. 307 one part. 236 Ornamental resolutions of the seventh. 242 Their figuring. 276 — How modulation. The Chord Effect of tonic : page 94 of the Dominant Seventh and dominant harmony. 232 The seventh a dissonance. 25 How to mark the roots of derivatives. 280— How 282 —The^ regard ambiguous chords. when to be avoided. 258. 286-291 modulating nearly related keys. cadences.Contents. 284— Examples of modulations analyzed. 253 Examples derivatives. 240 Reason of the importance Resolution on the submediof the chord of the dominant seventh. 260 The derivative of the tonic second inversion. 267 Exceptional resolutions. 262 The third inversion its usual resolution. 309 Passing Chords. 312 Changing — — — — — . 265 Changes in the position of a chord of the seventh before resolving. 295 — False Relation. 264 The derivative of the thurd inversion. to its rules for to irregular resolutions : to CHAPTER X. 224-226 Second inversions in the minor Icey. 293 — The choice of modulations. 269. 272— Unrelated keys. 244 247 The first inversion its various resolutions. — — — — — — — — — — — — — : — — — — — — — — — — — : — — — — — Relationship — Modulation to nearly related IX. 254-256 The second inversion of the first its most usual resolution. requiring resolution. 270 Key Relationship. 243 The inant chord. 259 Other resolutions. Passing page 131 Notes unessential to the harmony. 222 First inChords containing versions : how to avoid the augmented second. notes. 375 Irregular resolutions on fifth or seventh of chord. 414— The remaining derivatives. 374. 376 Position of the major ninth. 332. 329 Notes of a melody treated as accented auxiliary and passing notes. —A CHAPTER The Unessential Discords (II) Suspensions page 145 kinds of unessential discords. 368 Which note to omit. Contents. 384 Resolution of these derivatives. 333 Suspension defined. 402 More than one analysis sometimes possible. . 381 Derivatives of the dominant ninth. 320— Passing notes 322 —Auxiliary notes cannot make 323. 345 How to know a suspension from the figuring..XIV notes. 314— Auxiliary notes taken by 315 313 — Single changing —Passing passing a minor key. 398 Resolution. 324 employment of 325. 409— Other derivatives. 408— How to distinguish between chords that are identical in appearance. 338 Their position in the bar. 344. 410— ^-^^ Chord of the Added Sixth. notes. 331 Directions for work. 340 When it may be sounded with the note of its resolution. 392 Exercises. 378 The chord resolved on a different root. 326 — Summary of 328— and passing 327 — Exceptional treatment of notes. 399 Inversions. 336 Suspensions not to be marked in indicating roots. 385 Examples from the great masters. 346. 357-363 Double suspensions. notes. 364. 395 Which notes mostly omitted. 348-350 Ornamental resolutions. 390 Further derivatives . these chords how to tell their real nature. 334 Which notes can be suspended. 347 The inversions of suspensions. 339 Length of preparation. 337 Their preparation. 417—The subdominant chord a derivative of the dominant eleventh. the ninth proceeding to the root. 386-389 Changing the position of the chord before its resolution. auxiliary notes. 341 Incorrect progressions. 383 The Leading and Diminished Sevenths. 412— Resolved on a tonic chord. 400 — — Eleventh. 317 —Two 31 6 — Ditto — Chromatic passing 319 — Passing notes 318 321—Examples by by contrary motion. 365 Suspensions of complete chords. 413 Used in approaching a cadence. 366 Directions for work. 407 Ditto on a tonic chord. The Chord of the Dominant 401 Second inversion. 342 Always resolved on the chord over which it is suspended. 403 The other inversions. 416 The figuring of 415. 393. 372. notes. 343 Practical limitations to suspension. 391. XI. 394 The difference between the eleventh and the fourth. 397 Gradual resolution of the higher discords. 353-356 Suspensions re3SI> 352 solving upwards. 380 The inversions of the chord rare. 396 Figuring. false relation.373 The ninth proceeding to — — the third. 371 The chord resolving on its own root. 411— Resolved on a dominant chord. page 172 — — — — — — — — — — — — .. referred to. First inversion. 367. auxiliary rules for Anticipations. how figured. successive in several parts quitted leap. 379 Treatment of the fifth. choral harmonized with auxiliary notes. in leap. 370 Figuring. — — — — — — — — — — — — — CHAPTER The chord of XIII. 405— Ditto of the second inversion. Examples from the great masters. 406 Its resolution on a dorhinant chord. 404 Derivative of the first inversion (rare). 382 Inversions of the derivatives. 418. the supertonic chords of major and minor keys. — the eleventh. 330 Their introduction. different — — — — — — — — — — — — — — — — CHAPTER XII. 377. The Chord of the Dominant Ninth page 161 The chord of the dominant ninth different in major and minor keys. 435 — Alternative 436 — Resolution on the Root. how — and the 426 — Forms 427 Root. 506 Sequences of modulating sevenths. 498 The inversions of the chord. 460. 440— Ditto resolved on a chord. 459 The melodic chromatic scale. 500 Ditto in the first and second inversions. 484 The Supertonic Treatment of the third. 425 423 —The lower notes of the chord. 479 Which chords are restricted in their progression. tonic third. 434— Resolution on nant seventh. 430 chord. 461 462 In a minor key only the neighbouring minor keys borrowed from. 439 — Derivatives. 452 Chromatic chords defined. 468 469 Seldom used except as a passing chord. last inversion. 458 How formed from the diatonic its harmonic form. 431 —The Ditto on the 432— The and domi433 Hoot. 482. borrowed. in use. 447—Examples by Handel. 455 which they are borrowed. 486 TreatSeventh : its chromatic notes. 456—The keys from 454. — ^The thirteenth thirteenth . 476 Rarer chromatic chords. 483 The chromatic sevenths are the dominant sevenths of nearly related keys. 491 ^A seldom used progression. third. The Chord of the Dominant Thirteenth page 185 — — — 424— Resolutions. third. 481 Modulation by means — — — — — . from fundamental 444— Secondary sevenths. 453 Illustrations. thirteenth. 473 The major chord on the supertonic. 502 The derivatives. the tonic first inversion. 495 The Tonic Seventh: its resolution. seventh. chord. — — — — — — — — — — — — — — — — — — 507- . triad tonic the thirteenth in its differ sevenths. to distinguish figuring. 457 The chromatic scale. 478 List of chromatic common chords in a major key. how to indicate the roots. 421 The thirteenth a consonance with the root. 463 Three methods of averting the modulations suggested by chromatic notes. 489 The seventh rising to the fifth of the dominant chord. the seventh on the subdominant. 488— Examples of its employment. 428—Which and double. 448— A of secondary 450 — 449 — Secondary 451. Exercises. 464-466 How to mark the roots of chromatic chords. 493. 420 Contains every note of the diatonic scale. 485 ment of the seventh. thirteeenth. ninths. Why only nearly related keys are used for borrowing from. 497 Progression of the seventh. origin to for their treat- series sevenths. 467 The The ionic major chord. 474 Treatment of the third of the chord. 475 Examples analyzed. 499 Examples of the tonic seventh in root position. 443 Secondary Discords. 422 The inversions. the explanation. 503 Examples. chromatic common chords of a minor key. 442 —The chord of the complete form. Chromatic Triads Chromatic notes in a key. thirteenth completes the series of dominant chords. Chromatic chords are borrowed chords. 504. fifth. 419 It differs in major and minor keys. 470 The chord on the " Neapolitan sixth. 437 and 438— Other forms of the chord. 492 Examples of the inversions. —The Chromatic Scale — — — — — page 198 — — — — — — — — of chromatic chords. CHAPTER XV. the flattened supertonic. Chromatic Chords of the Seventh page 215 nature of chromatic chords. xt CHAPTER The XIV. 487 The inversions of the chord. CHAPTER The real XVI. 496 Progression of the third. 505 Modulation by means of chromatic sevenths. 441 — The on submediant. notes 429 — Resolution on dominant seventh. 471 Its second inversion. to ninth. how they be disregarded." 472 Its first inversion. 477.Contents. how from mediant chord. 446 — Rules 445 —Their harmonic ment. treated. 480 Examples of chromatic chords in a major key. 494 Derivatives of the chord. 501 Ditto in the last inversion. 490 The seventh leaping. 596— 598 — Examples. 563-565 II. ninth. 552 resolution: false notation. 540. 516— Resolution upon a different root. and thirteenth. 599-601 The German Sixth. 557 Derivatives of chromatic thirteenths rules for their identification. — — — — — tions. 581 Derived from two tonics. eleventh. 539 Extives. a " False Tetrad. and thirteenth. its resolutions. 510 Its derivatives. 512 The dominant major ninth in the minor key. 611 — Enharmonic modulation only with the German 612— When employed. 583 It has a " double generator. 536 Modulation by means of the diminished seventh. 590 the scale the commonest. 559 The derivatives I. 597 — 594 Its resolu- Its inversions. 568 IV. 543 Can be effected between any two keys by the diminished seventh. The 524 Examples of derivatives of the supertonic ninth. and thirteenth. 537 of major ninth. 571 VII. — — — : — — — — — — — — — — : — — — — — CHAPTER XIX The Chord The chord of the Augmented Sixth ' of the Augmented Sixth. 561 False notation " False Triads. seventh. 532-535 Ditto Rarer derivaseries of diminished sevenths. . and thirteenth . 511. 509 ninths. sixth. possible sixth. analyzed. 553 Its tonic eleventh. 569 V. 588 Distinctive names of the three forms. 576-579 The difficulty of these chords." 584 Resolutions of the interval of the augmented sixth. 570 thirteenth. Its inversions. Third. seventh ninth. 604-609 —Rare forms of the chord of the augmented 610— Modulation by means of the chord. Third. 591 The chord on the sixth degree of in analysis. 538 Enharmonic treme keys. 586 Its usual forms. 582 On which degrees of the scale found. Fifth. fifth. importance of careful analysis. 518 major key. 519 Law of the Sharpest Note. 517 The supertonic minor ninth taken in the gression of the ninth. ninth. 593 Its inversions. 556 Tonic and supertonic thirteenth." 566 Example by Mozart. 545 — — — . 555. 592 The Italian Sixth." 562 Examples. 514 Protion upon its own root. Fiflh. 558 Necessity of ascertaining the key. VI. False Notation. Resolution of the chord upon a supertonic false notation. 550 The tonic eleventh. — — — — — — — — — — —A — — — — — — — — — CHAPTER teenth XVIII. 613 — Examples. enharmonic change of notation. 529 tonic ninth : its resolution. its —Examples. ninth and thirteenth. ninth. 585 Peculiar construction of the chord. CHAPTER XVII tion —Enharmonic Chromatic Chords of the Ninth— False NotaModulation J>''ge 231 The chromatic ' The dominant minor Their various forms. 572-575 chords of the thirteenth. 523 When false notation is to be met with. 589 How the chords are indicated — page 269 — — — — The inversions. resolutions. 546 Caution to the student. and thirteenth used chroEnharmonic modulation by means of chromatic matically. ninth. ninth. 520-522 How to detect false notation. eleventh. Seventh. 508 ninth in a major key. 515 Its resoluchromatic dominant ninth. 554 Examples analyzed. 595 The French Sixth. and fifth. 528 discord. Third. Chromatic Chords of the Eleventh and Thirrare.seventh. 544 Example from Bach's Chromatic F'antasia Example by Beethoven. 614-618. 530 531 Examples of derivatives of the tonic minor ninth. 587 Its figuring. 513 Resolutions of the The supertonic ninth. 567 III. These chords comparatively page 250 548 The chromatic chord of the dominant eleventh in a major key. 542. 549. 525-527 Double Progression of the ninth. when possible. 551 The superThe chromatic dominant minor thirteenth. 580.xvi Contents. 602 — 603 — Examples. 54' modulation. Third. 560 Chords that are only partially chromatic. 547. 702." 696 The Harmonic Series Pitch and vibration. 700 How far modern scales are derived from nature. 684. (>"](>— The Dorian Mode. 658 Eight-part harmony. tion of consonance and dissonance. 635 double pedal. 683 The Mixolydian Mode. 666 The Authentic Modes. 677. 644 Two-part harmony. 686-688 The Ionian Mode. introduction of additional parts. 668 The Plagal Modes. 625 tonic 626 An " Inverted Pedal. 646 parts. 704 B—The Harmonic Series — —— — — — — — — 70s. 645 Examples separate parts. 621. 697 Ratios of intervals. 67 1 Transposition of the modes. 673 Characteristic notes unalterable. — — — — — — — — — — — APPENDIX Practical use of the study.Contents. 632-634 Ornamentation of a pedal note. 638 Characteristic notes to be retained. 665 How the modes were formed. 690 Nature of its interest. 642 Motion of the Examples. 669 How they differed from the Authentic Modes. 701 The use of the harmonic The scientific explanaseries in determining key-relationship. 672 Major and minor modes. 643 Examples given. 620—Which page 289 can be used as Pedals. 654. 641 The cadence. 691. 663. rotes ment of the harmony when the How to mark the analysis of dominant pedals. 622 TreatPedal is not a note of the chord. exceptions. — — — — — — — — — — — — — — — — — APPENDIX A The Difference — Ecclesiastical Modes page 311 between the ancient modes and modern keys. 630 Modulation on a pedal. 682. 667 The Dominant. 653-^Five-part harmony." 624. 656. 623 a " Pedal point. 636. 679-68 1 The Lydian Mode. 629 A pedal point generally ends with a chord of which the pedal note forms a part. 652 Which notes to double. 698 Compound tones. 694 " Upper partials. 693. 675 Alteration of non-characteristic notes. 662 Conclusion. Pedal above and below. 674 Modulation. 640 Position of chords in three-part harmony. 695 from C. 685 The Aeolian Mode. 628 A pedal in a middle voice. 655 Six-part harmony. 678 The Phrygian Mode. 651 Greater freedom of part-writing allowed. 657 Seven-part harmony. 670 Table of Plagal Modes. . 639 Broken chords. 703 Books recommended for study. 689 Difficulties of the subject. 631 Examples. xvii CHAPTER XX—Pedals A /Vi/a/ defined. page 322 692 How harmonics are produced." 627 — — —A — — — — A — — — CHAPTER XXI — Harmony Parts in Fewer and More than Four page 300 Harmony continuously in four parts rare. 659-661 Directions for work. Examples of pedal. 637 Three part harmony. 647-650 Harmony in more than four referred to. . but it*will be seen as we proceed that the question of melody is often so closely connected with that of harmony. may be so small as to De nardly recognizable by the ear . or it may be as great as between the lowest and highest notes of a together. and the other the lower.* if sounds of different pitch are It is the laws of harmony heard together. we get Harmony that we shall explain in this book . the relative time values of notes of different lengths. its being what is called a high or a /SaTnote). For a more complete definition of melody. is A musical sound is the air. INTRODUCTION. A certain amount of elementary knowledge of music will be necessary to the student before beginning the study of the It will be assumed that he is acquainted with present work. or note. (See Appendix B. 4. provided the motion is sufficiently The pitch of a rapid. . CHAPTER I. depends upon the rapidity of the vibration. the meanings of the various musical signs (accidentals.). only a very general definition . but for the present purpose the ideas of melody as a succession of sounds and of harmony as a combination of sounds will suffice. The difference in pitch between the two This difference sounds is called the Inte rval between them. see Musical Form. is * This sufficient to make a good melody Chapter I. When the air moving at a uniform rate comes in contact with the nerves of hearing. sound (that is. the names of the notes.HARMONY: ITS THEORY AND PRACTICE. If two it is different notes are sounded. that it is impossible to treat of one without also paying some attention to the other. get what is called Melody . there is produced. and such other matters as are treated of in ordinary text-books on the Elements of Music. what is called a musical sound. difference of pitch alone is not . If sounds of different pitch are heard one after another. we . either in succession or clear that one of the two must be the higher. 2. etc. that to say. produced by the periodic vibration of motion at a uniform rate. 1. its 3. For the present we ^re merely defining the meaning of the word " Interval. C and are on two different places of the staff . sound on correct. comes between them. or ClJ and B(). and C|f (or From B to C. but from not be a semitone . be seen that there is a difference between them. the nearest note to C is B on the one side (below). it will B A semitone of which the two notes are on different degrees of the staff is called a. jf If we look at the two 6.. ' ' ' ' ' ' ' ^ half a tone. [Chap. of intervals is possible . jf D G to A will G G (or . here given. A Tone is an two notes of which are on 'adjacent degrees of the But if we take two staff. and from F|f to G will be semitones. or degrees of the scale. but in music we Jiature of An infinite number make a selection. Similarly from F^ to We may and the Y\. and the other below C J]. such as F# and Gb. The word " semitone " means interval. nearest note to it. however. i. diatonic semitones one above another. A second meaning which is attached to the word will be explained later. but the latter note has an accidental before it. There are two kinds of semitone. the word ' diatonic means through the tones. this statement is not strictly accurate. one is on a line and the other on a space . but C and C \ are both on the same place in the staff. as the distance between any one note. has only twelve sounds in the octave.2 Harmony. large organ." called a Semitone . the statement in the text is . The smallest interval used in music is define a Semitone. and from C to D*') on the other side (above). or anything between the two. 7.. above or below. and which contains two semitones. the * In one sense diesis" {j.g. is sometimes used in modulation. For ordinary purposes. diatonic semitone . and one of the two is altered by an accidental {e. C (or b) are therefore both semitones.* 5. C to Cjf) the semitqjie is called chromatic." This use of the word will be further explained later.. as the "enharmonic the very small interval between two notes represented by the same the piano.e. a word literally meaning " coloured. the which will be explained later. for A is not the nearest note to Ab). on the piano. on any instrument which For example. one above. When the two notes of the semitone are on the same degree of the staff. Ex. has been already explained in § 6 9. or Octave _(ZaA«. And if we take two chromatic semitones.-^'^ 8. which is not a tone two notes are not on the next degrees of the staff to one another. * The two semitones composing a tone are not of exactly the same size. Scale is a succession of notes arranged according to feome regular plan Many different kinds of scales have been used at various times and in different parts of the world . The way in which the diatonic scales are constructed will be exexplained later {see Chapter II) . which are called the diatonic and the chromatic scale. There are two varieties of the diatonic scale. in modern European music only two are employed. see therefore that of the two semitones which make a tone. "octavus" and from this repetition of the first note at a different pitch note the series recommences. It will be seen that each of these This is because the scales contains only seven different notes. eighth). the resulting interval will be from B to |7 . the student need not regard it. It matters not which of the two is the lower..] Introduction. known as the major (or greater) and minor (or less) scale from the nature of the interval between the first and third notes of the scale. one must be diatonic and the other chromatic. 3. The word " diatonic as meaning ' ' through the degrees. on each line and space. it is resulting notes We A . diatonic scale is a succession of notes in which there is one note. neither more nor less. ' ' ' ' A — Major Scale. diatonic semitone is larger than a chromatic. at present we simply give the forms of them. as the Ex. . B. .4. i -&S =2^ Other forms of the minor scale frequently to be met with be explained later. neither semitone is therefore exactly ^a^the tone.* . It is only mentioned here for the A sake of accuracy. D equally clear that they will not make a tone . I. for now the C [7 and C % are both on the same degree of the staff. will = . but as the difference is of no practical importance in harmony. on each degree of the staff that is to say.Chap. P Minor Scale. % £z. is a eighth note. called the "Subtonic. has a very strong tendency to lead up. are the student should be perfectly familiar. We have now got appropriate names for the three chief notes in the key. This will be seen at once by beginning at the top of the scale and descending. I. seventh note of the scale. it is in the middle between the two. are the scales of C 11. is on that account called the Leading Note.e. It is therefore called the Mediant. i. is therefore called the Subdominant. HARMOiTY. " or note above the dominant but the name Submediant is much more usual. or ruling note of the key. them (§ 6). but. or lower mediant. and in the minor rather nearer to the tonic . As will be explained later. the middle note. The different degrees of the diatonic scale (§9) known by different names." from the tonic.. its position as the next note below . We shall see presently that in the the major scale it is rather nearer to the dominant. that is. roughly speaking. or rise to the tonic. The second note of the scale is called the Supertonic. it will be seen later. A chromatic scale and it tones. it equally consists of semitones. for instance. or Key-note. rChap. as they are of constant occurrence. the note above the tonic. The term " tonic " is used in harmony much more frequently than "key-note. The fourth note of the scale lies at the same distance below the tonic that the fifth note lies above it. just as the third lies between tonic and dominant. is is a scale consisting entirely of semicalled chromatic because some of its notes re- quire accidentals (flats or sharps) before Ez.6. with which it is necessary that major and C minor.4 10. and in every way preferable. The sixth degree of the scale lies midway between the tonic and subdominant. the chromatic scale is frequentlywritten in a different way from that here given . or lower dominant. It is sometimes. and it will be seen that they both begin with the note C. Some writers on We harmony call this note the " Superdominant. About midway between tonic and dominant lies third note of the scale. This is the note which gives its name to the scale and key. The scales in § 9. 12. This fourth note (the next in importance to the dominant). therefore call this sixth note the Submediant." The most important note in a key after the tonic is the fifth note of the scale. and the . For this reason it is called the Dominant. but. though rarely. The first note of the scale is called the Tonic. however written. which. Ex.. \)( . m -»- . is a combination of two sounds. Having shown the origin 13.7. 15. Degree of the Scale Second Third Fourth Fifth Sixth = Tonic (Key-note). i. I. 14. Submediant (Superdominant). Supertonic. it will be needful to define and explain two terms which we shall very frequently have to use in speaking of them. pausing between each. Dominant. chord is a chord of which all the notes make consonant intervals with one another. or Consonance. These are the terms Consonance and Dissonance. Before proceeding to treat of the names and classification of Intervals.Chap. if the be followed by some other combination.e. student will strike on the piano any of the following pairs of notes. and meaning of these different names. which by itself produces a more or less complete and satisfactory effect. we will First now tabulate them. Leading Note (Subtonic). Subdominant. Ex.. Seventh Mediant. which does not necessarily require to For example. A consonant interval. A consonant he will find that each is more or less satisfactory.8.] Intr od uction. * is a chord which conone dissonance among the intervals made between the various notes. including both the notes forming the interval.Harmony. We will put after each of these dissonances a consonance. Like a dissonant interval. it may be said that consonance is a position of rest. a consonant chord for its resolution. 123456 1^ ^ ^ te si- te=J:"^" J=. is also sometimes applied merely to the dissonant . In general. The number of an interval is always computed according to the number of degrees of the scale that it contains. The consonance which follows the dissonance is called the Resolution of the dissonance. let us put after each chord. Beginners are apt to get confused on this point. and that they require to be followed by something' else to be satisfactory. and it will be at once felt that the completeness which was before wanting has now been obtained. or Discord. and dissonance a position of unrest. . unless the conbe expressly stated.l2. Now. Thus " the third of C " always means the third above C if the third below is intended. Let the student play the following dissonant chords. and he will feel this. [Chap. trary . Thus from C to 18. \ra bs Intervals are always reckoned upwards. Ez. The laws according to which dissonances are resolved will be learned later. 11. as before with the dissonant intervals. The satisfactory effect is felt at once. because C. Ez. D. A tains at least Ex. E.Let us try. and * The term " Discord " note itself. dissonant chord. E is called a third. 10. Everyone will feel the incomplete effect of these combinations. it contains three degrees of the scale. it must be so described. 17. I. a dissonant chord has by itself an incomplete effect. and so The same reckoning. six 3rds.exercise for him to discover 19. (The octave is printed here as a small note. five 4ths.] Introduction. Thus A is the third below C. and seven 2nds. Thus the ^ is compounded of the octave. and the third. C to E. and E as the second. the interval contains the seven notes of the lower octave from C to B. four Sths. them for himself. ) Obviously. etc. The upper C is already counted as part of the third. note above C. It will be a useful. Therefore. and he will find within the compass of the octave there given two 7ths. in addition to the third at the top. A Compound . applies to the intervals below. three 6ths. Let the student examine the major scale of C in § 9. D is a fifth. from G on in all other cases. from F to D a sixth . Thus the number of a compound interval is always 7 more than that of the simple interval to which the octave is added. An interval larger than interval i an octave *^ ' is called a f^w/^«/Kif interval. but in the reverse direction. C to C. I.Chap. counted as the first note of the interval. D is the fourth below G. 7 to think of But the note D as C the to" first is itself Similarly. and diminished. Minor ands.—perfect. we change the name of the note. we also get a minor third from C to E|?. a 21. [ Minor 3rds. Thus. 'In order to obtain greater accuracy. ) Minor gths. But if we alter either note a diatonic semitone. lower E to D ft instead of E [>. 4th. though not strictly speaking an interval. now and explain. C to D ft is a second . but a second. the unison. Or if we leave the C alone. which. intervals are described by one or other of the following adjectives •. are termed -perfect. is not sufficiently precise to show its exact nature. and so on. etc. 13. C to Ai?a minor thirteenth. As a first reckon 4th. a 6th. third. and an octave. therefore. 3rd. that the general description of an interval as a second. and reckoned as such. Similarly if we of a kind which we shall explain directly. basis for our classification. is Of these intervals. I. we take the major scale. changed interval which is a chromatic semitone less than a major interval can be called a minor interva}.14. [Chap. Ex. the interval iirom D i? to E is no longer a third at all. clear. taking the tonic in each case as the lower note of the interval. C 22. the interval a major third.8 Harmonv. augmented. 6th. Ex. a sth. minor. ] Minor 6ths. and lower the E to Eb. and therefore of the interval. a 7th. C to E being a major 3rd. . and the 2nd. the lower note to Cfl. a 3rd. C ^ to E is a minor third. if we raise C to D I? instead of to C ||. Sth. | Minor 7ths. The compound ones. An is major. all the intervals upwards 'from the tonic.. for the two notes are on adjacent degrees of the stafif. These terms we shall major. into a minor. sth. fourth. either by raising the lower note or lower- A Thus from C to E is ing the upper one a chromatic semitone. and 7th major. It is evident that we shall obtain in succession a 2nd. If we raise. that is. thus intervals have the same prefixes as the simple to DIJ will be a major ninth. To these may be added the unison. When the relative position of two notes is changed by placing one of . and diminished augmented. Perfect intervals remain perfect when inverted . are of very frequent occurrence. I. But diminished srds. especially the last. and C to be an augmented 4th.] Introduction. the inversion of an interval can always be found by subtracting the number of the interval from 9. the interval is inverted. ^^=^^=\ is Here the first interval a perfect fifth . the interval is said to be inverted.to At} is an augmented 6th. for if we lower Dt> to Dl?]?. unison cannot strictly speaking be inverted.them an octave lower or higher than before. An interval perfect or a major a chromatic semitone larger than a Here we is called augmented. is a perfect fourth. — — 25. and its inversion The number of = A reduced to a unison is generally said to be inverted. and augmented sths sometimes to be met with. 15. etc. and we either raise the upper note. and minor major . we shall in either case get an interval smaller than a semitone what is called an " enhaimgpJG " interval and it has been already said~(f~57that the semi(§ 5. C to F j| or interval reverse C I? to Ft} will 6th. by means of an accidental. augmented intervals become diminished. augmented ands. the process of making the minor intervals. An interval which is a chromatic semitone less than a perfect or a minor interval is called diminished. The same objection will apply to a diminished 9th. Again C to A is a major A j| or CI?. major intervals become minor. an octave two notes is put an octave higher or lower. which is 9 23. or raise C to Cjjl. 5ths and 7ths. but it is said to be inverted when one of the Similarly. and 6ths are frequently. 24. The augmented srds and 7ths are not used in harmony .Chap. In the above example it is seen that an inverted 5th bedomes a 4th (9-5 4) . We obviously cannot diminish the minor 2nd. The reason of the rule just given will become clear to the student if he observes that the inversion of any simple interval is the difference between that interval and an octave. as it has no higher or lower note . 26. and the upper the lower. 4ths. Let the student refer to the table of minor intervals in § 22. or lower the lower note. a 2nd a 7th. if C be placed above G. As in the cases jiIsfTspoken oJT'it is immaterial to the nature of the interval which of the two notes composing it be altered. note) tone is the smallest interval used in music. in the same way a 3rd becomes a 6th. the lower one thus becoming the upper. £z. . 4ths. Thus C to F being a perfect 4th. C. dissonant. the same reasoning will apply to augmented and diminished A . octave.^ Thus a major to E. is a major thirteenth . and conversely. sevenths. to raise one note an\octave and at the same time to lower the other an octave.l6. major and minor third. according to the note of the 3rd of which the position is changed. and major and minor All other intervals of every kind all seconds. is itself consonant (f 422). — ninths. perfect perfect and imperfect consonances. a smaller (minor) will be left .) . will together make an octave. fourth. at {V) the lower note is raised two octaves . elevenths. always treated as a dissonance in the chords in which it is found. third of any kidd taken from an octave must leave a sixth . and invert it in each of these ways: Ex. * The but it is — and thirteenths. and perfect fifth are the perfect. and will produce no inversion. a minor 6th. It will therefore be necessary to raise or lower one note two 27. being the octave of the sixth. In each case the resultant inversion is the same minor third. 29. if a smaller (minor) third be taken Evidently from the octave. (See Chapter XIV. diminished intervals ^are dissonant. sixth. clear that raising or lowering either note an octave will not change their relative positions. 3rd. perfect fourth. 28. a larger (major) sixth will be left. C E to £z. intervals.* and all augmented and thirteenth. Intervals are divided into two classes. The consonant intervals are further subdivided into The unison. or (which produces the same result). which is also the inversion of a major sixth. and its inversion. perfect fifth. consonant and These terms have been already explained in §§ 15. 16. at (c) the upper note is lowered two octaves. and the major and minorthirds and major and minor sixths are the imperfect consonances. or E to E. it is octaves. [^^p. The inversion of any compound interval is always the same as that At {a) — of the simple interval from which it is compounded. and sixth if a larger (major) third be taken out. and at (i/) the lower note is raised an octave while the upper is lowered an octave. We will take a major thirteenth. octave.17. As a compound interval is larger than an octave (§19).lo Harmony. either C to C. The consonant intervals are the unison. indicating those that are consonant by (C) and those that are dissonant by (D):{a) (*) (. raised or lowered a chromatic semitone (§ 22) without changing the interval into a dissonance. or vice versa a. advised to make be seen that always a consonance. (i) Write the names of the following intervals.) The similar tables for himself from other notes. and of a student is It will Exercises to Chapter I.] Introduction. But a major third or sixth can be changed to a minor. II Neither note of a perfect consonance can be altered by an accidental that is. the inversion of a consonance is dissonance always a dissonance. minor — a major and still remain a consonance. This is one difference between perfect and imperfect consonances.) {d) {e) (/) {g) {^h) [i) (j) [k) f^=I . We shall conclude this chapter by giving a table of all the intervals and their inversions within an octave from the into — — note C. 30. (See next page.Cliap. 1. [CInV'l Diminished Augmented Perfect 1% Diminished Perfect .12 Harmony. i Diminished Augmented Major Minor Diminished \\ Minor Major 35 El I) % \\ Augmented . one key can be found within that compass. though the degree of relationship and its nature have differed as the art has progressed. if the first half of ' ' God save the one another. |M ^ i i> i r i =JCKt =lii=t: *=t m m f |=p: ^^ — g everyone can hear what is commonly called the tune that is. KEY. but it ceases one another have no connection.Chap. thus a^r^rr^CT"i^N we not only distort the . so to speak. 18. to be music at all for the notes as they follow 32. II. OR TONALITY. 6. . but only that all the notes used in. ^^^ melody beyond recognition. The student must remember that this definition does not imply that all music in one key must lie within the compass of an octave. or Tonality. 33. Thus in Ex. 31. should have some definite and clearly recognizable relation to For example. 13 CHAPTER II.. as in harmony. or Key-Note. it is necessary that the notes. and alter several of them by the addition of flats and sharps. as in a melody. King be played on the piano ' ' Ex. whether taken singly. all the notes of the key lie between the two C's. the necessity for the relationship of notes to one another has always been felt.] Key. they are in no key. of which the first is called the Tonic. From the very infancy of music. no common bond of union. to which note the other eleven bear a fixed and definite relationship. In other words. or combined. One of the first things which it is necessary that the student should understand is what is meant when we speak of the Key of a piece of music. can feel that the notes following each other have some definite relation to the first and last note. In order that music should produce a satisfactory effect. and to one another. But if we take the very same notes on the staff. defined : In its modern sense Key may be thus A collection of twelve notes within the compass of an octave. is called a major chord if the third be minor. ii. so called from the interval between the tonic and the mediant the third next above it (§ 9). and subdominant. In order to avoid confusion. contains five notes more than the former (the diatonic). Chord is a combination of not fewer than three notes. The lowest note. 10). placed each at the distance of either a major or a minor third above the note next below it. A — A ' ' ' ' * Much trouble is sometimes caused to students from the word Root being used in two senses by theorists as the lowest note of any combination of thirds. are identical. The fundamental modern music cannot be Harmony. or " primary " notes the tonic." and one that has a minor third above the tonic is called a minor key." 35." the major and the minor. to regard them as two modes of the same key. 37. the chord perfect fifth above the root. volume. The former includes all those notes which are in conformity with the key-signature. which are made by placing either a major or minor third and a If the third be major. the word Root will in this book always be employed in the former sense.14 34. They therefore occupy quite a different and subordinate position in the key to the diatonic notes and chords it is only of the laher that we have to speak in the present later in this chapter. . it is called a minor chord. This distinction — will become quite clear as we proceed. and that each of the additional five notes Both these scales are in the key of has an accidental before it. \ These are often spoken of as two distinct keys but it is better. — .'^ The most important. we shall see that they are borrowed from neighbouring keys. This will be seen by comparing the two scales given in Exs. dominant. and also as the fundamental tone in the key from which the combination is harmonically derived. and the latter (the latter all those which are inflected by an accidental. upon which the chord is built. which will be thus seen to contain two elements. and the mass of tone which forms the whole composition must be developed from this tonic. [Chap. 4 and 5. If the student will compare the two scales (Exs. and the most frequently used chords are those called Common Chords. The . is called its Roof. we come to speak of the chromatic notes and chords in a key. the •diatonic and the chromatic. principle for the development of better stated than in the words of : "The whole mass of Helmholtz {Sensations of Tone. and must finally return to it. 4 and 6). p. 383) tones and the connection of harmonies must stand in a close and always distinctly perceptible relationship to some arbitrarily selected tonic. C major. 36. and the note from which the combination is ultimately derived will be called its Generator. given in our last chapter (§§ 9. key which has a major third above the tonic is called a "major key. Every key has two "modes. as their three chief. he will see that the chromatic scale). When. and more accurate. Chap. II.] Key, or Tonality. " 15 scales given in scales of Examples 4 and 5 are therefore respectively the major " and " C minor." These names are more convenient and less cumbrous than and the the major minor mode of C. 38. It is implied in what is said in §§ 32, 34, that the tonic Most pieces of music is the most important note in every key. begin, and every piece should end, with a chord upon the tonic. Next in importance to the tonic are those notes in the key which are the most nearly related to it, that is, those which make perIf the student will look at the fect consonances with it.* scales in Exs. 4, 5, he will see that the only notes which make perfect consonances with C are the dominant G (a fifth above), and the subdominant, F (a fifth below). The tonic, dominant, and subdominant are therefore called the three Primary Notes C ' ' ' ' ' ' of every key. 39. Let us future take the major mode of C, which, for the always call by its usual name, the key of C We select this key, because it is what is known as the major. " natural " key, that is, its diatonic notes require neither sharps To obtain the diatonic material of the key, we take nor flats. the three primary notes, placing the tonic in the middle, with the dominant above, and the subdominant below, and make In a major each of these notes the root of a common chord. key, the three primary chords are all major. first we shall Ex. 20, C: IV 40. If the student will I V compare these chords with the major scale given in Ex. 4, he will see that every note of that scale is to be found in one or other of these three primary chords, though some of them (F, A, and D), are not in the same But it is clear that the entire diatonic contents of the octave. key are derived from these chords. 41. It is very desirable that the student should from the very commencement accustom himself to think of all chords in In order key to which they belong. with more certainty, he should indicate the root beFor this purpose the plan adopted in the neath every chord. example just given (first introduced, we believe, by Gottfried A letter followed by a colon Weber), should be followed. shows the key ; if this be major, the letter is a capital, as above their tonal relation to the to do this : C ; = C major. For C minor a small why letter (c : ) will be used. * See Appendix B for the reason most nearly related notes. the perfect consonances are the 16 Harmony. LChap.ii. degree of the If, as here, the thirds of the root of the chord. the chords are major, the numerals are capital letters ; if the thirds are minor, small numerals are employed, as will be seen when we come to speak of the minor key. Thus, in Ex. 20, show that the roots are the fourth, first, and fifth IV, I, and degrees of the scale, and, as the numerals are all capitals, that Modifications of, and additions to the chords are all major. these signs will be dealt with as the necessity arises. The system is perfectly simple, and we strongly advise all students to take the trouble to master it from the first. 42. If the student will look at the scale of C minor (Ex. S), he will see that its three primary notes are the same as those of C major. To obtain the diatohic material of the minor key, we build common chords on these three notes; but with the tonic and subdominant we shall now have minor chords above the roots, while for the dominant we still have a major chord. scale The Roman numerals under each chord show the which is V Ex. 21, c: Iv i V After what was said in § 41, the student should have no difficulty in underst^ding the way in which the key and roots are marked. The reason a major chord is taken upon the dominant is, that if a minor chord were taken, its third (Bj?), would be a tone, instead of a semitone, below the tonic, and the key would have no "leading-note." It will be seen later that a leading-note is equally necessary with major and with minor keys. Looking for a moment at the chords given in Ex. 21, it be seen that all consist of a major and a minor third placed one above another, and that the third which gives its name to the chord is always the lower of the two. It will further be noticed that the only notes which differ in the two keys are the third and sixth of the scale, which are a semitone lower in the minor than in the major key. To change a major key into its " tonic minor " (i.e., the minor with the same tonic), it is onljj 43. will necessary to flatten the third and sixth notes. The conver|e process will evidently change a minor key into its tonic major.' 44. Let us now turn back to the two scales given in Ex. 4 and 5, which contain all the diatonic notes of C major and C minor.* It will be seen that in the major key the semitones correct as regards the harmonies oi i\ie)cs:y; but when minor key (Chap. VII) it will be seen that there are two other notes which can be employed melodically as diatonic notes. is * This statement we come to treat of the Chap. II.] Key, or Tonality. 17 third and fourth, and the seventh and eighth degrees of *tie 'Oiie; while in a minor scale there are semitones between the second and third, fifth and sixth, and seventh and eighth degrees. Between the sixth and seventh degrees of a minor scale is the interval of the augmented second the only interval greater than a tone to be met with in any scale. 45. In older music many other forms of diatonic scale were in use besides the two that we have given (See Appendix A). These various forms were known as "modes." All the modes contained the same notes ; but each began on a different part of the scale, and consequently had the semitones between different At present only two modes, the major and minor, degrees. are employed *; the difference between one major or minor key and another is solely a difference of pitch. have hitherto spoken only of the key of C ; we shall now show that in keys with any other tonic than C sharps or flats -become necessary. For the present we speak only of major keys. ——^.46. If we examine the diatonic major scale of eight notes beginning from the tonic, we shall see that it can be divided into two sections of four notes each, and that these two sections are in their construction precisely similar, each containing the interval of a semitone between the two upper notes, and a tone A series of four notes thus arranged between the other notes. come between the — We and the Greek word signifying four strings ; two such tetrachords placed one above the other with the interval of a tone between the highest note is called a Tetrachord —a scale consists of of the lower tetrachord and the lowest note of the upper. This tone, separating the two tetrachords, is called the "tone of disjunction." Ex.22, •with the tonic, called the tonic important to notice that the lower tetrachord begins and the upper with the dominant the next most important note to the tonic. They may therefore also be It is — and dominant tetrachords. take 47. If we now G C the upper tetrachord of * Occasionally, even in as a tonic, or in other words make the lower tetrachord of a new scale, if modern music, the older modes are used, is a suecial archaic or ecclesiastical effect desired. 1 Harmony. shall find that if \Oxxp. n. we we its leave all the notes unaltered the upper tetiachord will have semitone in the wrong place Here the semitone is between the second and third notes of the upper tetrachord, instead of between the third and fourth. To correct this, F (the subdominant of C), must be raised to F^; leading note and we now have a semitone between the (§12) and the tonic, as in the key of C. It is important to notice that the sharpened note is the leading note of the new key, and that the sharp, because it belongs to the key, is marked once for all in the key-signature. 48. If we continue to take the upper tetrachord of each key as we obtain it as the lower tetrachord of a new key i.e., if we make each dominant into a new tonic, we shall clearly have to introduce a fresh sharp for each new leading note. The ' ' ' student is recommended to work out all after the pattern given above. The None. FJt. Ftf, result will the scales rising by fifths be the following Tonic. Signature. C G D A E B C8. C}f, CJt, F» C» G#. G#, Fjt, CS, G#, F«, C», G», FJt, C#, GJ, Ft, F#, D». D#, Aff. D#, A«, EJ. D8, Ajt, Eft, Bit. 49. It would be possible to continue this series, of which the next tonic would be ^ ; but as this would involve the use of a double-sharp, it is more convenient instead of GJ| to take G "enharmonic" (§ 5 note') which for all practical I?, purposes is the same note. We never therefore find a piece of music written with the signature of the key of major, though the key is occasionally used incidentally in the course of a piece. If we continue this series to its extreme limit, the next tonic will be D \, then will follow K\, E and B ^. We can Jf, go no further than this, because B^ is the enharmonic of C, and we have now completed the ' ' circle of fifths, " as it is termed, going through the sharp keys with ascending fifths. The inconconvenience of writing in these extreme keys is that they necessitate double-sharps in the signature. Thus the signature of +t major would be written its A G jif A (Jh"" V« ; and of B# major \ ^^*hr^ ; Chap, n.] Key, or Tonality. 19 We shaW show later in this chapter how to find the key-signature of these "extreme keys," as they are called. Observe that in the series we have just given the tonics always rise by perfect fifths. 50. All these sharp keys have been obtained by making the upper tetrachord of one key the lower tetrachord of the next, or, in other words, by making the dominant of one key the make tonic of the following. If we the lower tetrachord into get a different series. now reverse the process, and an upper one of a new key, we As before we begin with the key of C. Ex. 24, P the lower tetrachord here, we see that it has no semitone ; we also see that there is only a semitone between the two tetrachords, instead of the " tone of disjunction." In fact the highest note of the lower tetrachord is a semitone therefore lower this note with a flat, making it B ^, too high. and the scale of F is now correct. Just as the scale of G, the fifth above C, requires a sharp, so the scale of F, the fifth below 51. If we examine We ; and just as each dominant when taken as a one additional sharp, it will be evident that each new subdominant ('the fifth below the tonic),' when treated as a If the student has' fully tonic will require an additional flat. understood the explanations given above, it will be needless to repeat the process of forming the scales from the tetrachords. The series of descending fifths with their signatures will be as C, requires a flat tonic, required follows Tonic. Signature. C F Bl7 El? None. Bl7. Bt;, El?. Bt>, Et?, Abi. Bl7, Bt', Bt', Al; Eb, Db G> C> E^ Al?, Dl?. Al?, Eb, Bb, Eb, AK Al7, DK DK Gt». Dt?, G|?, Cl». Gb, Ct?, F|?. It is of course possible to continue the series further, as with the sharp keys, but as so doing would involve the use of doubleflats in the signature, it is more convenient to use the enharmonic For instance, instead of the key of keys which contain sharps. F i?, that of the E tf is taken, and so on with the others. 52. It should be noticed that in passing to the sharper key taking the dominant as a new tonic it is always the subdominant of the old key which is sharpened to become the new i.e., — 20 Harmony. rchap. II. leading note; and conversely in passing to a flatter key i.e., taking the tonic as a new dominant, it is always the leading note of the old key which is flattened to become the new subHence we obtain the easy rule for finding the tonic dominant. In sharp keys, the last of any major key from the signature. sharp is always the leading note, and in flat keys, the last flat is When we knovi the leading note or always the subdominant. the subdominant of any key, it is a matter of veiy simple calculation to find the tonic. S3. We defer for the present the discussion of the signatures of ; minor keys derstood keys, these will be later. We now sharps. ( commencing with C Keys with easily explained, and better ungive the signatures of all the major major, and marking the tonic of each more key. Tonics rising by Rfths. Ex, 25. ^^ =rs: flats. fcS g^gg^ tel Keys with p It will (Tonics falling by fifths.) fc =fcs= fes ^5= 1^— ^^ t^= gg^ ite be seen that the last three sharp keys are enharmonics of the last three flat keys ; B '^, with five sharps, being the enharmonic of Cl?, with seven flats; while Fj} (six sharps), and Gl? (six flats), likewise Cj( (seven sharps), and Dl? (five flats), are also enharmonics of one another. Let it be particularly noticed that the number of sharps in any one of the sharp keys added to the number of flats in its enharmonic key always amounts to the same number, 12. 54. By bearing this in mind, we shall be able to find the signature of any of the extreme keys referred to in § 49. All that is needful is to notice the number of flats or sharps in the enharmonic of the key whose signature we wish to ascertain, to subtract that number from 12. The remainder gives the required signature, and it must be remembered that all numbers above seven will represent double sharps or flats, as the case and may be. To make this quite clear, we will find the signatures of the two keys spoken of in §§ 49 and 51 Gjf and Ft' major. 1 2 4 8 ; t*, which has four flats ; ^ is the enharmonic of therefore G ^ has eight sharps Similarly, i.e. , one double-sharp. F I? is the enharmonic of E tf, with four sharps ; it therefore will have eight flats, or one double-flat. Of two enharmonic keys, one will always be a sharp and the other a flat key. 55. G A — — = , 56. There is another method of calculating the signatures of these extreme keys, which some students may perhaps find easier than that just given. If we compare the signatures of C tt Chap. II.] Key, or Tonality. ai and Ci' in Ex. 25 with that of Ct[, we shall see that the former has seven sharps more,, and the latter seven flats more than the "natural" key. This must obviously be so, because, if we put a sharp or flat before the tonic, it is evident we must put one before every other degree of the scale ; otherwise the semitones will not remain in the same places. Applying this reasoning to other keys, it is clear that the key of A | for example, must have ten (3 _|_ 7) sharps, and that every note which in the key of A was a natural will now be a sharp, while every note which before was a sharp will now be a double-sharp. Similarly, as B|? has two flats, Bi't', must have nine (2 -[- 7), with two doubleThe order of double-sharps and flats ; and so on in every case. double-flats will evidently be the same as that of sharps and flats, beginning with F x on the one side and B bl? on the other. We have already said (§ 49), that no entire piece of music is ever written in these extreme keys but their incidental employment in modern music is frequent enough to render it advisable for the student to be acquainted with them. ; Exercises to Chapter II. (i.) Write the three primary chords in the keys of D, EI^, Prefix the key -signature in each case. ^, At), and B b. (2.) Write major scales (one octave) from the following notes, putting no key-signature, but inserting a flat or sharp before each note that requires one E, Ab, Fit, Fb, Git, B, Bb, F tt> G — Ajl, Ebb. Thus: (it) f . For instance. or as harmonic progression. though ~P~{ is better than ( U «J J j 58. all the notes The progression of these next above the lowest another. parts may be considered in two aspects . the harmony has generally the same relative position to all the that is to say. the student will learn later (Chap. if the two notes are sounded together. the harmony is in three parts.(«) Ex. CHAPTER III. [Cbap. just as it would do were it sounded with B (Ex. Had F been the first note and B the second.33 Harmony.). In Harmony any number of notes. If each chord contain -four notes. moves to the E. If. The former is a diminished fifth. and the an augmented fourth. from two upwards. that is. A and simple. it is therefore best either to proceed by step of a second (called "conjunct motion ") that is. 26 a'). { b) . and so on. may be sounded at one time. if each contain three Each part in notes. 59. plained. one that flows naturally and easily . B would. The best progression for any dissonant interval is. Ill. VIII. etc. rules for melodic progression are few is The good melody — : | j || either latter is possible. a diminished interval is to be preferred to an augmented " one. or by leap ("disjunct motion"). that the second of the two notes forming the interval should proceed to that note which is the resolution of the dissonance (§17) made. are governed by certain general laws. for the same reason. all the upper notes of the harmony form one part. to the next note aboveor below. . 26 3). coming after B. all the lowest notes another part. . either as melodic progression. as sometimes happens. 57. the harmony is said to be in four parts. it is necessary to leap by a dissonant interval. the motion of each part regarded singly . that is. and not continue in the same direction. 26. have gone to C (Ex. If a part move by a diminished inverval it ought to return to a note within the interval. THE GENERAL LAWS OF PART-WRITING. of a consonant interval (§ 15). which will now be ex- other parts . that the diminished fifth just given will resolve thus Therefore F. the motion of each part with Both these kinds of progression relation to all the other parts. freely. 7?^ ^gfl^N?^ Bad. which we find in the minor scale (Ex. 5) between the sixth and seventh degrees may be used more 61. Bad. It is seldom good to introduce a leap of a seventh in the melody. successive leaps of a But if the in- termediate note be the octave of either the first or second note of th(P interval of the seventh. It is therefore much better that of the two notes should be approached downwards. two or three steps by conjunct motion. : understand this rule hetter in his earlier exercises when he has studied the he had better avoid the progression . . than they should be approached and left in the same directions. An augmented interval should seldom be used in melody unless both the notes belong to the same harmony. =ft«: {>>) fftt Good.] The General Laws of Part-Writing. same direction to an accented note I I it : is not I^ : P^ i^ P^ But there is no objection to leaping in the same direction to an unaccented note Ex. as at {F).) At («) the first the second be seen the leap of an octave upwards between and third notes. -r—y- ^ l ^ f^will * The student dominant discords altogether.W Ex. III. But the interval of the augmented second. (/) {g) Good. ^^ J r r ^^ Good. ^ Bad.30. and will the second E left downwards. ^ _ {c) {d) _ J-p-lGood. 23 60. unless all three notes form part of the same chord. After good to leap Ex. the leaps be upwards. 62. note isKiot a note of the chord. (. Good.* . Two fourthAs at (</) are particularly objectionable. the progression is good. 28. as at {f) (g) above. and the last note fall one degree.! in the 4. At (3) (J)) (it) the first three notes all belong to the same harmonj*—a chord of the seventh at (</) {i) the intermediate . l in t he-melody-is best approached quitted in the oppasi te rlirprtin n tn that in which it leaps. Good. with one intermediate note. A jarge_LQterva and Ex.27.Chap. 63. This refers to their relative rather than their actual positions . called " parallel "). The student can analyze the rest of the passage for himself in the same way.3l. or to leaping either to an accented or an unaccented note in the opposite direction to the steps : ]Sz. 32. Ex. Between the last chord of the first bar and the first chord of the second there is contrary motion between the two extreme parts. or down one part moves up or down while another remains stationary and contrary. even where (as in Ex. . [Chap.»4 Harmony. parts move in the same direction up. the next below this. though less frequently. 33) it written in the treble staff. 64. in fact. as has been said above. By harmonic progression. We shall now give the rules which the student must observe in part-writing. and oblique motion between each of the extreme parts and the middle part. the alto. and therefore the two lower parts move by similar motion. It is only right to say that these rules are not in all cases strictly adhered to by the great masters . is meant the way in which the parts move in their relation to one another. the student will learn by experience. in the first bar all three parts move in similar motion. or soprano. Ex. when two or more oblique. ^ U^^^--^^^ r m ri. but it may be laid down as a genUral principle that nobody can break rules with good effect till I . except when are moving in similar motion. 65. when one part ascends while another descends. =F S^ ^E*E I ^ In this passage. as his knowledge increases." The highest part is called the treble. is when it is safe to relax them . is Oblique..g. 33. If the least music all in more than two parts. being. and the lowest part the bass. it is evident that at two of these different kinds of motion must be combined. the tenor. Most music is written in four-part harmony. III. the third part. 66. and it is important to remember that the lowest part of the harmony is called the bass. and the parts are generally named after the four varieties of the human voice. •^\\sa. I I 1 J I J J ^ r r Similar. There are three kinds of motion similar (sometimes. counting downwards. e. often called "voices.. r¥^^^^ . — . rrr-rrr Contrary. Between the first and second chords of the second bar there is contrary motion between the upper part and each of the others. 35.(ih ^ Jj .] The General Laws of Part. licenses can be allowed. and the passage is quite correct. Neither is it considered to make fifths forbidden in Rule 2. In this example each chord contains an octave of the bass note but in the first chord the octave is between the tenor and bass. They aje allowed by con ^^c^'" ^n^j^jim-^'ptwepn the primary chords (§39 j" bt the'icey. congecutives if both parts leap an octave. therefore. e. and in the fourth between the tenor and bass again. : . No two of these octaves are therefore consecutive. but they are not consecutive unless they occur between the same parts. For the present.g. or in octaves with one another. 69. and fourth crotchets. in the second between the alto and bass. no C^ Rule I. as the parts are not then moving in The same remark applies to the consecutive octaves or unisons. in the third between the soprano and bass. moving in octaves between the iirst and second crotchets the soprano and tenor between the third and fourth and the alto and bass between the fifth and sixth. There is one exception to the prohibition of consecutive octaves. . that the repetition of the same octave or unison by two parts . No two parts in harmony may move in u nison. does not make consecutives.34.Writing. provided that one part leaps . At (a) the alto and tenor are moving in unison in the second. 67. It must be said here that octaves will be found in most chords in four -part harmony . Such passages are called It is important to remember consecutive unisons and octaves. H because the repetition of the same notes at the distance of an octave does not change the harmony. III. ^ Ex. «5 ' he knows how to keep them. Ex. At {b') the tenor and bass are third. 68.Chap. For instance. Paul.ecially if one of the parts be a middle part. C: IV VI Though the correct. ' ' ' ' ' ' j 1 Ex. to the words For the Lord God omnipotent reigneth is not considered as " consecutive octaves. III. the familiar passage in Handel's "Hallelujah" chorus. Rule II. nor to passages in which all the parts move in unisons and octaves. O Lord.38. fifth. Very bad. [Chap.36. They are. mostly tenor and bass. such as is fre- quently found in pianoforte and orchestral music. Consecutive fifths between the tonic and dominant chords are not . " Again. however. Ex. 37. 72. 70. Evidently this will be between two adjacent parts of the harmony. the harmony being in three parts throughout. 71. in Mendelssohn's St. it progressions shown in Exs.^and the progression be between primary chords. 36. much less objectionable when taken by contrary motion. I yield my spirit in unison. the soprano and alto sing the choral "To Thee.26 a fourth and the other a Harmony. similar progression —from unison — C: V I I IV Ex. This rule is ""^Et^S^ great much more freqi^eWy -TOjken by composers than the rule prohibiting consecutive octaves. A the unison to the octave. or the octave to the is also not infrequent between primarychords. esp. The rule prohibiting consecutive octaves does not apply to the doubling of a whole passage in octaves. 37 are perfectly will be safer for beginners to avoid consecutive octaves altogether. Co nsecutive perfect fifths by similar motion are ot all ow ed -between any two parts. But this is not called consecutive unisons. provided that 1^ This progression is qtftte con^ect*'''^ut a diminished fifth followed by a perfect fifth iafforbidden between the bass and any upper part. and from the third to the fourth bar. . Cc\rA HnnH. experience is required to understand when they may be properly introduced . If one of t he tw Q. At {a) will be found in the third bar consecutive fifths by contrary motion between the tenor and bass . V Bbbthovbn. These examples are not given for the student's imitation . at (f) are seen fifths by contrary motion between tenor and bass. not apply.Writing.] The Gbneral Laws of Part. or occasionally the upper part moves a semitone.J£tbs~i&-^aaMwsfaed7" the rule does perfect fifth comes first. Ex. III. but it is needful to mention By beginners the them here. . provided the lower. 73. for the sake of completeness. and. but allowed between two upper or middle parts. as in the first 27 infrequently and third of the following example Ex. met with. at ((/) four consecutive fifths between extreme parts. Pastoral Symphony. consecutive fifths between the extreme At the second bar of (1^) are fifths beparts by similar motion.Chap. tween alto and tenor . prohibition of consecutive fifths must be strictly attended to. 41. 39. Ex. when the sJpond^ofS is another position of the first. D.ri. Second. E.. Ex. with the roots in the bass). Let the student examine . 42. fifth.). being passed over. fifths.T:y.are-JbrbJddeB-bet'weai— the '"" p\trgri. If tchap.28_ 74. to C passes over the intermepart in leaping frqm If these notes are introdiate notes F. Rule III. such progressions are called two parts go by similar motion to octaves or perfect " hidden " octaves or fifths. 44.. ( rf). The lower are two parts moving to an octave by similar motion.pygpy-first. 75. .'as shown at {b).e. when the bass must position rise a fourth or fall a. C Similarly at If the in(~* the two parts leap to a fifth by similar motion. Ex.rtia) {i..(§ 172. Hidden octaves. there will be consecutive octaves (i-) D ~q to q. between |:|pm q ._j. 43. termediate notes are inserted.and third. as at we see the fifths p q DK a These octaves and fifths.45. In other cases they are not allowed.iii. instead of sounded. Ex. when the second of the two chords is a second inversion . are said to be hidden. Harmony. At (a) G duced. axidthe^upper part must movet^step: — . ^^'"""'^'' '^""f- ^^3^. the bass note being either the tonic or dominant of the key. to an octave by similar motion between any two parts. when one part moves a second. chords is not (as in the'case of octaves) restricted to root-position . the method of marking which has not yet been explained. however.* 76. and must be most carefully avoided.It is strictly forbidden to move from a seventh or ninth. and he just will see that thejfcdoTffot come under any of the exceptions mentioned. with the third in the upper part. to the chord of the dominant. jparts.. ^^^^^^ ^ (. Rule IV. Ex. at (a) and {d') below. 46. III. or subdOTainaHt lu tUU'Itj. 77. first. in a progression between primary chords (tonic to dominant. moving by step.) {a) {b) (d) second. Ex. with one important exception.49. 48.] The General Laws op Part- Writing. because some of the chords are inversions. 44-46. it' is in the first inversion except ' ' £z. witlt the upper part. * The roots are not marked in Exs. and the other a third. allowed between anyother of the parts than the two extreme parts.Chap. 47. ^""^-^ -^ ^ " This is the very worst kind of hidden octaves. . from the "Ifoot^position of the chqjfll^f the supertonic. 29 the three bad examples of hidden octaves here given. Hidden fifths are forbi dden between extreme Ex. Hidden octaves are. as The first of the two with hidden octaves. Rule VI. to be found in the works of the old masters. and others sometimes followed a dominant seventh (§ 232) by another seventh on the bass note next below. sevenths. 60. upp^ .^ Between any of the ' "pa(& congSfcutive fourths are not prohibited. Handel. Consecutive seconds.e. Consecutive fourths between the bass and an upper part are forbidden. iii] when a fifth. 62. hidden fifths are not prohibited. * Except between extreme parts.3© Harmony. 78. There is one somewhat important exception to this rule Corelli. Rule V. Ex. 80. and thirds from one to anot actly as with hidden octaves lositfon of the same chord.. the bass falls chap. X. Ex. or a passing note i. They are sometimes to be found between the bass and a middle part . but even these are not advisable. ex- Ex. and the upper part fells a third. We give two examples from Handel's works. unless one of the notes be a passing note. and ninths are forbidden between any two parts. except when the second of the two is \a part of a fundamental discord (§ 232). ^ood. \ note not belonging to the harmoiiy (Chap. 79. Handel. 61. Joshua. Even then it will be better for the student to avoid them. 6. but the student is advised to avoid it even in this case. Part-Song.] The General Laws of Part. and the progression is from the dominant to the tonic chord. but'' it should be added that in the works of the great masters instances We give a few exof its violation are sometimes to be -found. Ex. an exception to the rule given in § 61. Rule VIII. It is generally bad to approach or leave a unison by similar motion. # m * ^ This progression is sometimes used when the second is a passing note as at ( # ) . but because if no mention were made of such exceptions he might naturally infer. 65.Chap. It second into a unison. 82. that the We have already said that hardly rule here given was wrong. 54. El. 41.Writing. 81. Ex. In both these passages the unison is between the tenor and bass. any of the rules in this chapter are strictly adhered to by great composers . III. and even necessary for beginners. "Auf dem See. 57. This rule should be carefully observed by beginners . if he met with similar passages in the works of the great masters. These passages are ixot given for the student's imitation. and correctness." No. Rule VII. in the tenor. whose part -writing is remarkable for purity ^^ Op. but they are none the less useful. This is the case in which it is most frequently met with. . Mendelssohn. is forbidden for two parts to go from a . amples by Mendelssohn. 31 In the second of these examples is also seen. 58. No. 88. now give 83. Op. Hirtenlied. m. similar motion. [Chap. We one example of the unison quitted by Mendelssohn. . < . 3.3» Harmony. Some of them for example. — . Good. he will All the chief soon find that he is making' satisfactory progress. that given in § 86 will not be wanted at all at first.] The General Laws of Part- Writing. especially in the extreme 86. when he can honestly feel that he has done this. if neither of them has been sounded in the same tion it is better that they should enter voice in the preceding chord by contrary than by similar motion. (^such as When two — — parts. making sure that he thoroughly grasps each point before he goes on to the next one. one step at a time. III. 33 notes making a dissonance with one another a second.C3iap. before he can make This is not the case. difficulties of the study of harmony lie in the earlier stages and the student who thoroughly masters the first eight chapters of the present volume may rest assured that. or ninth) are taken without preparathat is. lated here for future use. 87. The student. must not allow himself to be discouraged by supposing that it is needful for him to commit to memory the whole of the rules given in this chapter. The rules are all tabufurther progress. Not good. seventh. If the beginner will proceed steadily. that they may be referred to when required. the worst of his troubles are past. and therefore a common chord. THE DIATONIC TRIADS OF THE MAJOR KEY. using the only diatonic notes no other notes of the key than the three primary notes will have major common chords above them. triad. But to write a common chord. 88. each note being at the distance of a third. ii. 1 .iv." In the present chapter we shall deal only above fifth. and in Ex. if the fifth be diminished. the highest of which was a A diord containing only three perfect fifth above the root. The triad on the leading note is therefore marked vii°. It was said in Chapter II (§ 36) that a Chord was a combination of not fewer than three notes placed one above another. 20 (§ 39) we put a diatonic triad above each of the primary notes of that key. shall therefore in future give our examples in four parts. 4 (Chap. above the note next below it. either major A Common Chord was or minor. but we shall see presently that every triad is not necessarily a common chord. containing only three notes. a small ° is added after the numeral. as above. defined as consisting of three notes. 91. 62. In the above example the triads sixth. I) we gave the scale of C major. in four parts it will evi- We . third.^E^ m IV on the second. CHAPTER IV. and seventh degrees all contain a minor third above the root.). which is therefore indicated by a small (not by a capital. a perfect fifth is always implied.34 Harmony. 89. it. But the fifth above the leading note is a diminished and a chord containing a minor third and a diminished fifth above its root is called a Diminished Triad. In Ex. whether capital or small (I. 36) of a ^C: ^ ^ I ii . 90. [O^p. It was said in the last chapter (§ 65) that most music is written in four-part harmony.) Roman numeral (§ 41). j . and saw that each of these triads was a major common chord. or a triad. When 'in marking the roots nothing is added to the Roman numerals. We wiU now take each note of triad. with the treatment of primary triads. etc. Each degree of the scale except the leading note has a perfect fifth. and the chord will be a common chord . All triads on other than the three primary notes of the key are called " secondary triads. Every common' chord is therefore a notes is called a Triad. scale as the root (§ it will be seen that £z. exceeded .Chap. In writing four-part harmony. 93. than are absolutely needful for a good progression of the parts. and even within them it is best to. and not to use more of the extreme notes. if ever. If in four-part harmony the three upper parts lie close in other words. These limits should be very rarely. and the tenor is more than an octave from the the treble. Tenor. and bass (§ 65). bered that this doubling of a note does not alter the nature of Though the word "triad" literally means a comthe chord. treble part lies low. alto. but if the treble is high. In most comIf the positions a mixture of both positions will be found. extended position will generally be advisable. that is to put the same note in two of the parts. in however many parts the harmony may be. 92. or at the distance It must be rememof an octave. Alto. If the parts lie at more equal distances. Ex.keep near the middle of the compass. the to prevent the tenor part from going below its compass . the four "voice-parts. . Ex. or even two or three octaves. either in unison. either high or low. close position will most likely be needful. The general compass of each voice is about the fol- lowing : Soprano. and at a distance from the bass — soprano and tenor are within an octave of one another. unless some additional note.] The Diatonic Triads of the Major Key. best notes to double. harmony is said to be in close position. are kept best as far as possible within the compass of the voices after which they are named. a triad does not cease to be such. 64. tenor." soprano. 35 dently be necessary to double one of the notes. and not a mere doubling of notes already present. be inWe shall see presently which are the troduced into the chord. bination of three notes. 66. if the together. harmony is said to be in extended position. IV. a third between tenor and alto. as the student may perhaps suppose. 1 Not so good Bad. single chord. 94. a sixth between tenor and alto. because of the interval of the twelfth between the tenor and bass. and a sixth between alto and soprano. in the this is possible. Good. examples of good and bad positions of the chord of C major the student can easily find out from what has been said why each is good or bad. the same relative position would have been quite good e. we should . it should. first chord there is a tenth between bass and tenor.36 Harmony. It will be seen that in the examples just given. and the chord is said to be "in its root position. but only because both alto and tenor are lying so high. instance. but the position of the same chord at Ex. It will sometimes happen that it is impossible to keep the voices at approximately equal distances without breaking If there must be a large interval between two some rule. The intervals between the voices are much more equal. 95. It : 5SE £x. there should never be a larger interval than an We give octave between soprano and alto. be between the two Excepting occasionally for a lowest. and a fourth between alto and soprano. 67. voices. or alto and tenor. IV. 64 in the last paragraph. 66. Had the bass been lower." But if the third or fifth of the chord were in the bass. 65 is generally preferable . This position is quite correct . sometimes the root.g. the relative positions of the chords vary widely . provided the same note Here the root is in the bass in each of the chord is in the bass. with very rare exceptions. W 96. for here there is a fifth between bass and tenor. I Ex. [Chap. T Very bad. The best position of harmony is mostly that which allows the parts to lie at approximately equal distances. the tenor and the bass. It must be clearly understood that the relative positions of the upper notes of a chord make no difference to its nature. at other times the third or fifth is at the top. when At Ex. should be mentioned that the reason why the position of the chord at {a) is marked "not so good" is not. pulsory to double the primary note gressions in which it is . be explained in 97. and is a semitone below the tonic. the leading note. Besides this. The_J2?t is therefore almost always the~brttcr-OfT:he two notes to double. Chapter VI.Chap. Here. it will so mptiinps \^p difficult. It must not be understood that it is comit is If the student refer to Ex. either in approaching bf"'in"quitting the chord. 98. it cannot be doubled in root position because the fift h of this chord is nq t_a^perfect. except in a sequence . Which of the two should be doubled? The answer is that this depends upon the position of the chord. and that the chords I and IV contain two. especially for beginners.68. 99. to double one of the other notes . a diminished triad is very seldom found in root position. 100. and our second rule for doubling is. 62. {a) J (*) (. and the question will naturally suggest itself. he will see that each triad contains at least one of the primary notes. better to double a primary than a secondary note of a key. an d we doub le t he fifth. With one exception. it is possible to double any of the notes of a triad . especially if in the upper part. to be mentioned directly.. This note is the third of the dominant chord. (§ 138). . toward which it has the strong upward tendency which gives it its name. In the majority of cases. If the dominant chord be followed by the tonic chord. or even better. These will 37 have inversions of the chord. to avoid consecutive fifths (§ 71).) Ez. is seldom good to do uble the fiftlL^ We shall see later that this rule does not apply to inversions (§ 166). It has just been seen that the chords I and IV contain each two primary notes . Double a primary. In the rmL -position otjLjJiaxd. . must rise. but a diminished fifth and we shall learn later that it is not generally good to double a dissonant note.] The Diatonic Triads of the Major Key. If the chord is in rTOt po sition. rather tha n a secondary n o te. we sometimes find proquite as good. but for general purposes it will be found a good working rule. IV. It will be noticed that in the chord vii° the fifth is the only primary note. The exception referred to above (§ 97) in speaking of the doubling of a note was that of the leading note.^. but they are by no means all equally good to double. however. the former being preferable because the third is a primary note. in At (3) (f) the dominant chord is followed by the chord of the submediant. or as one of the middle notes of the dominant chord when taken in arpeggio. or when it is followed by some other chord than the which case the leading note may either rise or fall. I 10 1. that is in succession while the harmony remains the same. does not The effect of the leading note falling is less unsatisfactory when it is in a middle voice. progression (a) satisfies the ear. tonic.38 feel that the Harmony. but this progression. and the leading note may either rise to the third or fall to the root of the next chord. though frequently used by Bach. The leading note however. the leading note chord is ^=F^1^^— Ex. Ex. is not to be recommended to do so. Excepting in the repetition of a sequence (§ 138) beginners. 70. consecutive octaves (§ 67) will result. and when the dominant followed by the tonic chord. and therefore better to double (§97). <1 C: V is. must never be doubled. It is evident that if the leading note is in two voices. and both rise a semitone. the note must always rise a semitone. free to its fall when the dominant chord merely changes position. while (Ji) [Chap.71. IV. At (if) (^) the dominant chord is followed by . as at (^r) . remaining and as the third is needed to fix the nature of the chord. in order to secure a correct progression of the parts. The exercises * In old music. the root of the in inversions. which ends with the it . — descent from supertonic to tonic chords as we shall see presently. and the fifth omitted. loz. But it not infrequently becomes necessary to omit the fifth. not only because contrary motion is . though much more . . as we shall see when treating of the minor key. the two last ^ Ex. as at the end of the " Kyrie " in Mozart's " Requiem " but this is exceptional.Chap. and either progression is 39 though (^) is mostly to be preferred to similar. . One note of a triad is sometimes omitted. much better. zi =^ ^^ C: V Here the melody descends to the tonic the bass also goes to the tonic and the leading note must rise to the tonic (§ 100) there is therefore only one part. the third is occasionally omitted. if we are harmonizing a melody in the key of C.] The Diatonic Triads of the Major Key. But if the bass rose from the dominant to the supertonic. rises. as at (/) (^). the supertonic. and to make 103.* Occasionally also. especially at the close of a piece in a minor key. In order that he may be able to do this correctly. as at {g) for if it as at (/) we shall get bad " hidden octaves " (§75) between extreme parts. chord is the note omitted student will now be able to begin to write simple on the primary triads of the key in their root positions. but also because at (. This is mostly the fifth of the chord very rarely the third. would be best for the leading note to fall. For example. . IV. The only correct way of harmonizing these chords will be -^ A Pm I . because the latter note shows whether the chord is major or minor. possible. must be dominant and tonic in their root positions. the alto.72. rarely than the fifth. this note is taken.?) we have objectionable hidden fifths (§77) between the extreme parts. But in the exercises now to be written it will be well to observe it strictly. 20 (§ 39). when not stationary. It frequently happens that one of the voices has two equally near notes in the following chord.40 his parts Harmony. Rule I. at (f) is repeated in the alto. and at (i/) in the tenor. i C: I V I V IV the tonic chord is in the position shown at (a). move smoothly. we shall see that there are only two notes of the scale the tonic and the dominant ^which are found in more than one chord. Rule II. there are three simple rules which it They are the following be necessary for him to observe. 74. We frequently meet with cases ^we have already seen one in Ex. 73. 106. the treble can go equally well to D and to B. it should in general be kept in the same voice. as at if . At (jz) the note C is repeated in the treble. where all the upper parts. 107. [Chap. as it will conduce greatly to the smoothness of the part-writing. IV. Each fart should generally go to its nearest note in ihe following chord. — — Ex. refer to the primary triads of C major. etc. It will therefore be best at first to keep these notes in the same voice whenever these chords occur in succession. 104. Let the student notice the hidden fifths between extreme parts at ((5 ) and the hidden octaves at (^T). But if it goes to D. 71 (i?) of § 101 in which it is much better not to keep the note in the same voice and we shall find others in our next chapter. For example. If the same note is found in two consecutive If we chords. and at (J>) in the tenor. By referring G to §§ 75» 77j he will see that both are among those that are allowed. given in Ex. in the progression from I to V. the former being a part of I and IV. are moving by step. It must be clearly understood that the rule just given is not one of such stringency or universal application as those prohibiting consecutive octaves. 73. and the latter of I and V. will — — Ex. This is shown in Ex. 105. the other parts of the harmony before deciding which of the two notes to select. 108.] The Diatonic Triads of the Major Key. upwards or downwards. the student should always look at. which is not the nearest The treble should therefore take B. . note of the chord to E. 1 .Chap. In such cases. which allows the tenor also to move to its nearest note. When the bass moves by step. \S Ex.. Rule III. which are of constant occurrence. the tenor will have to take B. fifths and octaves must move in contrary motion \p IT. IV. D. 75. 41 (3). Before we proceed further. The same three notes are also found in A minor . and the stems of If two parts the lower voices (alto and bass) downwards. 108. sometimes also the soprano. There will be no difficulty in putting the correct harmonies above this bass. either the root. the tonic is defined by the notes F and B. all the examples in this volume will be given in short score . by putting two notes side by side {=xs). but because the power of being able to read from score is most useful to the young musician. the better for him fs advised to use open score. 113. each voice is written on a separate III. F. succession of them Ex. The position of the first chord is optional.76. with the G clef. one up and the other down (p f ) or. in the case of a semibreve. In short score the music is written on two staves the treble and on the upper staff. We this Observe that chord. written on the same staff are in unison. is fixed by the third of the tonic chord. with the F clef.42 Harmony. 106. and B naturals. because (as will be seen later). [Chap. before its leading note. — — which it shows the progression of each voice. a minor key always has an accidental (^ or t[). which has no stem. if the student will bear in mind the three rules given in §§ 104. but the student who is familiar with the C clefs and if he is not. There is no other major key but C which contains all the three notes. third. not only because of the clearness with ' ' staff. iv. this is shown by putting alto — two stems to the note. or fifth may be placed in the treble. We IV simple passage begins and ends with the tonic is usual. E. and the tenor and bass on the lower one. In the key of C. while the mode (major or jf minor). the latter necessary (§ 38). must always be turned upwards. being From considerations of written each with its proper C clef space. The former will work it in all these positions. We will now show how to connect the primary triads will take the simplest possible of a key with one another. All our four-part examples in this chapter are written in this way . but this causes no confusion. 1X2. and it must be remembered that the stems of the higher part on each staff (the treble and tenor). the sooner he learns them. In " open score the alto and tenor. for every other tonic has either F or B j? in its scale . it should be said that the three primary triads absolutely define the key. . 77. (I) rr^ .Chap.] The Diatonic Triads of the Major Key. IV. (2) (3) (4) 43 Ex. the only one which it is needful for the student to know at present is that called the Full Cadence. 117. . and with no more ide& of their sound than a fly would have. The figure indicates that the (8. The last chord of a cadence should come upon an accented beat of a bar. ealled the Authentic. Our next dies. found somewhat more difficult than the exercises just worked. first simple harmonizations. he will see that each ends on an accented note. to produce a satisfactory effect. harmony exercises just as if they : and the fourth with a plagal cadence. 116. iv with a given bass. and IV-I. however short. If he will look at the four exercises he has just worked. placed under the first bass note. because the student will have to choose his own chords. or third of the first chord is to be placed in the treble voice. octave. the note C were preceded or followed by E. fifth. 5. using only the three step will be harmonization of simple meloThis will at first be primary triads. instead It will be of great assistof having them prescribed for him. or close. the best position of the first chord. 119. This gives two kinds of fiill cadence V-I. — — In these . the tonic chord must be preceded by the root position of one of the other primary triads. their this is by no means difficult. and that the first three finish with an authentic. the student's dominant which can belong to more than one chord. \ca3. the chord must be in root position. Which of the two chords should be used. in the case of what are known as " feminine endings (See Musical Form. ance to him if he can hear clearly in his mind the effect of what he is writing with such simple harmonies as these now to . In harmonizing melodies with only the three primary work will be considerably simplified by the fact that there are only two notes in the key the tonic and the triads.t. Too many pupils write were sums. in modem music the authentic cadence is much the more frequently used. It has been already said more than once that the final chord of a piece must be the tonic chord . or 3). be used. it would mostly be better to treat * These terms will be explained in Appendix A. There are occasional exceptions to " this rule. To make a full cadence. must end with a Cadence. Chapter II) . n8. Every piece of music. satisfactory progress can ever be made unless the notes convey to their writer a distinct impression of their effect. will chiefly depend upon the context. that alighted on Let it be emphatically stated that no really their music paper. There are various kinds of cadence . known as the Plagal cadence.* In older music the latter was the more common . it is best to avoid a stationary bass if therefore in the key of C. IV and V. but with these the student need not at present trouble himself.44 Harmony. have numbered each note for convenience of reference. it would be preferable to harmonize C with the tonic chord. 2 3 4. 78. Our first nant. 8 9 Ex. for an exercise should never begin with a subdominant chord. leaving lower parts that we are going to add to it. If We any choice. When it does not begin with the tonic. or. Hitherto we have written all our examples in the key of C. only two notes (3 and 5). Shall and second chords must be evidently tonic and domiwe begin in close or extended position ? Here the former will be better . ^ ^^ P ^23456789 * . If the same note be repeated in the melody. 6 7. Ex. either authentic or plagal. and 9). be avoided as much as possible. which must be a note of IV. i. In the case of the latter. In order. and the last two chords of each exercise should make a full cadence. for we shall see. 5. it is not necessary that the tonic should be in the upper part of the last chord. for the I Our next already fixed. however. 45 the C as the fifth of IV . We will now write a simple melody. that the student may not accustom himself to think exclusively in the key of C. 79. which admit of more than one possible chord and of these.] The Diatonic Triads of the Major Key. Large leaps should. 120. to change the position of some of the parts. therefore. which allow 121. if there be only one chord possible for that note. we examine this melody. the last must take the tonic chord (§ 117). but if the next note were A. 3. We have here. IV. we shall see that there are only four notes (Nos. S. and there is not the least difference in the difficulty of writing harmony between any one key and any other. and marking under the bass the roots of all the chords which are 122. as a pattern for the student. The first chord must also be the tonic . and harmonize it. we will write the present exercise in A major. excepting the leap of an octave in the bass.Chap. as we proceed (§ 125) that extended position would get us into trouble in the . it will begin with a dominant chord—almost always on an unaccented beat. room step will be to write out our melody. therefore. But there is no special virtue in this key. it would certainly be best to change the chord. alto. the matters not which ^in the bass. but no piece should ever begin with the progression from subdominant to tonic. for if it is in the tenor. 81. and must have it again for the sixth note. Ex. the middle of A 124. We shall therefore take I for our third chord. it will will turn back to Ex. 75 U) {d). where the progression be seen that in both cases the leading note is in a middle . as the primary note in the chord. We C in the tenor. to establish the key (§ 112) . not only The V * If the student V-IV is given. and if we take the lower G. it will be too high if we take the upper G. can only form part of the tonic chord. for a reason that will be seen directly (§ 125). It is therefore best to change the position of all the parts. As we have already had I twice in succession. C. and in many cases it would be But here the key is sufficiently established by its best to do so. as the last note of the alto was E. the key might have been E major .46 second bar. 80. tonic and dominant chords. ^ Z 3 4 S 6 =t= J r I E^ 1 y 1 following E can belong to either I or V. bass note must be E. In our next chord (V). and put B in the tenor. and to let the bass leap an octave. For our third note two chords. IV. [Chap. it is evidently best to take here. The G should be placed in the alto . I and IV. But in this position IV would not be good. The fourth note. ^mi^tA A: I V ? 123. '^ The beginner would naturally be inclined to introduce all his primary triads as early as possible. which. Had chords i and 2 occurred in nant a piece. is the best one to double . The progression V—IV always sounds more or less harsh if the third of the domiis in the upper voice. with the lower in the bass. are possible. 3 — therefore in the first chord write and either the upper or lower A—here E in the it Ex. as it will have to go to A in the next chord (§ 100). we keep it in the same voice (§ 104). and write it in the same position as chord I. Harmony. put the lower. in the fifth. but the alto and tenor will be a tenth apart (§95). It will also be seen why extended position at the beginning of the exercise would not have been good. we must either have had a stationary bass.Ch»p. and not the upper We should then in the fourth chord. Let it to 6. and 6 to 7. followed by the bad hidden octaves just seen (See Ex. or progression to a unison (^). at {c). there will therefore be notes common to the chords. and these must be kept in the same voice. for this would make consecutive fifths with the bass. the upper part would not be moving by step. and the prohave had the lower gression to E. IV. From 8 to 9 the melody descends from supertonic to tonic (See § 102). put B in the tenor. because the cise from the fourth to the seventh chords should therefore be written 4567 From 7 to 8 the bass moves by step. would have caused bad hidden octaves between extreme parts (§ 75) . The student will now see why in the third chord we in the bass. should The progressions from chords 5 now offer no difficulty. because the repetition of the be noted in passing that there are not consecutive fifths same notes at an octave's distance does not change the harmony (§ 67). We therefore omit the fifth (§ 102)- Obviously we cannot 125. 85 (a) below). though the chords are both primary. 82. 47 will there Be an unpleasant overlapping (§ 85) with the bass . The student will now readily understand the harmonizing of the . or tenor and bass both leaping an octave (f). The way of treating the upper parts has been explained in § 108. ^J 5 (*)3 „ 1 4 M3 L 4 Ex. roots are more than a second apart . A A («) tJ — I 2 3 4 I __. because.] The Diatonic Triads of the Major Key. • The exer- 126. After the third chord. might have been changed thus is Ex. Ex. 85. in the may be would think of harmonizing following chapters. the primary triads being. and to be familiar with their treatment.48 whole melody. planations* we have given in this chapter. 84. . it is necessary to know them thoroughly. the position of the chords from 4. before proceeding with the remaining chords. triads and inversions. naturally the Harmonize the following melodies (Y) (VI) in four parts. as already said. ^ esSx 123456789 U= ^V'^. A: If it I V I I V I IV : V I preferred to keep the tenor lower. the fifth in chord but have then to well to say that in actual composition no one this melody as it is done here. The result of restricting ourselves entirely to the primary triads in root position is that an effect of stiffness is produced. It ^ r I J ^ 'l ^ I ^' J I J IV I (' V V V s. he will not find much trouble with his work. the student has become acquainted with sec- ondary again. I we have 6. and it will be felt we will harmonize the same melody at once how much more easily and music flows. the most important chords of the key. The student can now attempt the harmonizing of a If he has thoroughly understood the exfew simple melodies. 128. But. (VII) . A: In this position omit it in chord 127. When. 129. they remove the impression of stiffness which. the third of the chord is the only primary note. Die Zauberflote. it will be seen that in the triads ii. and fifth. however. as the most important in the key. we spoke of how they — fourth. The employment of the primary chords. We have now to deal with the remaining triads the so-called "secondary triads.Chap.. and vi. and showed V. to treat of the inversions of 130. and we saw that all the secondary triads had minor thirds. gives great strength to the harmonic prostrong they may be termed the chords of the gressions key. chords of the major key. while The first thing one of them (vii°) has also a diminished fifth. which is^ the best note to double. the secondary triads produce an It is therefore generally advisable not to effect of weakness. we give a short passage by Mozart. In Ex. The chord vii° is so seldom met with in root position (§ 99) that we shall defer the discussion of which of its notes to double till we come. the primary triads of were to be treated. 49 CHAPTER SEQUENCES. To illustrate this. before making use of these triads in four. is. Ex. chords. THE DIATONIC TRIADS OF THE MAJOR KEY (CONTINUED). 62 (§ 89) we gave a table of all the triads. As compared with them. noticed that within the space of two bars we find all the diatonic common the bass. ' ' . v. and how to be connected one with another.] Triads of the Major Key. and should be carefully examined. IV I 132. results from the sole employment of the latter in root position. to be considered. in each case with the root in Next let it be observed that the tenor doubles the .part Bearing in mind harmony. 86. ' ' . Mozart. the rule given i^^^J^^hat it is generally better to double a primary chan a secondary note. . I 131. as we have seen (§ 127). when introduce too many secondary chords in succession judiciously intermixed with primary chords. iii. in the next chapter. In our last chapter the major key. This short passage is full of instructiveness for the Let it be first student." which are found on all the degrees of the scale except the first. as in the following passage from an old German Ex. A 133. With such a long pattern as this. though it would be if only two or three notes of the tenor. are four parts moving here. Here the pattern is tion . they differ in the quality of the intervals . the passage is not in four-part harmony. We shall see directly that it is possible for a sequence to modulate. Such a passage as this is called a Sequence. however. longer sequences are met with. the imitaa third higher. we seldom find more than one imitation . but in three-part harmony with one part doubled. the second pair are both minor. consecutive octaves is not broken by such a progression as this. mein Gemuthe. 87. there will be two. and is called a tonal sequence. the pattern being in A minor. or four . and the imitation in C major. 134. V. choral le-muhter. when each part proceeds in exactly the same way on each repetition as in the original pattern. Sequence may be defined as a progression of chords. There is no limitation as to the number of chords of In most cases which the pattern of a sequence may consist. moved in octaves with the soprano. 135. In Ex. most usual kind of sequence. [Chap. but they are a third lower. 86 it will be seen that the third and fourth chords are the same as the first and second. are exact copies of the first pair. four bars long . three. It will be seen further that in every alternate chord the fifth is This is because the second and third pairs of chords omitted. This illussoprano in the octave through the whole passage. The law against trates what was said in Chapter III (§ 70). and the third pair are major again. that the This is by far the music remains in the same key throughout. repeated on other degrees of the scale.5° Harmony. The fifth and sixth chords are a third lower than the third and fourth. if the pattern consist of only a few notes. as regards their position and the notes they contain. which in other respects they also resemble. occasionally." is an entire phrase. and is an example of a modulating sequence. inThough there stead of all. It must be noticed that while the third and fourth chords are in all other respects exact repetitions of the first and second. the first two chords are both major. but on different parts of the scale. The reason of this is. It will be seen that we have here the diminished triad in its root position (§ 99). four. interval above or below. in which a pattern of two notes is repeated a second higher each time. the second chord. and the doubled leading note . 'j.g. et- IV vii. Had the fourth bar of the example been given as a pattern it would have been faulty.. Practically. requires special notice. but seen that each repetition would be in a different key. the limit of a third is seldom if ever exceeded. It will also be noticed that the leading note is doubled (§ 100). At the fourth bar of the sequence given in Ex. 89. 88.Chap.A A A A A V iii ^ IV ii ^^4 ^^^-^E^ vi. ^'=- Such a sequence would be called a real sequence . as many imitations at a larger interval would soon carry us beyond the range of the voices.'j. Note that it is necessary that the distance of each repetition should be uniform . also that it would have been possible to keep the quality of the intervals the same in the repetitions as in the pattern Ex. 90. A A A. We Ex. marked with (*). ^P C: I. to illustrate a point not yet touched upon *.° V I Here we have a tonal sequence (§ 134). "^STTt-t^ ^j-F^^£ two : now give a simple sequence. v. S> three. or pattern set for a sequence may be imitated at any 136. we should have an "irregular" sequence. on a pattern of 137. The £z.] Triads of the Major Key. notes. even more imitations are to be met with. while the following ones rose only a Observe second. 89. it will be 138. e. however. justified by the fact that they occur in one of the repetitions of a sequence. if the second bar here were omitted. and that between the two notes of the bass in this bar is seen the unmelodic interval of the augmented fourth These departures from the rules already given are only (§ 60). and the first repetition were a third higher. or if their observance would would have been possible in this passage to have had Bb instead of making a transition for a moment into the key of F. The sequence we are examining might have been We might. sequence on this pattern. [Chap. suppose we work a to the rules just referred to. at §§ 104. It * B|j in the fourth bar. We preferred to give at fMBt iiposmonj'which allowed strict observance of the rules given in Chapter IV. not only because as a general rule contrary motion is preferable to similar.* 139.g if in the etc. £z. 106.52 Harmony. V. It will in many sequences be found impossible to attend For example. and there will It will therefore be necessary to arrange the be no sequence. 141. have put the arranged differently. "The horse and his rider. that the first and second of these rules may be disregarded in a sequence. however. ¥^7^^ y ^ A etc. 106. 93. 140. would not have been allowed. =1= second bar we attempt to keep the two notes F and A of the chord of D in the same voices in which they were in the preceding chord. 60." in "Israel in Egypt. still retaining the second as we have given it Ex. . The progression would then have been analogous to the well-known sequence in Handel's chorus.92. remembering.91. But the effect of the sequence will be better if carried out after the pattern last indicated . Ex. 108). but also because we thus obtain a less monotonous melody." quoted in Macfarren's " Six Lectures on Harmony. The student may now attempt exercises containing all the diatonic triads. as at (a) below. first chord in a different position. for instance." p. it is clear that the second bar will not correspond to the pattern set by the first. upper parts as at {b'). He should refresh his memory by referring to the three rules given in the last chapter (§§ 104. the where it is evidently impossible. (I) Add alto and tenor. not only to avoid hidden fifths in the outer parts. 71 (§ loi). but to improve the melody of the The third rule (§ 108). regard to doubling. It is possible to begin with any note of the first chord in the treble . We a blank staff roots before beginning to under each exercise. beginner. (II) rt^fe^^^ i ^ m~rT ^ ^ ^^ r -A — (V) St:^^ Si& w =1=32 ^ =?=: l=-f- l=t: [a) Begin in extended position. These should not be found difficult. as he has only to add alto and tenor parts. no further directions will be necessary. An instance will be seen in the first and second bars of Exercise IV below. a note from one part of the harmony to another. begin with a few exercises in which both treble and 142. is transferred to the treble in the third chord. for instance. though the roots of the chords in the second and third bars are secondary notes in the key. v. his keys and Treble and bass given. He should leave. as It is also allowable to transfer in (ff) (/) of Ex. 89. With treble. ) is doubled in the first chord of the pattern it is therefore necessary to do the same in the first chord of each succeeding bar. In Ex. where the D. S3 produce objectionable hidden octaves or fifths (§§ 75 to 77). we will only remind the 143. and mark fill up the chords.] Triads of the Major Key. except in the repetitions of a sequence. root (a primary note. his safest plan for the present will be mostly to double a primary note. which will be in one of the middle parts of the second chord.Chap. work exercises in which only After what has been already said. . must be strictly observed. if a better melody can be obtained thereby. the bass Our next is step will be to given. even by a bass are given. —In this exercise. and indicates which note is to be Finish each with the tonic in the treble. V. — Bass only given. [Chap. (VI) Add three upper parts. (VII) N.^^ ^\^ 8 r ^J i r i ^ (XI ^ \ ^^^ ^ ^ \ ^ \ ^ . that the student of what we said in the last chapter (§ 115).54 Harmony. figure under the first bass note of each exercise shows the best position for the first chord. begin the treble thus (IX) (X) HHMr m.\ r^^^ (XII) (XIII) Mi-f^-4J°-i>-r-r I r riJ-f% pfrrrrrt^an^r (XVI) • I r r JHrtp-rt^ (XVIII) ^^^^^^ . placed in the treble. B. there were only two notes of the scale (fhe tonic and the dominant. vi. each note will form part of three different chords. and only if the melody begins on an unaccented note. Before proceeding to harmonize melodies. more rarely.. these chords to select in harmonizing any particof a melody will largely depend upon the context . iii. V. vii°. SS (XIX) Double 144.. there are some important points that the student must clearly understand. when only primary chords were used. or This will be seen from the following the fifth of a chord. or.] Triads of the Major Key. . or 117. vii°. It is therefore impossible to lay down any fixed rules on the subject . but a few general principles may be given for the guidance of the student in his earlier attempts. I. ii. only such points are mentioned here as the student will require at his present stage. vii°. v. mediant subdominant dominant submediant leading-note .Chap. not infrequently two may be equally good. ) which could belong to more than one chord. But if we use all the triads of the key. The first thing to be remembered in the last chapter. V. every piece * This question is discussed in detail in Chapter II of Counterpoint. . is that. ii. I. IV. on which a few words must be said. . The first chord should also be I.) that.) (if the penultimate note of the melody be not a note of the dominant chord. It was seen in the last chapter (§ 119. IV. as mentioned must end with a Cadence (§§ The two final chords must therefore be V-I. table The The The The The The The ular note tonic is a note of chords supertonic . ) IV-I. . employing secondary as well as primary chords. 118.* Which of 145. Chant. IV. iii. iii. . But for all the intermediate notes there will be more choice and the selection will largely depend on the progressions of the roots. ii. V. I. as it may be either the root. the third. vi. . V. vi. which. these progressions will be just as good as the others. as that of a fourth upwards. All the above progressions are very good. the strongest and firmest are those in which the root rises or falls A a fourth. fifth downwards is the same. [Chap.g. 95. especially if two e. We (§ 99). but there are two of these upward step-progressions which require a little care. . third is practi- but the effect of the latter is generally more satisfactory than of the former. It is in general good for the root to rise by step of a second. In the progression iii-IV the effect is a series of rising. we have several times made the bass fall a fifth. either by step 146. at — 147.g. The progression of roots by leap of a . as regards the harmonic progression. either : upwards or downwards Ex. As the leap of a of a second. iii vi IV vii° VI 11 Vll" have here given an example of every progression in which the root rises a fourth . wards — It is e. as they contain the root-position of vii°. excepting those which contain vii° as one of the two chords. the same chords being chosen in both cases. or by leap of a third or fourth. 148. the student will see that the six Of these. seconds and sevenths. C: ii IV vi At (a) and at {b~) of falling thirds. V. should only be used in one of the repetitions of a sequence evident that if we read these progressions backall the roots {a) taking IV-I instead of I-IV.56 Harmony. root can move upwards or downwards. will fall a fourth . cable. except (</) and (^). or three such leaps occur in succession . piogressions just named are the only ones possible. to impress upon the student the identity of the root-progression. but the effect of the latter is more pleasant. Both passages are correct. and the same thing applies to thirds and sixths. and in the latter.l Triads of the Major Key. {d) Good. e.Chap.g. 1^^^^^^^ 149. (b) Good.) is Not good. {b) Good. Ez. (c) Good. in which it is not good in general to place both the thirds in the treble. would — A as either the fifth of {b) ii or the root ^=^.) A ^^ — — should not be in the upper part. r-r^"^^T V IV =^=i j- C: IV V IV V it If the notes mostly be better to treat of vi . C: I iii IV vi iii IV I iii IV ii iii IV The other progression just referred to is IV-V. 57 is not satisfactory unless the leading. 96. #A A\ —5^ ia) ' were given in the melody.g9. ^ ^^ B (a) Not very good.^.note (the taken and left by step in a descending scale . Ex. Ex.or -beth-of the chords should generally be inverte3r"The only good progressions in root position ^with which alone we are now concerned of roots falling by step are vi-V Land V-IV . . e.g. (a) Good {b) Good. {e) Good. 97.^ Ex. {c) — fifth of iii. WeshallJsarruJater that when the root proceeds by step downwardSj_Qiie. {d) Not good. the leading-note (the third of V. V. (a) Good. though it is not absolutely forbidden. (<:) Not good. is more that of minor than of C major. If. directly.lOl. We shall show the application of by harmonizing a melody as a pattern these principles Ex. we number each chord for and proceed to sketch our score. use a fair proportion of primary triads in harmonizing .S8 150. it will often siffiice to change the position of the same chord . 151. with only root positions. gether. leaving room for marking the roots under the bass staff". it should only be taken when it can be followed by vi. but. and may sometimes even disturb the feeling of the key. in spite of the primary chord IV. V.t 12345678 : melody worked in § 1 20. . 152. ii will define the key early. from § 145. As clearness of tonality is one of the first requisites of good writing. meanwhile one Avoid vii° altoor two further hints may be usefully given. what must be the first and the last two chords we therefore mark them first. 96 (a) {!>). or in a sequence. Harmony. 102. troduced as in Ex. it is better to change the chordt WTieh^we can use inversions. Remember that a key is defined by its primary chords (§112). since it contains the subdominant. Always just as well as IV. do not forget that too many secondary chords in succession have a weak effect. for example in C major we find the following progression. [Chap. 153. As in the reference. it will almost always be better to take a different A harmony. and be sparing in Except when inthe employment of the mediant chord (iii). . the primary chords should always be introduced After I and V have been employed. C: vi IV the impression produced. 100. except in the repetition of a sequence. 12345678 Ez. We know. we have given. by harmonizing a simple melody of Ei. We will now illustrate the instructions four bars. If a note of the melody is repeated. though we have not introduced our third primary chord. as here. 68. in the 'Nordisches Lied' in Schumann's . and the other two are equally good. F. in small notes. as it is possible to follow iii (§ 150). let the student ask himI. vi. The last will not be good here . fore select ii. but. belongs to the chords ii. and mark the alternative version. we see that the sixth and seventh notes are a sequential repetition of the fourth and fifth. IV gives slightly the stronger harmony. the second note of the melody.] Triads of the Major Key. it is not absolutely unprecedented for a piece to begin with the subdominant chord . after We now give the whole piece. advised to mark each root in his copy of the exercise. It will be unnecessary. which chords to choose. to point out that. we now take I. Here (§ 150). — — We now continue our harmonizing. f but in such a case it is never followed by the tonic chord. V we take the last. and 156. We therefore have a choice of I or vi . for the sake of defining the key. and. and the second as dominant. Here let us pause for a momeint. looking at the melody. the student 59 154. had I before V. vi.Chap. Though very unusual. G. or I. iii for the fourth by vi in the next chord chord. The following note. Our last chord was For the following C the chord can be either V. in which key they would be IV and I. When a piece begins with a downward root -progression of a fourth. and IV. We will thereit is possible to make a sequence in all the parts. the first chord will always be felt as tonic. v. vi. and as we self why. Bt>. we take chord must be vi. vii° is inadmissible The 158. (IV). while the upper F will make bad hidden fifths (§ 77). IV.* 155. In considering may find occasional reference to the table in § 144 helpful. by taking ii in the bass. therefore. to get more variety. and shall not be able to do so till the sixth chord for the fourth and fifth notes are not parts of the subdominant harmony the two chords I and V are here quite sufficient to establish the key. what the student has already learned. as one of the primary chords. The only other key besides F which contains both those chords is C. Our first three chords are therefore V. for the lower F will give a needlessly large leap in the bass. The last two chords we already know. iii. as fAn 'Album fur die Jugend. vi. is a note of the chords The last is impossible . sixth note. vii°. of course the fifth must be part of ii or IV. 157. We had V in the second chord. to explain in detail is * The student he proceeds.' example may be seen Op. except between the second and third chords.V which each chord I 23456 is filled up. it is (§ 146). The student should AVhen he has done this. 159. r ii I ' (IV) V V I Observe here the strong harmonic progressions . the roots always rise or fall a fourth Notice also that in every chord except the fifth. odies. (XXIV) ' (XXV) (N. Harmonize the following melodies in (XXII) four parts (XXIII) •= I \ 'J J Ig .6o the Harmony.B. Ex. taking care always to end with a proper cadence.) %) »3 (XXVI) ^^ ^ J 1^ J I j-li^ J I J J ijl r «! y (XXVII) . now harmonize the following melhe may attempt the composition of little melodies of four bars for himself. a primary note that is doubled. way in [Chap.—Floffal Cadence. 103. and so on. C. interval was defined (§ 25) as placing the lower note above the But it is possible to invert upper. etc. The first inversion of a chord. and Similarly a either of these notes can be placed in the bass. 160. which in the root position was a third above . {P)^ ^^^^^1=1 G— (a) and {V) of the chord of C. but the fifth of the chord. the student that the number of inversions of which any chord is susceptible must be one less than the number of notes which it Thus a triad. and at (^) the relative position of the two notes the inversion of a third. we shall see that at (a) E is a below G. for the root. VI. the root is A As in the root position. 161. because it contains two notes besides its root. it makes no has the third in the bass. has three inIf the third of the chord (the first note versions. is now inverted with respect to that note. we The number of the inversion have the second inversion. The inversion of an they can be. which was before a third below E. («) Ez. 6i CHAPTER VI. and E is a sixth above But the chord itself is not inverted. 104.Chap. inverted. ) be in the bass. difference to the nature of the chord which of the other notes stands next abgve the third. Hitherto all the chords we have used have been in their root positions. if the fifth (the second note above the root. G. inversions. THE INVERSIONS OF THE TRIADS OF A MAJOR KEY. chord of the seventh.] Inversions of Triads. ) be in the bass. and frequently are. we have the first inversion . but in order to obtain greater variety of harmony. 162. is in the third bass in both cases. The root. and is a sixth above it . which consists of three notes. has two contains. can always be found by noticing which note in the series of thirds above the root is in the bass. is changed. Both (a) and (Ji) are equally first inversions of the chord of C. as we have just said. or the upper below the lower. chord is said to be inverted when any other note than A moment's thought will show placed in the bass. because it contains four notes. above the root. some of the intervals of a chord without inverting the chord Thus if we compare the two positions itself. ) Whenever a bass note has no figures under it. and therefore whether we have an inversion. but is now more usually spoken of as Figured Bass. the chord of the sixth. Thus. when only the bass is that is. 6 (6Corg) «6 6 6 |26 « « b b 165. being almost invariably placed at the top. fref.6a E. 6l| or 6|7. excepting when it requires an accidental. in Ex. {See § 177. below the first note. when there is But. also. but only the position of the root. Figiired. A — ^)f6. But if the sixth required an accidental this would have to be written thus tj6 in that case the accidental 3. As a first inversion has the intervals of a third and sixth more than one. the common chord in its root position is not figured at all. for the student's assistance. 106. or one of the other notes of a chord. more usually. except the one given. as it contains the fifth and third of the — — bass note would be figured 5 — the larger figure. as a matter of actual practice. but it is not specially marked. This is a kind of musical short-hand. In § 41 we showed how to . what harmony is to be placed above it the bass note is the root. have therefore no figures under the bass. implied. J} accidental without a figure at its side always refers to the third of the bass note. [Chap. the third being always implied when the name is used. The first inversion of a triad is is still a third above it. which indicates. 105. therefore called the chord of the sixth and third. vi. An sharpened note is or !?6. and without the figure or 1^ is written Jf. Ez. are to follow one another on the same bass note. we use what was shorter — formerly called Thorough Bass. 164. sometimes also 6^. or when two or more chords one of which is a common chord. It must be always remembered that inversion does not change the root of a chord.in root position. C is still the root. by one or more figures placed under (or sometimes over) the bass note sometimes. A common chord in its root position. a root position of a triad is always The exercises in Chapters IV and implied. by the absence of any figures ^what notes are to be placed above the bass. whether given. by putting it in one of the upper parts instead of in the bass. except when one of its notes requires an accidental before it. In order that it may be known. 163. Harmony. or. its full figuring would be ' % ' But just as we speak of it merely as a " chord of the sixth. quently indicated by a stroke drawn through a figure thus The following examples will make this clear. V above the bass note. we mostly figure In a chord of the sixth the third is always it only with a 6. we omit need only be added that in the root position of a the ' a' as. 168. though the F and B be met with in its first inversion. the the second position. rather than a secondary note. and we shall thus have a chord of the sixth on every degree of the scale. letter after it indicates 166. We inversions. they produce a much less harsh effect than in their root position. in the first inversion of a diminished triad. \b and \c. It chord. we add after the Roman numeral the letters of the alphabet (a. In four-part harmony. because of the thin effect of a bare 167. b. etc. The rule erive^ i" § 97-1-*'" double £y I I primarv. one of these notes must be doubled. To indicate the position. and so on. while the fifth is often omitted in a root position (§ 102). ). Ei. are still dissonant to one another. bsy s != iii* IV* Vi5 vi* vii°* \b . double the fifth (the primary note of the chord). the second inversion is the third . Greater freedom is therefore allowed in their use and in their progression. For the same reason. of the chord no longer holds good . applies to first inversions' But the objection to doubling the fifth as well as to tc.. As the root and fifth of this chord are (as just said) dissonant to each other. except in the repetition of a sequence. we make the discord harsher. It is We clear that the root position first is Xht first position of any chord . being the leading note. because now both the notes are consonant to the bass. At * in the last example will be seen the first inversion of the diminished triad on the leading note. Though this chord is very rarely used in its root position (§ 99). 107. 63 indicate the roots . and the student will by this time have no difficulty in doing so with chords in root position. superfluous . Thus la indicates the tonic chord in root position. for the fifth is now the third above the bass. if a better progression can be obtained thereby. must on no As account be doubled. 62 can be used in their first inversion . it is hardly ever good to omit it in a first invCTsigji. just as in the root position. .(^\ pQBJtinns.position.Chap. the first and second inversions of the shall see later how to mark discords and their same chord. as well as inversion is the root of a chord. The root. a general rule. it is very often to Here. c. the But it is not forbidden to best note to double is the bass note.] Inversions of Triads. now show how to apply the same method with all inversions. the numeral without any a root position. All the triads given in Ex. VI. if we double the fifth. be seen thaf^ fe such a passage "as this It is not posdouble the primary note of each chord. Provided that the general laws of part-writing given in Chapter III are observed. 169. that is between other positions of chords. Mass. The same note of the chord must not be doubled in the ^rule Xsame parts in two consecutive first inversions. or the fifth be doubled by the same voices in each chord.64 Harmony. It will K sible to 171. Here. Ex. The fifth will then be a fourth below the root. there are no special restrictions as to the treatment of first inversions when they occur singly. But when two or more first inversions follow one another. it is clear that we shall have a series of consecutive fifths with When Hence we get the following important rule: the roots. as in the following example from Mozart clear that there will : Ex. No. 109. two or more first inversions follow one another. Mozart. leading . for instance. If. in the series of sixths given in Ex. From this we deduce another as at (a) consecutive fifths. in the first and second crotchets of the second bar. VI. 15. («) I 1 I I (*) 1 1 „ (') \b it is \\b iii* IVi \b \\b mb IVb U iib iiib IVi be consecutive octaves. and consecutive fourths are not forbidden between upper parts (§ 78). The usual plan adopted is to double the root and the third of the chord alterf nately. 1 70. the third. Another point to be attended to in a series of sixths is If either the the doubling of one of the notes of the chords. Ex. 108. sometimes also. [Chap. root. to double the G would make consecutive octaves. a little care is 'needed in their management. The student must be careful never to double his. especially if the bass moves by step. 107 we place the fifth of each chord in the upper part. 110. the root should mostly be in the upper part. ) that the figuring of a root-position of a chord would be \ first is inversion . or if the only be odd numbers. for the higher discords. sions were distinguished by a after the numeral (I^. We V to assist the student in finding the root of a chord at once from : the figured bass. in fact. such as a common chord in its root position on the same bass note. or there would be no means of distinguishing between this chord and the first inversion. and are therefore inverted with respect to it. and if there be more than one even number.Chap. This inversion is therefore called the chord of the sixth and fourth. as will be seen directly. If there be any even number in the figures.sijrtb&-as the above.] Inversions of Triads. " The lower cannot be omitted. is — both odd numbers which 6 — ^ (§ 164). not only to the triads of which we are now speaking. he will notice that its effect is much more unsatisfying than that of either the root position or the first inversion . to see which to double in the first chord of the series. This is because a fourth with the bass (though not between two upper parts) produces the For this reason the second inversions of of a dissonance. or more commonly " figure the chord of six-four. VI. The second inversion of a chord has the fifth in the bass. have already seen (§ 163. is the root. If there be no figures under the bass note. the lowest even number gives the root. from this point he should reckon back to the beginning of the series. chords require special treatment. If the student will play this chord on the piano. A little thought will make these rules quite clear. ^ It is figured H. 6$ ngte-ia-such a sfiries-o£. to be followed by some other chord. the full figuring of a the only even number the root in the second inversion both 4. the smaller of the two. Sometimes also he can help himself by doubling the fifth of the chord rthe third above 172. 173. The root is now a fourth and the third is a sixth above the bass note. and not the third of the chord. For instance. ii^. in . that number shows the root of the chord . the following rules will be of great service I. must be doubled . but to all chords of the seventh and ninth . etc. he will see that at {a) the root. doubling root and third by turns. Ex. In this chord both root and third are above the fifth. it requires. We 175. To avoid this. effect said in § 165 that in marking roots second inver174. 111. figures II. a little forethought will often be required. and These useful rules apply. the chord is in root-position. . (above numbers are even. ). in the above passage. each represents a chord of half the value of that note. \c followed by another chord on the same bass one of the cases in which it is necescommon chord (§ 163). We three chords less IVc. and the second one third of the whole value. afterwards giving examples of the frequently useT secon^nversions of secondary triads. the ninth). Ex. Though it is possible to take any triad in its second inversion.position of the dominant is called a Half Cadenc e 3 these are only found as middle. not with a full cadence. when the first chord will have two thirds. and. the authentic. are put under one bass note. in the majority of cases this The is employed cadentially. or its octave . in approaching a cadence. passage ends. VI.66 Harmony. the two final chords being \c and V. In a cadential ^. 178. Creation. ^ Ex. this is sary to figure the root-position of a & . 112. r is I ' 6 6 -^ 4 similar to the last.) that the most usual form. the employment of any but primary triads in this shall therefore first speak of the position is extremely rare. but with a difference. but on the somewhat Here the dominant chord. If \c of cadence. we have a " cadential 9. \c. much trouble in finding his roots. as will be seen later. A cadence the last chord of which is. and Nc. Haydn. 177. that is. unless it be dotted. as here. is made with the chords V-I. the root . Our next example. When two figures The B in the bass would be figured \' note. ^precedes V. The second inversion by far the oftenest met with is that of the tonic chord (I^). [Chap. Eb: IV If V I We have only marked the \% roots for the last chords here. student has already learned (§ 117. 176. 113. and for suspensions. they need But by their means the student will save himself modification. not . as here. roots.J Inversions of Triads. and the following chord may be either an inversion. full plagal cadence. It is not a. is The second root position. If we look at the last two examples. *^ ' . unless it has been also preceded by a chord on the same bass note. Last Judgment.^ Ex. VI. chord on the same bass note as well as are passing We by another Mendelssohn. inversion of the subdominant (IVf.) like mostly used cadentially. . * Ex. Spohr. In this When move by case. This is always necessary in a cadential A second inversion. As the bass note is now the tonic rf the key. as in Ex. Bx. * St. when followed by another chord on the same bass note must always be on a strong accent. or a root position." where the 4 chords are not cadential. next give an example of \c not followed 180. 116. the bass should step. The Bs in the treble and tenor followed by I. 67 as final cadences. it is clear that the cadence will now have a plagal character (§117). that of the tonic. 118 below.Chap. 179. Paul. 114. . ' ^ a second inversion is nortSed cadentially. In this example. instead of marking the shall see that we have figured the bass. in each case the 4 chord beat. 115. as in the well-known Sicilian Mariners' ' ' Hymn. we comes upon an accented 6. because IV is not in 181. * Here the second inversions of IV are preceded. and the progression will be IVc-I. notes (§ 316). 1 ^iji. the 9 chord may occur either on an accented or an unac- cented beat. t68 Harmony. [Chap. VI. This inversion of IV is less often used than \c, and it is rare to find it followed by a chord on the next degree of the scale. 182. It was said in § 173 that the fourth above the bass had the effect of a dissonance. The general tendency of a dissonance is to ^ fall one degree. When, therefore, a 4. ^ chord , is followed by to ^. a on the same bass note, the thould fall to 3 and the 6 be seen that this is the progression of the parts in Exs. 112, It impossible also for the 4 to rise to 5, in which 113, and 116. case 6 falls to 3 ii S^ It will Ex. 117. The student is advised for the but this is in general less good. present to adhere strictly to the rule just given. 183. The second inversion of the dominant chord (Vr,) is not uncommon, as in the following passage Bach. " Komm, Gott, Schopfcr." : Ex. 118. ''^s the bass note of this second*' mvefsion is the supertonic, V^ can never be used cadentially ; for V-ii does not form a cadence. Here therefore the bass should always move by step, as in this example. The only second inversions which can be followed by another chord on the same bass not^ are \c and IN c. 184. The second inversions of. secondary triads are very rare, and, like Nc, and for a similar reason, they cannot be used cadentially. We give a few examples of their employment. Ex. 119. Schumann. Parad.ise and the Peri. Here, at (iiir). seen the second inversion of the supertonic chord preceded by the first inversion (ii^) of the same chord, and the bass falls a step to the dominant. is * It is Chap. VI.] Inversions of Triads. 69 185. The triad on the mediant is less often met with than the other chords of the major key, and its second inversion (\\\c, ) The following is one of the best examples of is exceedingly rare. its use W. S. Bennett: Part Song, " Come, live with me." Ex. 120. As left in the preceding examples, we have marked is the V chord with *. Note that here the bass of the chord step. approached and by 186. In the following example of the second inversion of the submediant chord (vi^:) Ex. 121i ^ Mendelssohn. Lieder, No. 4. the bass will also is again approached and left by step. In this passage be seen a cadential ^ (Ic V). 187. The second inversion of the diminished triad on the leading note (yi\°c,) is only very rarely to be found in four-part harmony. /* Bach. Cantata, " Dazu ist erschienen." Ez,122. ^^^ from a Church Cantata by Bach, and it gives an In the second illustration of the freedom of his part-writing. bar will be seen consecutive fifths between the treble and tenor. But here the treble note (A I?) is not a note of the harmony, but an anticipation of a note of the next chord, as will be explained Our extract is later (§ 325). The student is advised not to imitate such licences until he has acquired the skill in part-writing which Bach possessed. The progression of the alto at the end of this example illustrates taking the leading note Bach's partiality (referred to in § 100) for down to the fifth of a chord in a cadence. 70 Harmony. [Chap. VI. 188. In consequence of the dissonant effect of the fourth with the bass, it is necessary to be careful in approaching, as well as in quitting a . chord. The rules for approaching this chord, which are deduced from the practice of the great masters, and 'which are all illustrated by the examples above given are the following I. A second inversion may be approached either by leap, as in Ex. 113, or by step, as in Exs. 112, 120, 121, from the root pqsidon of another chord. II. It may be approached by leap, as in Exs. 116, 119, from knother positio n of the same chord. IT. It may be approached by step {but not by leap) from the inversion of ano ther chord, as in Exs. 115, 118. ^{^l^i^fr'TTraa.y be preceded by a different chord upon the same bass note, as in Ex. 114. 189. No less important than the rules just given are those These rules are regulate. the leaving a second inversion. 'three in number I. The bass of any second inversion may move by step of a tone (Exs. 115, 118, 119, 120,) or a semitone (Exs. 121, 122,) upwards or downwards ; and the following chord may be either in root position (Exs. 118, 119, 120,) or in an inversion (Exs. which 115, 121, 122). i_ II. The second IVV , inversions of the tonic ) and subdominant •fehords only ( Ic, may be same bass note or its followed by another chord on the octave (Exs. 112, 113, 114, 116, 117), it when the 5 must be on a strong accent, unless has been also preceded by a chord on the same bass note.* III. The bass of a second inversion may, while the harmony remains unchanged, leap to another note of the same chord,, provided that, when the harmony changes, it returns either to_ * ^*.In a cadence on the first in triple time, Ic is often found on the second, instead of beat of the bar, as in ' God save the King.' Bb: ii* If V I The not really broken here. Every bar in music contains an accented and an unaccented part ; in duple time each part is of equal length ( in triple time the accented part is double the length of the ) ; rule given in the text is ^^ unaccented (^ J' °°' J «!)• "^^^ second beat therefore accented beat, though less strongly accented than the first. is part of the Chap. VI.] Inversions of Triads. ; 71 e.g. its former note, or to the next note above or below {a) Good. (*) Good. (<:) Good, {d) Notj Ex. 123. F: Ifj: it is V Ic IV* \c IV not good for it to leap.* 190. The best note to double in a second inversion is not the root of the chord, even when this is a primary note ; because the root is in this position dissonant to the bass (§ 173). The ha-;<; nntp itsplf is almost always the best to dou ble: but it is possible, and occasionally even advisable, to double either the In the extremely rare iiif, (see third or the root of the chord. Ex. 120,) the bass note, being the leading note, must of course not be doubled; here the third of the chord (the primary note,) is, as in other positions of the same chord, the best to double. 191. There is no point which gives the beginner so much trouble when he attempts to harmonize a melody as the management of second inversions. Before proceeding further, therefore, we give a few short exercises on these alone, restricting ourselves In Other cases to the primary triads. The . of the secondary triads had better be avoided by beginners altogether. Each of the following exercises consists of only three chords, of which we give the second. The student will see by its position whether the given chord is the first or second of the bar. He must carefully attend to all the rules in §§ 188, 189. Each exercise should be worked in two different ways. the I. Precede each of the following chords by another position of same chord, and treat it cadentially (§177.) Mark the roots. (#) , ( X^) , .M id) , * An apparent, but not real, exception to this rule is when the bass of a ? chord rises a seventh to the octave of the note below ; e.g. instead 6 4 4 2 72 Harmony. [Chap. VI. II. Precede each of the preceding chords by the root position of a different chord, and follow as before. III. Precede each of these chords by the inversion of a chord, following as before. differejit IV. Precede each of the following chords by a different chord, either in root position or in an inversion ; and follow each by a chord upon a different bass note. e exercises above a ine 192. The student shTSHId now write We strongly advise him in all cases to mark given figured bass. his roots on a blank staff under the bass, that he may see the harmonic progressions clearly a thorough understanding of these will be of great assistance to him when, at the end of this chapter, The he has to choose his own chords for harmonizing melodies. method of finding the roots has been explained in § 174. In the first two of the following exercises, the treble, as well as the bass, is given. ; Add Alto and Tenor parts to the following Treble and Bass. Bass only given. (VII) Add the three upper parts. Inversions of Triads. 6666 i i 66 665 4 3 N.B. —This progressife^ second inversion show the only case in which one can be ftmbwedArfeanother. The student must take care not MrtJJJCluced to to write consecutive fourths above XSS bass. (XIV) 3 6 6 6 6 6 is written to illustrate the use of two Observe that here, as in Exercise successive second inversions. XIII, they are on adjacent degrees of the scale. The following exercise {XVI 74 (XVII) Harmony. [Chap. VI, S 6 (XVIII) Double Chant. 8 6 6 6 6 6 6 6 4 (XIX) Double Chant. is an example of a Double Chant per rede et "forwards and backwards." This is a chant in which the third phrase is the iirst read backwards, and the fourth is the second read backwards. This is the case, not only with the bass, but with all the upper parts. The working of this exercise will probably be found less difficult than the student may The following retro, that is anticipate. (XX) Double Chant {per recte et retro). (XXI) Hymn Tune. 6 6 e 6 6 6 6 6 6 4 5 3 (XXII) Hymn Tune. 3 6 6 4 6 6 4 5 3 The employment of (XXIII) following tune is written to illustrate the occasional the second inversions of secondary triads. Hymn Tune. f^rr (i -L^-^-ir 6 6 r i mfr- 'r f' ' - " 75 (XXIV) Hymn Tune. .Chap. VI.] Inversions of Triads. but ii^-iii5 is bad. even when the bass moves The only case in which there is no note by step (§ 109). 195. for all the intermediate notes . 124 {a) the student will see that when inversions are combined with root positions. and take the same melody which we there harmonized with only the root positions of primary triads. Ex. " A: first . course. of accented beat (§ 179). I VI we shall 201. using inversions as well as root positions. When the root proceeds by step downwards (§ 149). is [Chap. \c V The inversions of secondary triads (ii^. In deciding whether to use a root position or an inversion of a chord. and should be avoided. necessary that the chord should be on an tonic. 197. The same as before we and the two last chords must evidently be the therefore mark the roots below them. ) should not be approached or quitted by a larger leap in the bass than a This rule does not third. the eifect of a large leap being weak. iii^. in approaching a cadence. an inversion. except in the downward progression from the mediant . the third chord from the it is always best to use \c rather than I or \b. advise him to compare the new harmony. 178). common to two chords is when the roots are on adjacent degrees of the scale. vi.) is derived from the dominant one of the primary chords. except in the caden- (§§ 177. chord by We chord. 196. it is possible to have a note common to two chords. a stationary bass tial undesirable. both chords being in root The first chord may be either in root position or in position. 84 (§ 126). But have a choice (§ 144). iii^-ii^ is good. (§ 261. 199. with that previously given in Ex. as we shall see later. 126. In general. If. vii5. end be the It is. apply to vii°i^. formula. and the natural flow of the other voices. 200. We now fulfil the promise given in Chapter IV (§ 127). By referring to Ex.76 Harmony. the second of the two chords should always be inverted. This will be seen when we harmonize a short melody presently in general a smoothly moving bass is preferable to one with too — many leaps. one should be largely guided by the resulting movement of the bass. It would be easy to write a melody which would offer more variety of harmony than this but the comparison of the two results will be instructive to the student. which. except in the progressions vi-V and V-IV. now allowing ourselves the employment of the whole of the diatonic triads of the key. 198. ) derived from the dominant. we shall choose vi. 128. is (as will be seen later. 129. iii. E is not could take I again. or vii°^ for the second chord . but the root of vii°. instead that the bass is of leaping. as it contains both the fourth and seventh degrees of the scale. 3456 I Ex. though it is a primary chord . C. mediant chord would be bad here. it always. but. the third of V. though not one of the three primary chords. clearly defines the key (§ 112). as before. now in the first inversion moving by — . VI. I -r viW lb ? The fourth note. the latter. and. I ^ J U yi ? ? Observe that in the last chord we have doubled a secondary . forms part of I. £z. taking the 202. (lb). 234 J -1- Ex. For our third chord IV would be bad here. while IV^ would make a large leap from one inversion to another. in root position it would give hidden fifths with outer parts. which vi would be possible here but far the best is mostly undesirable progression would be to take I again. as before.Chap. 127. to a note of vi. as giving the stronger progression. to obtain more variety. and the fifth of iii. show as many chords as we can. A: I vii°* ? chord is A further advantage of choosing this step.] Inversw^s of Triads. in root position . Our We let root position. can now not only be. although it could be followed by vi (§ 150). when it follows the tonic chord. V. G. the student ask himself why. or vi. because the fifth note. The last would not be very good. because it is best to begin a piece by defining the key by means It is therefore better here either to take of its primary chords. 77 The second note. as before. bass Evidently the must fall . 203. [Chap. we. XXV. A: It will I vii°* lb 'vi Vb \ ii (IV) V I harmonization of the melody is much more pleasant to listen to. instead ol a primary note. and less stiff. thsm that in Ex. he will now be ready to begin to harmonize the following melodies. to obtain a smoother motion of the alto. To assist him. we have only the shall learn later that y\\°b is very seldom seventh to fill up. 204. to avoid bad hidden Here I will be better than y\b. the student must select his own positions for the chords. well as primary triads as that we have mixed inversions with be felt at once that this root positions. and mark the roots. fifths. but not the positions of the chords. Tenor. and Bass below the following melodies. student must decide for himself whether he will take the chord in root position or in one of the inversions. In Exs. have. VI. with the alternative chords for the seventh note. It would be quite possible to take iii for the fifth chord but the same considerations of smoothness cause us to select Nb. marked the roots. 130.) that a numeral with no letter after it indicates the root The position of a chord does not apply to these two exercises. If the student has thoroughly grasped the instructions given in this chapter. ? V I already know our last two chords. Obviously the leading note as the bass will then move by step. The reason is not so much that we have used secondary as 84. and it now therefore give the whole matters not which we choose. Add Alto. in the bass must rise in the sixth chord. in the first two. melody. The rule (§ 165. XXVI (XXV) . 131. 456789 V* I Ex. As we We V We Ex.78 Harmony. Figure the basses. good before . but ii and IV are equally good here. 79 (XXVI) (XXVIII) 1 j'j'i . VI.Chap.1 r 1 .] iNyERSIONS OF TRIADS. from below. it will be needful to say something about other and older forms of the scale. he will see that the only note which differs in the two scales is the seventh. CHAPTER THE MINOR KEY 206. which. 2 1 that the primary triads on the tonic and subdominant of a minor key are minor. ITS DIATONIC TRIADS. and before speaking of 207. . Ez. is known as the Harmonic Minor of comparatively modern introducit. and of the chords made from it. we have the form of minor scale seen in Ex. If we arrange them in order. notes. 132. given in Ex. harmonic minor scale and observes the intervals between each note. while. 5. we shall have the old ' ' '^olian scale. the result being. Scale. for melodic than for harmonic purposes. from the fact that the harmonies chiefly used in modem music are made from it. . keys. It was said in § 45 that many other diatonic scales besides those we have already given were formerly in use. instead of a semitone. ' now speaking. and using only natural If we begin with the note A. and not a semitone below the tonic the ^olian scale had in fact no leading note. which are still employed. AND THEIR INVERSIONS. VII. as seen in Ex. the three primary triads of the minor key contain all the notes of the scale. of which A we are scale. treating in Chapter II (§§ 42-44.) of major it was pointed out that the difference between that in the latter the mediant and submediant are a semitone lower than the former. . [Chap. . because of the necessity of a leading note. This subject will be treated in Appendix of this volume . in the music of the present day. which in the ^olian scale is a tone.8o Harmony. though more often. As with the major key (§ 40). 5 (§9). When and minor the two is. all that need be said here is. But it was soon felt that no satisfactory cadence could be obtained if the tonic were approached by a tone. VII. 133. the triad on the dominant is the same as in a major key. This form of scale is tion . that the old ecclesiastical scales. as a tonic. If the student compares this scale with the # * Ex. were made by taking each note of the excepting B natural. and augmented intervals were forbidden. as in the following passage from Handel's 7th Suite de Pieces. 208. reached by a leap. * See the article Musicians. The Dorian mode. But from F i) to G ^ in the now altered scale is an interval of an augmented second. and the G j| being felt indispensable. 132 This will be seen in being generally retained in descending.Chap. 135. the form of scale last given is chiefly used in ascending passages. the sharp never appeared in the key-signature. 81 It was therefore understood that in approaching a cadence the seventh of the scale was to be sharpened. . Suite de Pieces. 134. 7. No. if he plays the scale of D on white keys only and its seventh. which began on D. Occasionally the form of the scale with the sharpened sixth and seventh is found a"lso in descending passages. Handbl. however. As a rfatter of history. £z. as well as a minor third. 136. though in old music the sharp was not always marked.] Triads of the Minor Key. though (as will be seen later) harmonic purposes. As the necessity of the interval of a semitone between the seventh of the scale and the tonic is not felt in descending. 2. like that of the ^olian mode. the Here another of the old modes was sixth note of the scale. Mozart. This not being allowed. as being difficult to sing. as the student will see. C minor. in approaching the tonic. had a major sixth from the tonic. «—*°- P in use for melodic. but would be indicated by an accidental. -^ Ex. Concerto in C minor. made available. it became necessary also to sharpen the F. could be sharpened This gave another form of minor scale. taken from the finale of Mozart's which is still rarely for concerto in Ex. VII. This alteration changes the ^olian into our harmonic minor scale.* As the seventh was not invariably sharpened. the two following scales. ' Musica Ficta ' in Grove's 'Dictionary of Music and . the older ^olian form given in Ex. this resulf was not The old music was mostly written for voices.' Vol. that if the sharp were marked in the signature. Op. 134) music of the eighteenth century. 138. which in the minor key is sharpened to form a leading note. Harmony. we shall see that the only note which differs in the two scales is G. -^t^ 210.^Eolian scale (§ 207). 5. is very common in instrumental music. VII. and In the therefore a minor third between tonic and mediant. Sonata. the ^olian and Dorian forms of in more the scale wete the oftenest used. .82 209. with sharps rising by fifths and flats falling by fifths. and not infreWe give one example. that has been explained in Chapter II. and in the modern harmonic minor. ^ It must — . 135 above modern compositions the harmonic form. A minor. it would entirely disorganize the regular arrangement of key-signatures. for instance would be # and of C minor while D minor would be even more confusing- be clearly understood that the leading note of the minor key. 4 (§ 9). with its augmented second. . 'j~ -*=- P with the scale of C major given in Ex.* The point in which all these scales agree is that they all have a semitone between the second and third degrees. quent even in vocal music. (Ex. as they are really older forms. 137. the and the first is that the seventh is not invariably sharpened second. No. In speaking above of the . and by no means merely arbitrary alterations. Beethoven.) the ^olian (Ex. If we compare the harmonic form of the scale of A minor — Ex. * Some writers call these forms of the minor scale "arbitrary"' an unfortunate word. 2. the leading note is also always written There are two good reasons for this with an accidental. as in Ex. and more cogent is. The same was true of the leading note of the Dorian scale (§ 137). We have therefore three different forms of minor scale.) and the Dorian the last two are generally described as Melodic minor scales. . it was said that the sharp before the leading note never appeared in the key-signature. the Harmonic (Ex. but was either implied or written as an accidental. 132. -. [Chap. Ex. The signature of . C G f f A E B FJ D Bb D A E B Fit r-f%l| m P Eb Ab Cf Db GJ Gb Bb :^^i& i i Eb DJ AJf CJ Cb Ab It will be be seen that the extreme niinor keys. 211. Major keys. the tonic of a major key is always a minor third above the tonic of its relative minor.) from any neighbouring key.Chap. conversely. retain the In Germany the term " parallel " is used instead of " relative. The dominant chord in root-position has always either a or a i[. is not a chromatic note . * There is no harmonic relation between the two keys . 139. minor keys. * and the tonic of a minor key is always a minor third below the tonic of its relative major. except when it is itself the bass note. VII. without a figure at its jf side (§ 164. 25 (§ 53). have enharmonic equivalents. 83 although it has an accidental before it.] . like the major. as we have already seen ( § 42) between a major key and its tonic midbr. . it belongs to the diatonic scale. As the G K in Ex. such relation is found. it always requires to be indicated by an accidental in the figured bass of a minor key. as the leading note is not written in the signature. it is evident that the keys of A minor and C major must have the same signature. Relative Major keys. It must also be noticed that. and is not borrowed (§ 35. though the German equivalent is perhaps preferable. while the augmented triad (§ 214) in root position will be figured || 5 or t) 5. we now give their relative Ex. 1 38 is always written as an accidental. while. A major and a minor key which have the same signature are called Relative major and minor keys . Triads of the Minor Key. Signature." usual English term. Signature. minors . according to the key. Relative minor keys. The major key -signatures were given in Ex. We .) below it. Observe that the key is now indicated by a small. 214. Mendelssohn. letter. if we place a diatonic triad mbove each degree. 62 (§89). in the third and sixth notes of the scale. not by a capital. . that we shall obtain quite a different series of chords from those of the major key. c: 1 P 3g= ii° ^^ iv ~g ij > III' If we compare this series of triads Ex. Like the diminished triad on the leading note of the major key. instead of a perfect fifth. VII. •[Chap. 5. 212. or (which comes to the same thing) three flats fewer. because it has a major third (§ 41). At {a) is seen a chord of a kind not previously met with. It contains a major third. By examining the table in Ex. It is called an AUGMENTED TRIAD. The diminished triad on the supertonic is however more frequently to be found in this form. to be referred to later. the augmented fifth is shown by the acute accent (') placed after and above the numeral. 140. and is therefore not a common chord. Toccata in F. It is obvious that taking away a sharp and putting on a flat produce the same result that of lowering a note by a semitone. as well as the leading note. the corresponding chord in the minor key is rare in its root position. 213. we shall see that the only two which are identical are V and vii°. The tonic and subdominant now take a minor chord above them. than its tonic minor . owing to the difference form of the scale given in Ex. as in the following examples. the diatonic triads of the minor key are made from the harmonic But. major and a minor scale which begin upon the same key-note are called Tonic Major and Minor scales. the student will see that every major scale has three sharps more. and an augmented. St. now bears a diminished triad. we put a capital numeral to this chord. while the supertonic. A — («) Ex. 215. at *. 139. and is only found on the mediant of the minor key. With occasional exceptions. In marking our roots. V VI vii° with those of the major key given in Ex. and the keys to which these scales belong are called Tonic Major and Minor keys. and the submediant a major one .84 Harmony. we find. because every other triad contains either the third or the sixth of the scale.. Paul. 141i Bach. and conversely that every minor key has three flats more or three sharps fewer than its tonic major. VII. It is best followed. It was said in § 208 that the Dorian mode had a major sixth as well as a minor third. followed the first time by the incomplete chord of \\\°b. 143." Evidently it gives a major. — ! ^^ *i Handel. and followed by the chord of the dominant seventh. Here the major chord on the subdominant is preceded by \b.] Triads of the Minor Key. fourth (III'-VI). in whose time the employment of the Dorian mode was still common. like the mediant chord in the major key the root rising a (§ 150. Messiah. Similarly. it is called the " Dorian sixth. Thus in old church music we often find C minor with only B fe and Eb in the signature. . 218 Another very fine instance of the use of the Dorian sixth is found in Handel' s ' ' Behold the Lamb ^ of God. Here we see at * the major chord on the subdominant. in the Dorian mode the A would be natural. When this sikth is used in a minor key. with the third omitted. that this is a very frequent resolution for a discord. ' ' in the 'Messiah. chord on the subdominant. In marking * This use of the Dorian mode is the explanation of the fact that in music of the seventeenth and the first part of the eighteenth centuries the signatures of minor lieys generally contain one flat less than they would have on our present plan. 1 I I *. Bach's great organ fugue in minor (Dorian. 217. the effect of the dissonance being rather harsh.Chap.) has no Bb in the D signature.) by the chord of the submediant. The augmented triad on the mediant is not very frequently employed. Ez. instead of a minor. when we have to treat of dissonant chords. This applies also to the first inversion of the same chord (III'/J-VI). it happens that both are here in the key of A minor. 216. Such a chord is very often found in the works of Bach and Handel. and the second time by i. 8S Though both these extracts are from pieces in major keys.* We give a few characteristic examples. Handel. I Israel in Egypt. It will be seen that in each case the chord following the dissonance has a root a fourth above that of the dissonance itself We shall find later. f: \yc i VI ib IV \c V In this passage the roots are marked. It is therefore better avoided. =S= 221. The following example by Bach shows the chord in question. ^^Sk^Aj. which then. These examples are given because of their historical importance. VII. Our feeling of tonality is so much more definite than that which existed 150 years ago. More rare than the employment of the major (Dorian. or the converse. 220. An interesting example of the peculiar effect of its employment will be found in the following passage The Bride. We often meet with the progression from dominant to submediant. 144. Ex. not iv.. Cantata " Ich bin ein guter Hirt. as below. becomes identical with the chord (ii." Ex. and are not intended for the imitation of the student. at the time the passage just quoted was written. . 146. The general rules for the progression of parts and the doubling of notes already given apply equally to the minor and to the major key but there is one very important rule in addition.86 Harmony. . 145. and it is especially unpleasant when the subdominant chord comes between the tonic and the dominant.) in the major key. 219.. instead of being a diminished triad (§ 213). it must of course be indicated IV. the roots of passages containing this chord. [Chap. ^^^^W 3 Ex. Bach. In modern music the use of this chord is much rarer. that the major sixth of the scale produces a disturbing effect on the key unless very carefully managed. to illustrate what was said in the last paragraph. which concerns the minor key exclusively.J1^^ 1^ The last chord of this example will be explained presently (§229). sixth of the scale in the subdominant chord is its use as the fifth of the supertonic chord. as at (/) (/) {s) In the (^). which is the case here. Ex. will equally The rule. 147. (a) {b) {c) (d). ^ ^f^ iKt 4II ^ : be needful to double the third in the second chord. key like those of The . is this Whenever in a minor key the chord of the dominant precedes or follows than of the submediant. The only right way is to double the third same way. iv. In a minor key the submediant is seldom a good note to double . we shall have the same bad progressions 'shown in Ex. P n it 53 A. 147. the interval of the augmented second. If we double the root in the submediant chord of a minor key when it is followed by the dominant chord.l Triads of the Minor Key. It will be noticed that the submediant is a secondary note of the key. which is not At {d ) the treble and alto parts cross. 87 from submediant to dominant. The reason is that. we shall find ourselves in difficulties. which must be most > 222. and besides this we still have distinctly the effect of fifths and octaves as at {a). and care must be taken to avoid. if the dominant chord comes first. We evidently cannot fifths . carefully observed. the root is the only note of the dominant chord to which in most cases the submediant can go . because an augmented interval in the melody is seldom good unless both the notes belong to the same harmony. as we saw in Ex. instead of the root in the submediant chord. and when it occurs in any chord (ii°. 147. it should not be doubled at all.Chap. and if this note be doubled. as at {/). for this gives consecutive and octaves neither can we avoid these as at {b') or {c). Thus the following progression at 223. and that the tonic the third of the submediant chord is a primary note (§97). wherever possible. or VI) which is followed by the dominant chord. VII. — — general rules given in the sixth chapter (§§ 169-171) are still to be observed. can be used in their first inversion. bad. proceed as at (a). the third {and not the root) must be doubled] in the submediant chord. All the diatonic triads of the minor the major. as in the following passage 225. 132. 150. The following is an excellent example of the employment of this chord. But in modem music it is not unusual to find in the melody the fall of a diminished seventh from submediant to leading-note. The student can always avoid the augmented second. ^ ^ i. ^^^^ % Beethoven. . n <n 2 24. descending by step from tonic to submediant other chords of which the seventh degree of the scale is one of the notes. '^ In addition to the first inversions of all the triads given in is one first inversion to be met with under special conditions with which we have not yet made acquaintance. 149. to a dominant discord in the second inversion. bear a chord either in root position or in an inversion. VII. lo. like many others. Mendelssohn. Overture. in tions that is. there Ex. [Chap. Op. 148. Ex.88 (a) is Harmony. * This rule. § 213. T. is given for the guidance of the beginner. 301 (Chapter XII). instead of a tone. — — Ex. If the bass moves by step from tonic down to submediant it sometimes takes the minor seventh of the scale on its way instead of the leading note . if he will remember the following rule: Whenever in a minor key the submediant and leading-note are found in two adjacent chords. Ruy Bias. This minor seventh is evidently a survival of the ^olian though in modern music its employment It is sometimes also found. and in this case only (but not in the reverse direction) the minor seventh is allowed to bear a first inversion. No. and should be corrected as at (^). as in Ex. faulty. however. they must not be both in the same voice. This chord is only allowed when preceded by the tonic in the bass and also followed by the note below . and should be strictly observed in the early stages of his work. It will be seen that on its second occurence the bass descends a semitone. under the same restricis restricted. Sonata. ^ _ ^ scale seen in Ex. either of these notes may. is the fifth of the chord at (3) it is the root. * * This example will require a little explanation. at (c) it. shows the minor seventh of the scale in all the triads of which it forms a part. which consists. Gounod . At (a) the DJ). At * there is the first inversion of a major chord (instead of an augmented 226. interesting. Bach. ) The Ex. subdominant and dominant chords are by far the most common. the minor seventh of the key. we consider only the nature of the intervals above them. and at (f) the third. 89 Here is a descending series of chords of the sixth over a " pedal bass. Book 2. Prelude 20. All the triads of the minor key can be used in their second inversion . it is clear that the three chords at (a) the shown in our last example will be indicated thus chord will be \\\b. and. as we did with the major key but a few of the rarer second inversions will be The pedal note. following interesting passage. but. those of the tonic. here proves the later. now takes a major common chord above it. it is not reckoned as a note of tTie chords in marking the roots. and if B were a tonic the C and A in the first and third chords would be sharp. will be vb (not Vi5). will be learned . 228. B. Das Wohltemperirte Clavier. As in marking our roots. as in the major. It is needless to give a complete set of examples. on the mediant.Chap. VII. does not form a note of all. 227. ). ." that is. a continued dominant (See Chapter XX). 101. Mireille. As the pedal note. of the chords placed above it. key to be E minor . Ex. as is seen. The bVII shows that the usual seventh of the scale (the leading-note) has been lowered a semitone. but only of some.] Triads of the Minor Key. B. at {b) it will be yjWb . The passage also gives a good example of a descending sequence. like the last example. 152. : — . triad. of a series of sixths over a dominant pedal. for (as only the dominant and tonic can be used as pedals. It must be pointed out that when two or more notes of a chord are taken in arpeggio. 153. in conformity to the The D ji and C|| in the bass are both first rule given in § 189. the major third in the final chord of a minor movement was called the Tierce de Pzcardie. In setting the basses. Care must be taken to avoid augmented intervals in any voice . Occasionally also the third is omitted altogether. these are much more numerous than in a major key. and a major tonic chord was substituted for a minor to conclude the piece. especially in church music and. produce is A second inversions of the triad on the leading note. not i. and the F and that above C % just as if the upper notes were played The chords marked * are therefore the together as quavers. even when that movement is The effect of such a close was considered written in a minor key. as in the following examples ' ' . we have altogether avoided the " Dorian sixth" (§ 217). " It is still not infrequently emplfiyed. Ex. In old music it is comparatively rare to find a minor chord at the end of a movement. and the piece ends with a bare fifth. VII. and their use will be explained later.9° Harmony. It will be seen that the bass of each second inversion moves by step. : Mozart. Requiem. the major third is not considered as a chromatic note in the minor key. and have only used the minor seventh as the bass of a first inversion. unsatisfactory. this passage the GJf and B form the chord above D. 164 230. 145. or Picardy third. The student should now work the following exercises. in this connection only. chromatic notes in the key. . ' d^P^*d=J=J: Ex. and of the common chord on the submediant. For some reason which it is impossible to ascertain with certainty.* The student will see an excellent example of the employment of this chord in the extract from Bach given in Ex. the harmony they In the same as if they had been sounded together. 229. * The root of this chord must of course be marked I. We advise the adoption of the same plan in harmonizing the given melodies. [Chap. as is so often the case in pianoforte music. Chap. (I) Add (II) Alto and Tenor. )t 6 J6 ' 6 6 1 ff « Bass only given. 9» Treble and Bass given.] Triads of the Minor Key. VII. J6 (IV) 6 S 6 S flS 6 S . (Ill) Add three upper parts. 92 (XIII) Harmony. 6 B 55 6 6 6 J 6 4 6 4 6 11 (XIV) ^1^ f> i i -p I ^ r' \ I 86 6 ^^ 6 =1=1?: ti5 a 6 6 4 r=P"rT 6 6 4 a 6 a 6 FL 6 fl J 4 11 (XV) 3 a 6 6 ]] 96 4 6 4 5 S 6 6 t #6 «5 6 5 t 4 « (XVII) Double Chant. vn. . 56 f6 6 66f 6 6 66 t t (XVIII) Double Chant. 5 f6 6 6 f {5 (XIX) Double Chant. [Chap. ] Triads of the Minor Key. VII.Cnap. d 4 r I r f I '' 6 -! 8 I 6 6 J6 =l=t '6 '=*=^6 6 Jf6 a=t= )(6 it 5 6 "e 6 6 4 i 6 4 (XXII) Hymn Tune. ISjSt . 93 S 6 » P J I 6 6 « 6 6 4 6 4 5$ t (XXI) Hymn Tune. From this it will be seen that the dominant chord of a key is not fitted for concluding a piece. combinations of three notes made by placing two thirds one above another. If the student will take a simple progression of the diatonic triads with which he is already acquainted. and the dominant a chord of unrest. Hitherto all the chords we have used have been triads. he will find that the character of tonic and dominant harmony is quite different. [Chap. The feeling of finality is gone one requires something else to succeed . C: It will I V I W IV vii°* I V I V I be felt that the effect of the alternation of tonic and dominant chords ending with a tonic chord is one of completeness we require nothing to follow. but also the generator (§ 36.94 Harmony. and the most important. but if {b') is played after {a). adding the chord at {a). for instance. but that. play on the piano the following passage. note'). that is. the reposeful feeling is restored. Now let him play the passage again. vni. 231. that on the dominant is the most frequently used. that is. {a) (b) Ex. a perfect fifth. and a minor seventh from the generator. P In this chord the dominant is not only the root. it is evident that this third will be a seventh from the root. 16S. as compared with the tonic chord. 232. Such a chord will be called a Chord of the Seventh. CHAPTER . Let him. In their relation to one another we may say of these two chords what was said (§ 17) of consonance and dissonance that the tonic chord is a chord of rest. We here meet for the first time with a " fundamental discord. its effect is one of incompleteness. Of all the possible chords of the seventh. a discord composed of the harmonics ' ' . It will be necessary as we proceed to consider it in both these aspects. If we place another third on the top of a triad. stopping at the first double bar. THE CHORD OF THE DOMINANT SEVENTH. — . It is very important that the student should thoroughly grasp the fact that the intervals of this chord are a major third. and will observe the mental effect which they produce. VIII. The chord of the seventh is simply figured 7. would become an augmented fourth (§ 30). 233. VIII. below the V showing the dominant chord. 156. taken in a different position. In the present case the third of the chord. being the leading note. the seventh would fall a But if the chord were instead of only a semitone. rises a second.] Chord of the Dominant Seventh. This will be seen in the treble and alto parts of the last two chords of the * See Appendix B. thus V7. which was before to some extent noticeable It is no longer possible to end on it. as at (3) above. being now inverted. and two notes forming an augmented interval have a tendency to diverge. the interval of the diminished fifth. but every such discord always contains as its thirds next above the generator the notes which make the three intervals just specified. 234. namely the diminished fifth between the third and the seventh. C: I V I I^ IV vii°i I V7 I the feeling of unrest becomes intensified. and therefore requires resolution that is. P C minor.Chap. The general rule governing the progression that two notes forming a diminished interval have a tendency to approach one another. 95 of the fundamental tone or generator. because the interval of a seventh is always a dissonance (§ 28).'^ The upper notes of a fundamental discord are in some cases variable . the fifth and third being implied (as in the common chord) unless one of these notes requires In indicating our roots. which determines the resolution of the discord. If the key of the piece were tone. and the seyenth falls a second. to be followed by a consonance. we shall see that in addition to the seventh from the root there is another dissonance in the chord. to E V. If we examine the chord of the seventh given in § 232. and the seventh were below the third. If we substitute for one of the dominant chords of the passage in § 231 a chord of the dominant seventh (*) — Hx. — P It is this interval that to is. the way in which these two notes shall move with regard is one another. . we add a 7 after and an accidental. Let us now take the chord of the dominant seventh. because the progression of both notes is fixed.. which the student cannot too thoroughly impress upon his memory. we shall either get consecutive octaves or unisons. [Chap. and if one of them appear in two voices. the third ing must rise one degree. passage in § 233. and in this case the root is doubled.l . resolve it on the tonic chord its most usual resolution. — and Ex. if both move correctly. Neither the third nor the seventh of the chord can be doubled. 236. or else one of them must move wrongly. The important general rule. and the seventh must fall one degree. is the followIn resolving the chord of the dominant seventh.96 Harmony. all its 235. The few exceptions to this rule will be explained later in this : — chapter. The chord of the seventh is very frequently found with four notes present . VIII. but the fifth is sometimes omitted. 97 237. It is not uncommon for another note of the chord to be interposed between the seventh either the root or the fifth and its resolution. Messiah. no account is taken of passing notes. iv \c ivb Here the seventh the student. To assist we have both figured the bass. the seventh falls to the fifth of the chord. the A in the alto is an accented passing note. Ex. which at that moment changes from root-position to first inversion. these being what are called "unessential discords.g ^3r ^^k . ^m ^ ^ Webeh. ^^^r e£e =1= Handel. The 4 at the third crotchet of the same bar is a suspension.Chap. invariably requires an accidental. In a minor key. as will be explained Note particularly the figuring of the chord of in Chapter X. it is always needful to mark the third of the chord . as it appears to be a second inversion (ii°f ) . or suspensions. 238. 1 ^ harmony changes.168. falling to the third of the tonic chord on the change of harmony. In our next example. | »+_f. it With regard to the former. that is. In indicating the roots. notes which are not actually part of the harmony. must be said that the . to the tonic chord The following passage ^1 ^ when the J. as in the following examples — : ^ Handel. Euryanthe. returning. rises to the root of its own chord. and marked the roots. Samson. 169.] Chord of the Dominant Seventh. Ex. as in the preceding example. in the third quaver is not. VIII. — ' ' fcfe Ex. a discord that will be explained in Chapter XI. the dominant seventh at the first chord of the second bar. for the leading -note (as we have learned in the last chapter. 160. instead of the bass note. or V in F major. resolutions that the voice which had the seventh must always. If the student marks his roots (as we strongly recommend him to do. other resolutions are possible. after taking the root or fifth. In this progression. the third and seventh move. In this case the root rises one degree. as in the above examples. the dominant seventh of C major might be the same chord in C minor . [Chap. instead of an ornamental resolution. key . 158 . we shall have hidden octaves of a kind that are specially forbidden: (§ 76): ' ' Ez.) before he begins to work his exercises. therefore. 242. it is quite possible. of the tonic chord must here be mentioned. one degree. 239. here the sixth of the latter chord is doubled. instead of a fourth. for a chord of the seventh never resolves on its own root. If in this case. which is never met with in any other case. as usual. proceed to the third of the tonic chord. 241. in a chord of the dominant seventh. as furnishing an example. The most common of these is the resolution on the chord of the submediant. it must be pointed out that the great importance of the chord arises from the fact that. he can always instantly recognize an ornamental resolution of the seventh by the progression 'V7-V. shows at * the same progression of the seventh that we saw in Ex. Though rarely met with. the seventh must rise. In addition to the resolution of the dominant seventh on the tonic chord. the former upwards and the latter downwards . to proceed by similar motion to the same note. An exceptional resolution of the dominant seventh on ih& first inversion. instead of falling. instead of being as before . 162. otherwise. when followed by the tonic chord. while I in C major could also be IV in G major. ^m is it allowed for the root and the seventh. But it is evident that the two chords taken together cannot possibly belong to any other key than C major. Such resolutions as the above are called "ornamental It must particularly be remembered of the seventh. but it is also instructive. there is no resolution at all. or its octave. viii. by step. Under no circumstances whatever Ei.gS Harmony. 240. instead of the root -position. of the resolution of the chord on the second inversion of the tonic chord (§ 236). as before. Before proceeding to speak of other resolutions of the dominant seventh. but the fifth.l6l. it absolutely defines Either chord by itself might belong to more than one the key. the seventh fall one degree. in the first two quavers of the second bar. VIII. for this would make conHence a general rule Whenever -. Seasons.gecutive octaves with the bass. Here the seventh. and the root rises one degree to the third of the next chord. or we shall one degree (§236). instead of falling. the third This. to four-part harmony. 161. refers. of course. Ex. . 166. The following is a . as in the cases hitherto noticed. third of the submediant chord is a primary note of the key. 166.] Chord of the Dominant Seventh. If the fifth of the — : Ex. but still not so rare as to be exceptional. octaves between treble and tenor It is equally impossible to double the root. is on the first inversion of the chord of the sub- dominant. the third rises by step. common than the one just noticed. ^ g iu:irless rr^ J 243.^ i: ij. like of the latter chord must be doubled. r Note that the doubled our other rules. as before. as at {a) below . 164. 163. remains to be the root of the next chord . for this gives the worst kind of hidden those seen in Ex. as at (3) below. it will still be bad to double the fifth in the submediant chord. chord of the seventh be omitted and the root doubled. the fifth falls one degree. This resolution is of such frequent occurence that give one example of it here. we need only Ex. Ex. Haydn. 99 free to rise or fall {a). as at have consecutive fifths with the root. Another resolution of the chord of the dominant seventh. must fall to the third.Chap. the dominant seventh is resolved on the submediant chord. 3 245. it must of course be susceptible of three inversions. figuring of the various positions of a common chord. those of the As a chord of dominant seventh will cause him but little difficulty . similar reasoning. as the first — — therefore figured \. the full figuring being 5 all odd numbers. is the same inversion of the dominant triad. and we know from Rule II of § 174 that 6 is the root. the 3 being implied. as the sixth in this inversion the leading note. Evidently the seventh is the note below the root the inversion of a seventh being a second and must therefore be figured 5. 175. and compare the first two of them with the inversions of a is common chord.) that the root -position of a chord of the dominant seventh 7 figured 7. is By a. I the seventh contains three notes besides the root. this resolution : good example of Ex. Let us now take the three inversions of the same chord. 168. but in a minor key. with the seventh added. Schumann. </ *l [Chap. as the second inversion of a triad figured the second inversion of a dominant seventh would be figured the chord 4. however.. for this chord is simply a major common chord with an additional third above it. we will explain their figuring. We already know (§ 232. 167. The first inversion is first The inversion. and the way in which the roots If the student thoroughly understands the are to be marked. Let the student remember the simple rules for finding the root of a chord given in §§ 174. the 6 figured . and 3 is .loo Harmony. which always requires an . Before speaking of the treatment of each inversion separately. VIII. Paradise and the Peri. which has the third in the bass. as above is is superfluous. Ez. In a major key. as in the first inversion of a triad. 246. The first inversion of a triad is figured 6 . fifi 244. if below the root. The full figuring will therefore is be 4 2 . Yyd Vyd Vji I I I Observe that it is now possible to have the fifth in both chords. If it have a diminished fifth followed by a perfect fifth—a progression which is forbidden (§73) between the bass and an upper part. In marking the roots. This rule whatever be the position of the chord. and fifth are respectively a second. needful to give the (<5) full figuring. 168 would be figured 3 247. C'')- (^)_ (-^L V7* vi* vii Vyi y\b . is and figured j*t As 4 2 O'' 2) the leading note. the latter being preferable. VIII. the dissonant notes the third and seventh of the chord. the 6 the chord is usually omitted. If we look at the third inversion. we shall see that the root. fourth. because they are not both in root -position (§ 236). But if the fifth be above the root. 249.170. — in § 234. inversion. the root will rise one degree. a third inversion is shown by the addition o{ ' d' after the numeral. shown in Ex. key of C minor the chord at Ex. it is accidental (§ 210).). while the fifth of the first chord can either rise or fall a second. 168 (. and the fifth of the chord. the falls.. The seventh will fall. third. 169. which is now in the bass. Ex. may either rise or fall one degree. 248. as at ((/) to avoid consecutive fifths as at {c'). the figuring in a minor key will be according to the key. as at (Ji). one degree. 168. and the fifth the former rising. If the first upon the submediant chord. above it obey the rule given and the latter falling. as unnecessary. as in the second inversion. The root of the Yiii generally remains as the fifth of I. because the leading note in the bass as at (a) below. as before. In the jJ6 4. which in this position are the bass note applies. we shall S'')^'^ Ex. inversion of the dominant seventh resolve latter must also be in the first must rise.Chap. In resolving the first inversion.] Chord of the Dominant Seventh. it must fall. but here. as seen in Ex. and sixth above the seventh. . the much seen that vii° Nib without the oftener used vii°^ is. 252. it can no longer be the is ultimately derived root is meant the lowest of a series of thirds root. as we put the matter as clearly as possible. as we shall = . As the distinction between inversions and derivatives is one of the utmost importance for the proper understanding of many of the chords which we shall meet with later. as it is absent. C: V7* ivi 251. that is. for by The root is now the leading note placed one above another. vin. *C: vii" This chord is therefore in reality the chord of the dominant seventh without the generator . be omitted. if the lowest note. and here we see for the first time the importance of the distinction between root and generator. proceed. as the leading note is now free to fall (§ 101). we have an inversion of the discord . that all the diatonic discords in every key. 173. and in this case the lowest of the — . but a derivative of the dominant seventh. elevenths. the ultimate derivation of the chord from its generator should be added in brackets thirds that is actually present below the generator root. which in the first inversion rarely happens. If the root of this chord. Ex. referred to in the foot-note to § 36." If the dominant be present in one of the upper parts. 250. the note from which the chord but. we shall have the root position of the diminished triad on the leading note (§ 99.. ' ' ' ' becomes the root. it is well to We shall see. It is seldom that V73 resolves on a subdominant chord does. come from the dominant as their ultimate origin. and their "generator. Ex. which it must be remembered is also the generator. 253. The dominant is always the generator of this chord.171. This resolution is in its much rarer than when the chord of the seventh root position. "C: Nib VJc but. of the chord be absent. the best position of the latter will be the second inversion if it : Ex. 172. In marking the roots of derivatives. it is also possible to resolve the chord on the first inversion of the sub- dominant. ninths. whether sevenths. and the chord is not an inversion.I02 Harmony. or notes. We have just similarly. we have a derivative . is [Chap. or thirteenths. 103 see presently.) Evidently in the first of these two chords. Ex. N']c without the generator. Graun. Our next example is similar. We therefore mark &: vii° yii°i (V7i) (V7. D: I IVc V7i I V* Here we see the most usual progression of V7(5. except in a repetition of a sequence. will be D. _ — — — ?fe\4' 1 . VIII. 176.] Chord of the Dominant Seventh. Ex. Te Deum. both with and without the generator. the roots thus Ex. 174.Chap. 254. but in a minor key. 176. because of the fixed progression of the other notes. to the root position of I. the only note to double. In vii°3 as we have already seen in § 168. it is possible to double either D or F the third or the fifth of the chord. We now give a few examples from the great masters of the use of the first inversion of the dominant seventh. ) The chord and its figuring have has the fifth in the bass. and the leading note in the tenor falling to the fifth of that chord. 189. Johannes Passion. By far the most usual resolution of this inversion is on the tonic chord. The rules given in Chapter already been seen in Ex. VIII.) with Bach. (V7i) The F in the bass at the beginning of the second bar is an }f Notice example of the "Dorian sixth" spoken of in § 217. and must be strictly attended to. The second inversion of the dominant seventh (^^"7^. a very common procedure. (*) (0 {d) fe ^^ 4 . 257.) for approaching and quitting a second inversion apply to the second inversions of discords as well as of concords. 178. for the same reason as before. [Chap. Ex. 168 {b"). also the 'Tierce de Picardie' (§229. In our last example of this chord we again mark the roots of only the two chords particularly under notice. as already said (§ 100. VI (§§ 188. 256.I04 Harmony.) in the final chord. Bach. ) Ex. It would. however. Ex. If this inversion resolve on \h^& first inversion of the tonic chord (I^). StudiOj No.] Chord of the Dominant Seventh. instead of on the root position. * the bass of the second is approached by leap firom the root-position of another chord. and moves by step to the next chord. Notice how at bars are in the original. 4th Mass. second below the root. The following examples will illustrate the above resolution : Ex. Cramer. because thereby a primary note is doubled in the But in the position (d). falls to the third.^^T^\IT?T^ ^IT^T^^IT^. if the root leapt away to the root of the next chord. =S=g^ ^^ =* ^ I* Eb: V7f IV . in i°S fifths seen the first and second The parts cross here.182. where the seventh is a tonic chord. be possible here for the seventh to rise. l. 4 3 4 3 »1 lb c: 3 B6 4 ib C: N^c \b V7f ib N-jc Y^c ib At (a) and at (i) it (c) the seventh rises to the fifth of the tonic chord . 33. as at (<?). it must fall (§81). the seventh may either rise or fall one degree. 259. seventh to rise. inversion («) {b) (. 183.) (d) (.Vin.chap. 181. 258. The consecutive fifths at (a) are In such positions it is usually better for the allowed (§ 73). ^^^^ ^^ ^ g: Vy^ Haydn. * G A 260.' is seen the r r r * rT* Here. 182 there is a modulation from F minor. it is only needful to add that in the second bar of Ex. If it does so. It is rare for the second inversion to resolve on either a submediant or a subdominant chord. we have (V7r) In consequence of the absence of the generator. but a first inversion. a somewhat analogous case to that seen in \ 240. as in the following passage from one of Bach's * In a well-known passage following in Dr. 4th Mass. 184. the seventh is only allowed to rise when the following tonic chord is in its first inversion. the following chord will be inverted. Dykes's tune ' HoUingside. though it still most frequently moves by step. our old acquaintance vii°^. in this inversion of a dominant seventh. it is evident that. This is because the root in the treble falls to G. Before the proceeding. is also free to leap. 184. be imitated by the student. G: IV I V7f After the explanations already given. and the bass. it may not be superfluous to remind the student that. The progression is exceptional. and that in the third chord from the end in Ex. {a) Ex. not when it is in root position. VIII. Ex. 185. the seventh rises though the bass falls. Haydn. in V7f. and had better not . [Chap.T06 Harmony. If the generator be omitted in this inversion. the chord in this position is now no longer a second. to and F in the alto and tenor are passing notes. ^ vi* (*) =S=^ Vic V7« IVo 261. the resolution of the seventh. as the bass of Vy^ can only move by step. a passing note. 263. one of the notes rising and the other falling. Ex. 187.' Ex. The D here is only note of the next chord. Messiah. Ex. This short extract contains three derivatives of the second inversion. 181 . Messiah. as in the following. The third. as well as to fall. must fall one degree. must rise to the tonic. By far the most frequent resolution is . and does not change the harmony. The leading note. vii°^ vi Besides this liberty. Handel. the third (the original seventh). 107 chorals: " O Ewigkeit. Bach. VIII j Chord op the Dominant Seventh. ) can of course not be doubled. 186. and last inversfen'Wthe dominant seventh has the seventh in the bass. as in the following familiar passage from the " Hallelujah " chorus. 189. as now also we saw in Ex. du Donnerwort. (now the root. Handel. Ex. At (d) the third is doubled. 183. one rising and One of the thirds may also leap to another the other falling. The employment of Vyf is extremely rare with Handel. and the leading note (the fourth above the bass). it is frequently doubled. At (a) and (c) the bass is doubled. and the third rises in each case. who almost always omits the generator.Chap. 262. In resolving this chord the seventh (the bass note). is also free to rise. ip8 Harmony. VIII. first [Chap.) . on the inversion of the tonic chord {a) (b) (.190. 4 2 4 2 6 C: V7rf V7^ . #^^^=g=^^ \jjr Ex. Beethoven. not to change its position again. {See Exs. A ^- . An example of this chord has been given in Ex.) Andante in F. The chord v\c has here the character of a "passing chord" (See Chapter X. which. in Ex. is vii°^. and the other receiving its regular resolution. 194. (See also in illustration of this the first bar of the extract from A Schumann £x. 109 moving by step.] Chord of the Dominant Seventh. Beethoven. Symphony in D. 195. 194. 167. 195 below. The progression we are discussing {yid.) But it is best when one of the dissonant notes (the third or the seventh) has been transferred to the bass. VIII. one of the sevenths leaping to another note of the chord. 196. vii°^). 196. the student will see. 265. vir. very important point to be noticed with regard to 266. as at (Exs. doubled even when the generator is present. 122. provided that they are properly resolved in the part in which In this case the seventh is not infrequently they last appear. It is very rare in four -part harmony to meet with the derivative of this inversion.). but to resolve it in that voice.Qup. 197) below. the treatment of fimdamental discords is that the dissonant notes may be transferred from one part of the harmony to another. is never found in a minor key. Ex. 198. full seventh very nearly. 199. especially in the works of Handel. the octave should fall to 7. inant seventh are to be found.Harmony. C: 6 4 Ic V7 I But the 4 be in the upper part. 198 above.201. In a is [Chap. C: If the Ic V7 I 4 rise to 5 (as in Ex. 267. We add a few others here not as models for the student's imitation. in which the chord is followed by a chord of the seventh on the subdominant. Handel. VIII. Ex. 117). thus omitting the fifth in V7. and the octave of the bass in the ^ chord should go to 7. A pleteness. — cadence the root-position of the dominant if not quite. few exceptional resolutions of the chord of the dom268. 200. as often employed as the dominant triad (V). it is possible for 6 to rise to 7. if Ex. to precede the final tonic chord. but for the sake of comas in Ex. Messiah. . If instead of \ we have 7. If it be one of the commonest forms of cadence itself preceded by \c It was ^beginners are apt to write the progression clumsily. and having it instead in I (§ 236). has been already noticed (§ 80) and examples given of it. Handei. — said in § 182 that when ^ is followed by ^j the 6 should go to 5. L' Allegro. the same rule should be observed. and the four to 3. One of these. Ez. Ex.. defer As we till are at present treating only of diatonic chords. with the fifth omitted. .Chap. (a) A line placed under a bass note is to signifies that the harmony of the pre- ceding bass note (11) Andante.] Chord of the Dominant Seventh. we have to speak of modulation . The last two progressions are rarely if ever met with excepting in the accompaniment of recitative. as the student should by this time have gained sufficient experience him to dispense with the additional aid afforded by our giving the treble also. in [We to enable shall in future give only the bass of the exercises. 200 the mediant chord. later the explanation of the various chromatic resolu- which the seventh rises a chromatid semitone. tions of the dominant seventh. This may be regarded as akin to the ornamental resolutions spoken of in § 239. vm. be continued or repeated. As the exercises are now the basses of short pieces of music. 201 the third inversion of the seventh is resolved on the root position of the tonic chord instead of on its first inversion . Some of these progressions will be dealt with when. Samson. At Ex. f Ill Handel. 202 the seventh is irregularly resolved by rising to the root. to assist the student in understanding the character of the music in- tended. time indications are added. in the next chapter.] (I) Moderate. others will be more suitably examined in connection with the chromatic chords of a key. is interposed between the chord of the seventh and its regular resolution on the submediant. and at Ex. At Ex. we 269. or the third falls the same interval. while (8 and 7. ) are minims.:i2 (IV) AUegretla. . lines under the first note of bar 6 have the same meaning as that at (a) in Exercise I. S- 5 4 "2 * A G ^3p^^^ 3 7 6 4 4 2 6 (VII) Moderato. [Chap. and The Here C % must be a semibreve. 7 % (a) The line placed after the % shows that the note must be continued. ^¥ ( ^ 6 $4 2 6 $6 ^ (^ 239) g S^ 7 6 7 6 6 6 4 4 XI ) Andante {a) The Z here indicates that the third of the chord is ' to be omitted and the loot doubled. The third is added in the following beat. (X) 'Moderate. ^=it l=it: 6 5 4 f^-^4^^4£ 4 3 (VIII) Moderato. Harmony. VIII. VIII.] Chord of the Dominant Seventh. _ (? 264. _ "3 (XII) Allegretto.) .Chap. following melodies. VIII. and mark the roots. B. (XX) Hymn Tune. (XXVI) .] — (XXni) (V7) (o) It is (V7 i)(V7) (V7) recommended that two chords be used to (V7) accompany (V7) this note. In the first three of these melodies. Tenor. the places for [N. [Chap. r r ir riri^irT=f ^^^^ Add Alto.114 Harmony. and Bass below the Figure the basses. 6 5 3 7 6 6 6 6 6 4 6 4 — — ^^ ^ (XXI) Hymn Tune. but the position of the chord is left to the pupil in every case. the suitable introduction of the chord of the dominant seventh are indicated by (V7) under the note. and often\. are also related. which we shall now proceed to explain. the last will be in a different key from the first. or unrelated key . but more distantly: they stand in the second degree of relationship. This word is used by some writers to designate a modulation to a remote. it is called a Transition. MODULATION TO NEARLY RELATED KEYS FAI. for example. to indicate a momentary. 271. If the modulation be the shortest^ possible. These therefore are the nearest related major keys to C. and should not be imitated by the student. and the perfect fourth. The first question to be answered is. Thus. The only perfect consonances. in pieces containing more than one movement. the major and minor thirds and sixths.SE RELATION.\s. are the perfect fifth. Two when their tonics are consonant » * Occasionally. the former below and the latter above. the relationship is nearer than if it be imperfect. or vice versaJ^ A change of key is called a Modulation. besides the unison and octave. If all music remained in one key the resources at the disposal of the composer would be very limited. In all pieces therefore of more than a few bars' length. Every movement should end with the same note as a tonic with \hich it begins." in which the introduction is in minor. though the mode of the key may be. and the effect would soon become extremely monotonous.] Modulation 115 CHAPTER KEY RELATIONSHIP IX. and a return being subsequently made to the original key. which evidently will not change the tonic. F and G are both perfect fifths from C. changes of key are introduced. 272. or "transient" modulation. and why do some modulations sound more natural than others ? The answer to this question depends on what is known as Key Relationship. IX. a new note being taken as the tonic for a time. A . 270. .Chap. The imperfect consonances. and the succeeding allegro in C major. as we shall do throughout this volume. as. Such cases are exceptional and irregular. For the present we deal only with the most nearly related keys. the inversion of which gives the perfect fifth. but it is better to employ it. which keys are the best to modulate into. and consist of only two chords. in Weber's Overture to " Preciosa. changed from major to minor. major keys are said to be related to one another if the consonance be perfect. we shall see that here also (as said in § 210) all the notes of the scale are identical with one exception G. major. minor. C F). even though they look identical. that nearly related minor keys have fewer notes. or differs in C and we examine two nearly related major keys {e. 273. are derived from the same generators) a relative minor key is considered to be one of the nearly related keys to its relative major. 6 with the harmonic form of the relative minor (A minor) given in Ex. one another will be similar therefore be . 51). The key of minor therefore. it may be said. and that there are also four their diatonic scales are identical. But the relations of their tonics to keys to A minor will D minor F major. such keys are often Modulation spoken of as " remote. Similarly. G Putting the matter concisely and as a general rule. If we now compare the major scale of A G — Table of nearly related keys. and the nearly related A C Minor major. G G common to the keys of C and F. If and G. the only note which the scales of C and is F. E minor. G E A minor. in which we place the sharper keys to the right and the flatter to the left of the tonic. we shall get a similar series . and therefore fewer chords. B (§§ 47. We thus obtain the following table of nearly related keys. [Chap. and for this reason (though none of its chords.g. An examination of the table of the triads of C given in Ex. but with this difference. excepting in one note. or are distant an augmented or diminished interval from each other. the nearest related keys to any major key are its dominant and subdominant. are regarded as among the nearly related keys to the tonic. contains four chords in common with the key of C . ' ' 274. Two keys whose tonics are dissonant with one another are said to be unrelated . we shall see that. 275. 276. the relative minors of the dominant and subdominant keys. that. If we take any minor key as a starting point. C Major. C in Ex.ii6 Harmony. minor. in common. and the relative minors of these three keys . like and F.. and in the scales of C and F. being so closely connected with their own relative majors. F D major. . than nearly related major keys. Therefore every common chord in the key of C which does not contain the note F also belongs to the key of . and if the tonics are a semitone apart. major. 62 will show us that there are four chords common to the keys of C and G. 138. ix. Thus. to unrelated or remote keys will be dealt with later. and every chord in the key of C which does not contain B belongs also to F. it would be needful to indicate the alteration of the third in the chord of the new dominant. (adding Cjf to the above chord). It should be noticed that two keys which are nearly related to one another never differ in their signature by more than For this reason tonic major and minor keys one sharp or flat. and so in other cases. and sometimes more. 277. 279. for the same chord may also be the dominant of G minor. is A that to say — — . 117 and the nearest related keys to any minor key are its dominant and subdominant minors. bass would be figured thus @ g— . in spite of their close harmonic connection. for instance. but are included among keys in the second degree of relationship. are not considered to be nearly related. see § 164. the bass note would be figured @ g— 7 . that we wish to modulate from C a key. and it would be quite possible to follow it by harmony If we take the dominant 7th on D in any of these keys. the tonic of D major. because no single chord can ever define Suppose. we restrict our choice considerably but this chord may still be either in G minor or G major. In the case of a modulation without a change of key-signature. t the modulation were to F major. and only the context will show us which. but foreign to that which we are leaving. This last condition is essential. Naturally we think of using the chord of to G. it would be necessary to indicate the I? to the B in the figuring.) modulation were effected by means of the dominant seventh of the the new key.] Modulation. must be regarded in their relation to one another. (§ 212). 278. A modulation to a nearly related key is effected by introducing a chord containing a note belonging to the new key. But the introduction of this chord alone is quite insufficient . Similarly. the D in the . the subdominant of A major.Chap. and we are modulating to G by means of the chord of D major. To determine any key. major D I ^L-j ^ ziz]. It was said in § 163 that a common chord in its root position was not figured unless one of the notes required an accidental. or the submediant of F tt minor . and the relative majors of these three keys. XI. and by following that chord by other chords defining and fixing the new key. ' (For the explanation of If the ji without a figure at the side of it. as in the last paragraph. as being the dominant chord of the new key. Supposing the key of the piece to be C. at least two chords. if modulation can either be effected immediately by introducing a characteristic chord of the new key directly after a chord characteristic of that which we are leaving or it can be effected gradually that is by interposing 280. belonging to both the keys of C and G. the roots in the above example. and therefore leave the tonality doubtful) introduced. established by the introduction of a note or notes foreign to itself If it be thought desirable to mark the exact point of contact. IX. so to speak of the two keys. The effect of the latter modulation is therefore smoother than that of the former. This is because the dominant of the The . characteristic chords of the [Chap. except between tonic major and minor keys. The larger the passages £x. I The last two of each passage are identical .ii8 Harmony. while at {b') six ambiguous chords. Let the student compare the following. the student must notice in what key the music is at the moment. 282. common to both. It must not be forgotten that every modulation. 203. though they might also be regarded in their relation This is because a key once established can only be disto G. but chord containing Fj| follows immediately on one containing F t}. the six ambiguous chords are all indicated as in the key of C. It will be seen that in marking. student should observe where these ambiguous chords occur but it would needlessly complicate the analysis to mark them for such a simple harmonic progression as that here shown. 204. the roots in the Isist four bars might have been indicated thus first bar and the at (a) the Ex. In modulating from a major key to the supertonic minor it is necessary to avoid putting the dominant chords of the two keys too near one another. are seen before the new key is introduced at *. 6 6 7 C: I IV I^ V vi 4 Ic 5 ( I G:V7^ IV V. the more gradual will be the modulation. between the are two keys chords which number of ambiguous chords (that is chords which belong to both keys. 283. 281. changes at least one of the primary notes . in considering which notes are best to double. while the most frequent modulations for a major key are to the other nearly related major keys. For this reason. which will be treated of in subsequent chapters. The number of chords common to two nearly related keys is largely increased by the addition of chromatic chords. We shall now give some examples. with such remarks as may help the student to understand the way in which they are managed. either its relative major. of modulation into nearly related keys.] Modulation. 286. Solomon. from the works of the great masters. For instance. occurrence. but only a note This is a case of frequent 284. 146. or its submediant major (the relative major of its subdominant). If these two chords come next to one another we shall have the very unpleasant progression shown in Ex. It is therefore "asually advisable in making this modulation to introduce the minor sixth of the new key before introducing its leading note. to both keys. This rule. however. 285. \pSp3 Ex. . it will be seen that of all the diatonic triads there is only one in common to each pair of keys. the only chord common to C minor and G minor is the tonic chord of the former.Chap. with which it has four chords in common. with which its has three. If we compare any minor key with the minor keys of dominant and subdominant. Handel. 205. 119 key is the subdominant of the second. since the diatonic chords can be employed in their inversions as well as in their root positions. and its chord would be a major chord on the subdominant of the minor key. IX. & ^— Here we have no chord common common to a chord in both keys. while the only chord common to C minor and F minor is the tonic chord of the latter. it EZi 206. considerable variety is possible. does not apply when the tonic chord of the major key is immediately followed by the dominant chord of first the minor. But -even without using these. a minor key most often modulates to one of the related major keys. IX This passage shows us at (i) a modulation to the dominant effected abruptly. \p^ —nv . and leaving it as the tonic of the new key.Harmony. passage is varied from the fifth bar as at {b). From D the music modulates to E minor at ( 2 ) by taking the first inversion of the chord of E minor as the supertonic of D. [Chap. with the chord of the dominant seventh On the repetition of the phrase. by introducing C|f immediately after C{[. the fixing the key (§ 241). following it by a cadence in E minor. and — . AuBER. and at 211 by^ the reverse process. key of C. the first inversion of the subdominant being here left as the first inversion It should be mentioned that the in the of the new tonic. The key is changed in each case at the third bar of the extract. j| as a A third bar of Ex. is not a harmony note. 289. The second chord of this bar is a chromatic chord in the 207. from a major key to its mediant minor treating the tonic chord of the first key as the submediant chord of the second. in the present instance C major is quitted as soon as it mon." Op. 5. Our last example will show a modulation from a tonic minor to the relative major of its dominant minor in this case This modulation is not very comfrom D minor to C major. Our next illustrations show modulations from a minor tonic to the dominant minor (Ex. (See Chapter X. is A modulation made by usually as below. but an auxiliary " Im Herbst. IX. z il note. No. which will be explained later. 9. Ex. Masantello.] Modulation.) Mendelssohn. 290. 211). 210) and the subdominant minor (Ex. and following it accordingly. 291. at 210 by treating the previous tonic subdominant .Chap. EXi 209i :it. 210. . and at the last chord of the bar. or fall a semitone or a tone. 68. or its seventh rise a semitone. The general rule for modulating to a nearly related key which may be gathered from the examination of the extracts we have given is." Op. [Chap. Schumann. 213. and leaving it as a constituent of the new key. 208. Voice. related keys contain at least one chord in common. 209. 292. the music modulates to A minor. An example of each procedure will make this clear. " Nordisches Lied. 211. Ex. 206. as in Exs. 207. 1-. IX entered. or by taking a chord common to both keys. Another method of modulating consists of irregularly resolving the chord of the dominant seventh by making its third rise a tone. which will be spoken of in a later chapter . 212.—I- taken as the tonic of D The second chord is a chromatic chord in the key of C. A Ex. that the modulation may be effected either by immediately altering one of the notes of the key we are leaving by means of an accidental. the third chord is part of the dominant eleventh of C. as in Exs. All nearly 293. The first chord of the second bar supertcjpic of is minor and quitted as C major. 210. 212.122 is Harmony. with which the student is not yet acquainted. consisting of not more than two chords. or fewer sharps. to a key containing more sharps. in minor keys. for instance. not of returning to the key of the tonic. 123 Humoreske. the seventh in the chord of the dominant seventh of C rises a chromatic semitone. but of going into a dominant key. we modulate from C to F and make a long stay in the latter key. If. a modulation to the choice of modulations. is a subordinate key compared to the tonic.g. There is yet one more point to be considered in the As a general rule. or fewer flats is to be preferred. the tonic still maintains its position as the source whence the whole music springs. 214. 215. IX. as also are all other — — — keys with more sharps than itself. Here the third rises Ei. dominant side of the tonic that is. greater freedom prevails. Die Melstersinger. 20. when We modulate into one of these keys the original tonic sinks into a secondary position. and the modulation is confirmed by the tonic chord of that key. C is the dominant of F. Op. that is. S chuma nn.] MODULA TION. therefore. a key having more to one to the subdominant side The reason of this is that the dominant flats. we modulate into one of these keys. . to which a modulation is made. 294. In our next example Wagnee. we shall when we return to C most likely get the mental impression. and the mediant of and 1. dominant ninth in G. Some of the most natural. and frequently employed transitions are those in — A .Chap. In § 270 a Transition was defined as a passing modulation. a chord which will be treated of later. and the same disturbing eifect is not so readily produced. and becomes the leading note of the key of The chord marked * is a G. 295. as a first modulation. For this reason the feeling of the key is much more readily disturbed and much sooner obliterated by a modulation to the flat side of the key than to the sharp side This applies chiefly to major keys . owing to their more artificial origin. But the tonic itself is a subordinate note in keys having more flats than itself e. When. Ez. in the chord of the dominant seventh in B flat a tone to the third of the same chord in C minor. 124 Harmony. : Ez. however. the mental effect of that tonality is never really lost. they are seldom found. Such dominants we term Transitional Dominants. : we merely mark them * C:I(d:V) It ii(e:V) iii (F: V7) IV (G:' V) must be clearly understood that this method can only be used when the tonic following the dominant chord is a chord of the If it be not. 216 must not be regarded as an average specimen of the employment of transitional dominants . ) actually foreign to the key. there is a transition in every bar . chord is not only i in D minor.. and if the music immediately returned to the latter key. in Ex. 216. greatly simplifies our analysis. Thus we mark the roots in Ex. in four or five consecutive bars . not merely one. It should be added that Ex. but. Here. . as there. if in brackets. 216 thus Ex. as the tonic chord following each new dominant is still a chord in the key of C. it and in indicating the roots. because the first chords in the second and third bars are not in the key of C. Single transitional dominants are. [Chap. 205 (§ 283. : Ex. 217. key of C can be thus attended by its own dominant . e. IX which the new tonic chords are also chords in the previously For instance. and we have a transition : e. 218. These are not transitional dominants.g. the chord of A major might be regarded as the Each common chord in the dominant of the supertonic of C. we should really have only one chord which was necessarily foreign to C. while the transitional dominants stand in the same line with the rest. the passage was written to illustrate the possibility of their employment on the various degrees of the scale. if it be remembered that the latter are always placed under another root. of constant occurrence. strictly speaking.g.) the third established key. but also ii in C major. giving the following chord its root as in the already prevailing key. * There will be no confusion in the mind of the student between these bracketed roots and those employed to indicate derivatives (J 253). In that case. there are two chords (and already prevailing key. called a False Relation. It should be that the interposition of one intermediate chord will not y the effect of a bad false relation. A Ez. At {b') we proceed to D minor. if properly treated. first chord Ez. False relation. progression at (a) is. Good. as at (f). the third of the of C being the fifth of the chord of A. because the essence of elation . Bad. If this be done. the third of the chord of C. . as I. The o be altered should therefore be kept in the same voice.<] 6. 221. fNeither e chromatic chords in a key (to be explained in a later .r) generally cause false relation. 219. ' *^ Bad. and the seein the alto.g. no false relation occurs by another moving to the same note. beas C |f lt forms part of a chord of the dominant seventh. 220. is Ez. 125 When in two consecutive chords a note forming part is chromatically altered to become a note of icond chord. is the confusion or obscurity of key which it proand chromatic chords. have not this But even in this case. But the latter is not objectionable. =J^ ) -[- rJ" we can modulate from C major to minor without bad because E. 1 Modulation. e. pThe false relation is ot considered to exist when the altered note forms part of lamental discord (§ 232). has no bad effect when the third of the first chord is the root or the fifth of the dominant chord of a new key. iTor instance in Ex. 206 (a) rst chord of the third bar has C t| in the bass. root as the preceding or succeeding diatonic chord. it is frequently best to keep it in the same This is especially the case when the roots of the two > are the same. the be kept in the same voice. le Good. when the chromatic chord has the i note should iver. is the root of the 1 chord. should have no difficulty in knowing into what keys the music modulates. 4 3 »2* 6 {6 4 ^^^ 6 t|6 fS 4 J (IV) Moderato. more widely over without notice and there is probably no rule to which there are so many exOnly experience will enable the student to know ceptions. 87 ^s a f6 6 (V) Andantino. 297. many passing and when allowable. ( I) Vivace. student.126 Harmony. he should mark it in its relation to both. IX. There are few questions on which than that of false relation. 204. theorists differ it [Chap. ^^ as 6 ^^F 6 4 5 3 6 $6 m. (il) Andantino. he must be careful to indicate every We change of key . if he notices the accidentals introduced. as we have done in Ex. and when the modulation is made by means of a chord common to the two keys. The now give a series of exercises on modulations. 6 7 7 4 6 3 . 3 6 7 6 5 6 16 1 4J 6 5 4 3 j]4. with certainty when an apparently false relation is objectionable. 6 4 2 6 2 6 5 ^^m 8 1)6 (III) Moderato. In marking his roots. ] MODULA TION. 127 (VI) Andante. g 6 It UB 4 6 6 6 |75 6 . IX.Ch»p. (a) Maestoso. 6 5 1(6 6 J4 2 6 16 4 06 5 (5 6 7 4 43 X 6 6 5 7 X 4 X— (IX) Pastorale. /-v. S (6 6 4 3 ^ 5 \ ^ i:j.128 Harmony. i . ji. 3 6 jt4 6 t6 "T"! t «4 2 6 (6 4 2 (XIV) Double Chant. IX. mt^i:^ jr \ (XII) LarghMo.j^jJJ4 j-^^t^-i^ i 6 t 6f6 6jt6 6 "16 6 m S=s= 7 1(6 ffi^ $6 5 6 n ^ ^^ 6tf7 4 4*4 (6 "4*4 6 7 J5 f 4 « 4 3 4 J 6 6 "e'JS 5 4 ^^ ^ 2 3 6 S5*# *=(S* t=*=t 6 6 7 2 it (XIII) Double Chant. [Chap. the "half cadence. With both chords inverted: Nb-\b. or both of the two final chords of a full cadence be inverted. him. among the most common : are '^']b-\.Chap. 129 (XIX) Hymn Tune. that "middle cadences" it is therefore generally better to employ other forms. (§ 178) . IX. 117. We every piece of music must end with a full (§ cadence but. we have an Inverted Cadence. Y^d-lb. the effect would be extremely monotonous. Y-jc-lb. instead of their being both in root-posiOf this there are several tion. . * For fuller details on the subject of cadences. were a full cadence introduced at the end of every For the phrase. («) With vii°^-I. see Counterpoint." ending on the root posicadences. V7C-I. 3 6 6 5 6 S6 4 3 5 6 f6 6 t5 4 X 298. Yc-lb. there are two others which must now be briefly de- — — scribed. The Student will now be able to attempt the hannonization of chorals containing modulations . there are a few additional hints to be given already know The first refers to the cadences. one has been already explained tion of the dominant chord. in which case a full Of the various middle cadence in the new key is allowable. If one. yu°b-lb. possible varieties .] Modulation.* 299. but before he proceeds to do this. With tonic chord inverted V-IiJ.) . (J>) (<r) dominant chord inverted : V^-I. unless the music modulates. Chapter XV. tonic chord 300. will In simple pieces of regular construction. a modulation ' ' to the dominant in this case with a " feminine ending. 25. We have not chosen any which contain auxiliary or passing notes. e. (The student is [Chap. should in each case He must remember that the come upon an accented beat. shall in future. we have an Interrupted Cadence. that is. be followed by any other chord than the tonic. CHORALS TO BE HARMONIZED : Nos. it mostly indicates a modulation to the relative minor key. as the penultimate chord in a cadence. IX. 16. Ex. but by far the most frequently used form. Ex. Almost any chord is possible after the dominant . advised to write these progressions in four parts. and in every second bar in quadruple time. * Published by Augener & Co.I30 Harmony. .'^ For his present work. 46. — — Ex. 42. 223. while if a phrase ends with the descent from the leading note to the submediant. In the melodies now to be given. Full information on this point will be found in Chapter XVI of Counterpoint . whenever they are irregular. 302. 303. 27. 20. 13. the treatment of which will be explained in the next chapter. refer the student to the large collection to be found in Additional we Exercises to Counterpoint. 10. 7. it will suffice to say now that if a phrase ends with the descent from leading-note through submediant to dominant. In order not to unduly increase the bulk of this volume. 301. by the form of the melody itself. 30. 3. without such accidentals.g. instead of giving melodies to be harmonized. the position of the cadences. the cadences mostly be found at every fourth bar in duple or triple.in various keys. ) An example of this cadence will be seen in § 242. 222. The key to which a modulation is to be made can sometimes be determined by the accidentals seen in the melody but it is also possible for a modulation to be implied. 165. an ending on an unaccented note is generally implied . If the dominant. and the only one with which the student need at present trouble himself is V—vi (VI in a minor key. will be indicated by a pause (z^) placed over the last note. 5. 33. we select the following from among the fifty Chorals given on pages 10 to 19 of that book. as it is not itself an essential part of the chord. like the dissonant sevenths treated of in Chapter VIII. PASSING NOTES. and . it should be the next note of the diatonic scale of the key in which the music is. of such notes. unless such harmony note be the major third of a chord.Chap. it should be a semitone below it. whether that note be a tone or a semitone above but if it be below the harmony note. As all seconds are discords. 224. the auxiliary note will always be dissonant to at least a part of the chord with which it is sounded but. the great masters to illustrate the chords alreadytreated of. 305. is frequently taken. In explaining the various examples quoted from the of. When an auxiliary note is above the harmony note. NOTES. 306. and (excepting be specified presently) should always be left. Ex. it is called an unessential discord. by step of a second. It may occur on either a stronger or a weaker accent than the harmony note to which it belongs. An auxiliary note in certain cases to 307. in which case the auxiliary note may be either a tone or a semitone below it.] Auxiliary JVotes. works 304. __ — Or At (ff) are shown auxiliary notes above the harmony notes. X. and it may be at a distance from that harmony note of either a tone or a diatonic semitone above or below. 131 CHAPTER UNESSENTIAL DISCORDS (I) X. —AUXILIARY AND ANTICIPATIONS. it has sometimes been needful to mention that some of the notes in the extracts were not notes of the harmony. An Auxiliary Note is a note preceding or following a note of the harmony at a distance of a second above or below. but It is now time to show the nature auxiliary or passing notes. as do the E in But if all three the alto of (/) and the C in the treble of {g).132 Harmony IChap. given in Ex. major. If auxiliary In each case the chord remains the chord of C. however. as at (<?). Ex.* 308. at (<:) modem in this paragraph is almost universally observed by composers. they may C II and be used as auxiliary notes below D and E. At ((5) of the example just given will be seen the If we look at the chromatic notes C ^ and D tt in the key of C. and at (d') in the bass. but we shall see many cases later in the chapter in which they are taken by leap." * The rule given In both these passages a modei^ composer would have unquestionably written the auxiliary notes a semitone. notes are taken in treble and alto together. as well as above the harmony note. we shall find ^ and E t' given as the notes lying respectively between C and D. as in the two following fugue subjects from the " Wohltemperirte Clavier. the feeling of the At {a) added is the chord of C in the treble. scale of C. provided that characteristic notes of the harmony remain in some of the parts. cannot be used as harmony notes in C. and not a tone. auxiliary notes are taken together. Auxiliary notes may be taken in more than one part of the harmony simultaneously. example they are both taken and left by step . below the dominant. frequently adheres to the diatonic scale for an auxiliary note below. can be used as auxiliary notes below Similarly G || and || D D D We D jjl A A and B respectively. X. The restriction of a key to twelve notes applies only to notes of the harmony. 309. But though out getting more than twelve notes into the key. the C in the bass still preserves the feeling of the chord. as chromatic notes. When later in this volume we treat of chromatic chords in the key. 6 (Chapter I). At (Ji) an auxiliary note is in the alto. Bach. as at 0i). at {b) they are given below. we shall show that |? and E 1? are really the notes employed for chromatic harmony (Chapter cannot therefore also have their enharmonics withXV). . In this. and and E. 211 in the third bar the Att is an accented auxiliary note. C. 312. taken by leap of a third and left by step. and the chord is a "passing chord." 310. shake and the upper and lower notes of any turn are always auxiliary notes. They are of two kinds. — We give examples of this kind presently (§ 320). At Ex. and B are but harmony notes. or would have a different resolution. F. 176 the Etj in bar i is an In Ex. 313. and we have instead of the second inver- sion of the dominant seventh no longer auxiliary. With regard to the first kind. 226. is an auxiliary note to D taken and left by step. If in the example just given the chords were mostly moving in minims shall or semibreves. instead of returning direct to that note. have been' met with in some of our examples. It was said in § 307 that the auxiliary note below a major third might be either a tone or a semitone below it. In Ex. The notes D. the second quaver. this largely depends on the length of the chord and its position in the bar. may. and the harmony changed at each crotchet. 159. as at {K) above. and marked '^ic. on G. and those in which the resulting chord could either not be used at all. are approached and left by step. the fifth of the chord have also an auxiliary note below it. which will be at the distance of a semitone. Ex. Passing chords are indicated in analysis by the letters "P.] Auxiliary Notes 133 it chord of C is gone. There are two cases in which an auxiliary note can be Such a note. however. or -al leail uiiuugh of-Aem-to-Jemove the impressson of the previous harmony. it would be best to regard the second chord of {K) as a passing chord . the auxiliary note of the third must also be a semitone below. Let the student now examine the auxiliary notes that At Ex. instead of by step. auxiliary note to F. if the time were slower. If. those in which the resulting combination of auxiliary notes gives a chord which might be an independent chord. X. leap a third to another auxiliary note on the opposite side provided that this second note return . it is impossible to give a hard and fast rule as to when it should be so considered . C. 182 the Bfes in the first bar and C Js in the second are auxiliary Similarly the upper note of any notes to C and D respectively.Chap." 311. taken by leap and left by step. taken by step of a second from a harmony note. in the second bar. Passing Chords are those in which all the notes. the chord should be treated as an independent chord. if quitted by leap of a third. Ex. once to the harmony note from which the which lies between the two auxiliary notes. The second case in which an auxiliary note may be quitted by leap is when the harmony notes are a second apart. and the first note moves a second to an auxiliary note on the opposite side to the next harmony note. Haydn. 2nd Mass. (Compare note to § 307. Rondo in A minor. Such diatonic progressions were more common in the i8th century than now. 228. and ** Ei. 229. 230. Ex. Such notes may be called ' single changing notes. * * * * Ex. In the third crotchet of the second bar is an auxiliary note a tone. we have a series of similar notes in quick time. will be found in Handel's chorus "For unto us a child is born. ** Two auxiliary notes used in this manner are usually called An excellent example of them in two parts changing notes. is evidently a falls : '\c V7 i. 227. the following passage. ' ' Mozart. This extract also furnishes an excellent illustration of auxiliary notes a tone below the third of the chord. The very rare . The In C and then a third to B. first [Chap.X.) 314. to which it then leaps a third.134 at Harmony. This progression is much more common when the step is upward and the leap downward than in the reverse direction. instead of a semitone below the root. Here the harmonic progression in the first chord rises to D. and a semitone below the root and fifth. moved." Handel. ] Auxiliary Notes. Invitation i la Valse. When the notes of a chord are taken in succession. Ex.Chap. * is quoted from HuUah's " Transition Period of Musical History.' at £x. Lawes. There is no restriction as to taking auxiliary notes by though there is as to leaving them. 231. ' While I listen to thy voice." 315. X. The latter may be either on the accented or the unaccented part of the beat. /I/lH . note preceded by an auxiliary note. —Song. 133 converse case — the falling second and rising third H. Weber. 232. it is not uncommon to find each leap. It is possible in ** r-* Ex. 236. but this is very unusual. Ex. [Chap. or in the reverse direction from leading note to dominant. ^ J J A ^°^ jJ=t: J. it is customary to use for passing notes the two melodic forms of the scale given in Exs. Ex. if the music at the time were in the key of C. in order to avoid the interval of the augmented second between the sixth and seventh degrees of the scale. 317. and not of G. 134. and. 239. 235. the minor seventh of the scale will be used.136 Harmony. Ex. 318. 238. 132. Ex. Therefore in passing from the dominant to the leading note of the minor key. as. If the two harmony notes are a fourth apart.J ' Bd ll ^g Similarly. both these cases to employ the harmonic form of the scale . the major sixth of the key is mostly taken as the passing note. or from tonic to submediant. Good. A but the secoad note must proceed in the same direction till it reaches the next note of the first chord. X. 138. 237. for instance. E. there will evidently be two passing notes between them. l-«feW> (. Ex. Bad. In the minor key. . . even though by a change of the harmony the first may have become a harmony note. in rising from the fifth to the root of a chord. r -l I second passing note should never return to the first. which may or may not have become a note of a different chord. in passing from submediant to tonic. 234. it then becomes a passing note . instead of the harmx)nic form given in Ex. this passing note must be F tj and not F jj. ) in the rare resolution of Vy^on vi^ . and the passing note instead of going direct to the second harmony note. could be used as independent discords . the student will (§ in explaining the progression. but it would be impossible in that case to follow them as they are here followed. X.") be seen the progression Y^d y\c y\\°b I. but if a chromatic note has been introduced it is best to continue the progression by semitones until the next harmony note is reached. 242 is reached . ^ 241. 240. 235. . Passing notes may be taken in more than one part of harmony by contrary motion from a harmony note. I J J . it is usual to employ the melodic forms of the minor scale. explained later. until another the consonant chord Ex. In this example the chromatic notes are written as C tt and D |..] Auxiliary Notes. leaps a third to the now understand why. which we met with 264. and always by step. as well as diatonic. Chromatic notes. e. \\c was spoken of as having the character of a passing chord. 321. Not r-9 fix. 320.J . it would have been This point will be more fully better* to write them as flats. and continue by contrary motion. if they were descending. This is because they are not as DI? and El' (See § 308.) moving upwards . Ex. or in falling from the root to the fifth. g. — It is progressions of this kind that cause the second kind of Some of these chords passing chords spoken of in § 310. 137 two passing notes follow one another in rising from the fifth minor key. and the minor seventh and sixth in deIf to the root of the tonic chord in a scending. with the major sixth and seventh in ascending. 319. may be used as passing notes . The only case in which a passing note may be quitted by leap is when the two harmony notes which it connects are at a distance of a third apart. 236. as in Exs.. .Chap. (we In the last four chords of (^) will will not say "resolved. Harmony. * £z. and unaccented in the fifth and sixth. as with the auxiliary notes. F jf. we see on the last quaver of the second bar an example of an accented passing note. [Chap. here the effect of the B I? in the soprano against the bass is most poignant and striking. Requiem. and E t}. because though they contain exactly the same notes. distance of a diminished octave from the harmony note is A * Some exceptional progressions of auxiliary notes this chapter . 141 (J)) the second quaver of the bar. 232 accented passing notes are seen in the second bar. It is important to notice that auxiliary and passing notes cannot make " false relation " (§ 296). 244. 136 are instructive. G. and E t) are passing notes. B tf in the tlie curious example of an auxiliary note in the bass at 324. 201 the quaver B is an accented passing note. In Ex. At Ex. but these will be shown later in do not invalidate the general rules here given. The two scales quoted from Handel in Ex. In Ex. 121. A. . as they are differently accompanied. and that even the interval of the diminished octave may be sometimes used with very fine effect. We will now. C. In the first scale C. 243. A still more striking example is shown in Ex. where the at the bej( ginning of the second bar is not only a passing note on the first beat of the bar. B. no G 323. and at Ex. and then returns. One of the best known and most beautiful examples is seen in the " Recordare " of Mozart's Requiem : Mozart. refer to the passing notes in some of the extracts quoted in previous paragraphs. E. This is another variety of the "changing notes" mentioned in § 313-* 322. X.138 Other side of it. and in the second C. the passing notes are different. is an unaccented passing note. Ex. but is of greater value than the harmony notes which precede and follow it. the 'A' over the notes of the melody . Bach. In Ex. Besides the two kinds of auxiliary notes already spoken there is a third species somewhat resembling them. 246 the root of the final chord is anticipated in the and in Ex. of. In Ex. It is in cadences such as these but they are that anticipations are most frequently to be seen also employed in other ways: e. 139 found in one of Bach's Church Cantatas. Bach. ' Herr Gott. 247. but to extract its harsher than in the passage from Mozart is not given for the student's show harmonic possibility. Ez . . both root and third are anticipated. Here the just effect is much the quoted. 248. 193 we see in the final cadence the anticipation of the complete chord of the tonic. and imitation. Ibt.' El. Sometimes one or more parts of the harmony proceed prematurely to their notes in the next chord. D : I V I^ vn°i U Vji 1 Ic V Here we have marked the roots. J. 4th Partita. S.g. This effect is known as an Anticipation. Messiah. X. J. " Gieb dich zufrieden.Chap. 246. Ex.] Auxiliary Notes. Handel. S. dich loben alle wir. while the others remain. 325. to show the points at which the harmony changes. treble.246. 247. though possessing features of its own. the note E of the alto in the third crotchet of the bar is anticipated in the treble . an anticipation In our next example. . 251 the first quaver in the third bar of the bass is similarly treated. Changing notes (§ 313. or by leap from a different harmony note. —" Es ist dir gesagt. either be taken They can Passing notes can be introduced between any two harnotes which are a third apart. two consecutive passing notes can be employed. though rarely. as in the following examples Bach. Ab.) can very seldom be employed with good effect. Cantata. auxiliary Auxiliary notes note. In Ex. in which case they must be preceded by the same harmony note which follows them. and in Ex.140 indicates Harmony.) can be used either when the same harmony note is repeated. and then taken Occasionally. Sonata in [Chap. 250. 250. or when the second harmony note is a third above or below the first. IV.) had better be only employed when the harmony note which follows it is at the disr tance of a second below that which precedes it. and are the root and fifth of the same chord. 231. ^P We will now briefly summarize and passing notes. The converse progression (see Ebc. voice. . Weber. Ex. not only harmony notes but passing notes are anticipated. Ex." Ex. the laws for the employ- ment of I. 327. may be taken either above or below a harmony by step. 251. 249. mony III. 326. X. II. a note is anticipated in one in another. in which case the second may never return to the first (§ 318). If the two harmony notes be a fourth apart. A single changing note (§ 314. The following passages must be looked upon as licences. 252. 329. 251. bach. They are therefore not recommended Ex. 253 will be seen auxiliary notes leaping a fourth and a diminished fifth. instead of a third. This is a matter entirely at the discretion of the composer. ) while at Ex. 255. it is impossible to give similar rules as to when and where they should be introduced. •• ^^ ^ Athalia. A A — * Ex. bar of Ex. to the harmony note.- rr-r-pi P^ f^rT3^^g^ Handel. 254 is clearly an auxiliary note. as they cannot be explained by any of the rules given in this chapter. 255 it leaps a fifth. Ex. Exceptional treatment of auxiliary notes is sometimes found in the works of the great masters. because the harmony is defined as being that of the common chord of F by the arpeggio in the bass. * Ex. At Exs. ^ for imitation. (^See § 228. 263. 141 328.^^ Mozart. Symphony in Eb. ^^^ag. and would thus present some analogy to Ex. Bach. X. The student will do well to conform to the rules we have given till he has gained sufficient experience to know when they may be safely relaxed. 254. Though we have given rules for the treatment of auxiliary notes. Was Gott thut. 252.] Auxiliary I^otes. At Ex. The F in this last example may also be considered as an anticipation of the implied harmony of the following chord (the dominant seventh).Chap. Here the auxiliary note leaps a sixth. 253 we also have an excellent example of the anticipations spoken of in The note D at the end of the first § 325. We therefore do not give any . n. 330. No. 256). XIV). the 4 B yi (E|>: ^ 2 6 c. passing. that. We will therefore take a melody from the Additional Exercises to Counterpoint. no figure under it. advisable. special exercises for such notes in his future -work the student can employ auxiliary and passing notes whenever he thinks it Excepting occasionally with accented auxiliary notes. to determine which notes it is expedient to treat as In most melodies. kind that he will at present have to harmonize. etc. 256. the harmony will mostly change at a regular rate on each crotchet or minim. V (f:Vi) (V70 . e.142 Harmony.n. it will be generally better to treat one of the two as an auxiliary or passing note than to give a separate chord to each. nor (as remarked in § 315. (See bars 7 and 8 of the next exarftple. excepting on the last note of a phrase or sentence. Vn\ ' V Nnd ' \b vii°* W p. auxiliary. if the harmony move in minims. 12. In our analysis. this is shown by a roots.' We take choral " Nun ruhen alle Walder " (p.n. which contains passing notes. .as the case may be. . and harmonize it. and changing notes will be . introducing passing notes in the other voices. If two notes of half the value of the standard two crotchets. they are hardly ever indicated in the iigured bass.n. If this note have as will be seen in our next example ("Ex. when harmonizing a melody. of the simple auxiliary notes.) is any notice taken of them in marking the If the passing notes are in the bass. — — — marked respectively 'a. X. 6en... chorals. /. Ez. it signifies the root position But of a triad. [Chap.n. ) there is one hint which may help the learner. line continued under them from the preceding harmony note. but only a line.n. two quavers if it move in crotchets. etc. I p.' and 'c. This principle will be best shown by practical illustration.' 'p. are found on adjacent degrees of the scale. there is generally some uniform rate of what we may term harmonic pulsation. Chap.X.] Auxiliary JVotes. 143 vi V U p.n, p.n. i p.n. ib bb:V7^ V A]?: vi U p.n. p.n. V f: V We have numbered the bars, for reference. In the first and second bars are seen passing notes in the treble ; and in the The third bar are auxiliary and passing notes in bass and tenor. cadence in bar 4 may be regarded as a modulation into E flat we have marked the second chord as a transitional dominant (§ 295,) because it is the only chord which cannot be regarded as possibly in A flat.' In the bass of bar 5 are seen single changing notes in the first half of the bar ; on the second quaver of this bar the auxiliary notes in the bass and alto give IV as a " passing chord" (§ 310). Another passing chord is found at the sixth quaver of bar 7. In bar 11 we have marked the F in the tenor as an auxiliary note, rather than the following G as a passing note,. because the former would have given the progression ii I, It should be noticed that F, being an which is bad (§ 195). We might accented auxiliary note, is indicated in the figuring. have considered that there were two chords (ii. vii°i^,) here; but as the harmony moves in crotchets, it is better to regard F as an auxiliary note. A similar case is seen in bar 12, when the D of the alto, a passing note, changes V into V7. Such a' seventh, when of small value, is called a "passing seventh," and may be marked "p. 7." — 331. It will not always be necessary, nor even advisable, many auxiliary notes as we have done in this choral, we have purposely used them freely, to give the student to introduce so — examples of many different ways in which they could be employed. We will now conclude this chapter with an example of a melody in which it will be well to treat several of the notes as accented auxiliary and passing notes. Instead of harmonizing it in fiill, we give merely the melody, indicating beneath it the roots of the The student should write it out in full for himself. We 144 select for our Harmony. [Chap. X. example the old English air " The Bailiff's Daughter of Islington" {Add. Exs. to Counterpoint, p. 20, No. iii.) c.n. CD. Ex. 257, V4 L.n. I a.D. vi IV I y^c \b I IV ii I* vi^ V* V II* \c V7 The harmonization given here is very simple ; we need only say that in the fourth bar we have marked three chords under the dotted minim, to keep the flow of crotchets unbroken. 332. The student will now be ready to begin the harmoniOf these he will zation of melodies containing auxiliary notes. find a large collection in the Additional Exercises to Counterpoint. He should in the first instance select (or his teacher should select for him, ) simple chorals and such melodies as are not too elaborate and florid. If the theme selected contain many notes of short value {e.g.. No. on p. 2*2, or No. on X XX would be a grave mistake to put a separate chord to each note. If two such notes are a second apart, one of the two had better be treated as an auxiliary or passing note ; if they are more than a second apart, and the first is accented, they We adshould be considered as two notes of the same chord. vise the student to plan out his harmony, and to sketch in his p. 37,) it bass — subject, of course, to possible subsequent alteration — before middle parts. He can introduce auxiliary and passing notes wherever he thinks it advisable but he must remember always to take care that such notes do not make consecutive fifths or octaves with the harmony notes that immediately precede or follow them. filling in his ; Chap. XI.] SuSPSJfSWJfS. I45 CHAPTER UNESSENTIAL DISCORDS XI. SUSPENSIONS. (II) ter, 333. Of the unessential discords treated of in the last chapthe auxiliary and passing notes are used to connect two ; chords of neither of which they are component parts rarely used anticipations are notes of the the more harmony that follows, We have now to speak but not of that which precedes them. of another class of unessential discords, in which the dissonant note is a note not of the following, but of the preceding chord. Such discords are called Suspensions. suspension may be very simply defined as a noU of 334. one chord held over another of which it forms no part. The sounding of such a note as a note of a chord is called the preparation of the suspension ; the holding of the note over the following chord, to which it does not belong, is the suspension itself; and the ultimate progression of the suspended note to its place in the chord is called its resolution.^ are extremely simple. A governing the treatment of suspensions be convenient first to enunciate them as clearly as possible, and then to give examples enforcing the rules from the works of the great masters. 335. rules It will The general 336. I. Any note of one chord may be suspended over the following chord, provided that it is able to move by step of a second upward or downward to one of the notes of that chord. For example Ex, 258, H '"'JTA J v^^J^ -^r C: -' N^^IiTJ-^ Vi ii V* I f**=^ V^ I at (a) the D of the first chord is held over the chord of C, and moves down by step to the octave of the root ; and {b') it rises But at (f) there is no susby step to the third of the chord. pension because the D is a note of the second chord, and moves by leap of a third ; besides which a suspension cannot form a part of the chord over which it is held. (§334-) The suspension is indicated by " S." 337. The figuring of suspensions will be explained later ; we stop here, before giving further rules, to remark that, being ; * Evidently a suspension cannot be prepared by a passing would not be a note of the preceding chord. note, for that 146 unessential roots is ; Harmony. [Chap. XI. discords, they are not indicated in marking the the true nature of the chord is seen when the suspension resolved. We now proceed with our rules. 338. II. The preparation of a suspension (that is, the sounding in the preceding chord of a note to be suspended) must be This is shown at in the same voice with the suspension itself But if the in those examples were {a) and (J)) of Ex. 258. not prepared in the same voice, Ex. 259. e.g. — D I i the second note auxiliary note. would be not a suspension, but an accented 339. III. The suspension must always be on an accented beat of a bar (in triple time, either the first or second beat see § 189, note) ; the suspended note may be either tied or repeated ; and the resolution of the suspension must be on a less strongly accented beat than the suspension itself — latter 340. IV. If the suspension be tied to its preparation, the should be of at least equal length with the suspension ; it may be longer, but it should not be shorter. When the suspended note is sounded again, this rule is not so strictly observed; e.g. Handel. Samson. Ex. 260. 4 3 is not a part of the domia suspension, of the value of a dotted minim Occasional exceptions but its preparation is only a crotchet. from this general rule are to be found, as in the following passage flat Here the B in the second chord nant triad ; it is Bebthovkn. Mass in D. Ex. 261. where a suspended crotchet student is is prepared by a quaver, but the advised to adhere strictly to the rule here given. 341. V. The note on which a suspension resolves maybe sounded at a distance of at least an octave below the suspension but should not be heard above it, excepting when it is approached Chap. XI.] SirSI'SNS/ONS. 147 by step, and in contrary (a) motion ; e.g. (i) Ex. 262. r -'s This exception is illustrated in Ex. 261, where the D in the upper part, on which the suspended E in the middle of the harmony resolves, is approached from C. I mr^ Not good. Good. r m r^ 342. the VI. As a suspension is only a temporary substitute for harmony note which follows it, a progression which would is be incorrect without a suspension For example, not justified thereby. the suspension (a) involves the same consecutive octaves as are seen at {c) ; and (i5) the same consecutive fifths as at (</). This rule, however, is not always strictly observed by the old masters in the case of fifths, where the progression is less unpleasing than with the octaves. Ex. 264. ^^ ^ 1 Haydn. Creation. * 6 7 T 6 W :?= =t= ^^ If the suspensions are fifths is Ig7 6 =^=FP 7 omitted here, we have clearly consecutive between the two upper parts ; but the effect of the passage quite unobjectionable. A suspension always resolves on the chord over suspended ; but it is by no means unusual for the chord to change its position on the resolution of the suspension, as in the following example 343. VII. it which is Bach. Matthaus Passion. —6 — Here the G in the last bar of the alto is a ninth suspended over minor. At the moment of and the suspension is resolved on the first inversion of the same chord. The student will hardly need to be reminded that G and B in the bass are passing the root position of the chord of F resolution the bass goes to A flat, 148 notes. Harmony. But if [Chap. XI. resolution, the preceding chord the root of the chord changes at the moment of is not really a suspension. 344. It was said just now (§ 336) that any note of a chord can be suspended over the next chord, provided it can move by But to this general rule there are step to a note of that chord. certain practical limitations. £x, 266. S (a) !^ {i) , (a), the ninth, and at (/5) the seventh, are suspended over is here spoken of as a the root of the chord. Observe that ninth, and not as a second above the root, because a suspended ninth resolving downwards may never be at a distance of a second from the root ; otherwise its resolution gives the forbidden progression (§ 81,) from a second to a unison. At (f) the fourth is suspended over the third; and at '(</) we suspend the second (which can now really be one,) over the third. At (<?) and (/) we see the sixth and the fourth suspended over the fifth The upward moving suspensions at (^) and (_/") of the chord. are rare ; that at ((5) is somewhat more common ; but in general suspensions resolving downwards are far more frequently used than those resolving upwards. At D 345. The practical limitations of which we spoke just now are seen as soon as we try to make a suspension over any of the dissonant notes of a fundamental chord. The note above the seventh is the root, and the note below it (as we shall learn later, ) is the thirteenth of the chord similarly, the notes above and below the ninth, are the third and root, above and below the eleventh, the fifth and third, and above and below the thirteenth, the seventh and fifth. All these are notes of the chord ; and a suspension has been already defined (§ 334,) as a note of one chord held over another of which it forms no part. In practice, therefore, the only notes over which suspensions can be held are the notes of a triad the root, third, and fifth. ; — 346. In § 175 it was said that the rules given for finding the root of a chord from the figured bass (§ 174,) needed modification in the case of suspensions ; we must now show the nature of these modifications. At (a) in Ex. 266, the 9 under C would appear to indicate that we have here a chord of the ninth. But-when in the next chapter we treat of these chords, we shall find that the root position of a chord of the ninth will be accompanied by the minor seventh ; the absence of that note here Chap. XI.] SuSPENSIOtrs. 149 proves the D to be a suspension. At (d) the 7 cannot possibly be a chord of the seventh for no chord of the seventh can resolve upon its own root (Ch. VIII). At (c) the figure 4 cannot show that F is the root, for the G is not a part of the chord of F; neither, for a similar reason, can 2 at (r/) indicate D as the root ; for neither C nor G form part of the chord of D. The suspension 6 5 at (tf) is ambiguous, for the progression might possibly be vii I for this reason this suspension is less frequently employed than others. A good rule for the guidance of the student will be the following^: Whenever two figures next to one another (9 8, 4 3, 2 3, etc. ) are found under the same bass note, /ke second of the two being a consonance, the first of the two will indicate a suspension, in the absence of positive proof to the contrary. ; ; 347. clause, if The student will we vary Ex. 266 see what is meant by this qualifying (a;). Ex, 267. C: V F:V9 V7 Here the addition of Bb- changes the suspension into a genuine dominant ninth in the key of F. But 9 8 alone will show a suspension. 348. The suspensions shown s in Ex. 266 can be taken in 8. their inversions. We s first give the inversions of 9 Hz, 268, It will be seen that the figurings of the inversions (a) (Ji) (c) are identical with those of the chord of the seventh first and and its and third if mistake inversions. But the student need never make a he will notice the chord by which each is followed. As to (i/) there can be no mistake. A 7 followed by 6, a ^ fol- lowed by 4, and a % with both these notes remaining stationary over the following bass note, always show inversions of a 9 8 suspension. Therefore the 7 must not be accompanied by the 350.) This example requires no explanation . as in the case of the inversions of the 9 8. (V7. are all possible. fifth. Like the chord of the seventh (§§ 237-239). and interposing between it and the note of its resolution either a note of the chord taken by step or leap. being different from any which the student has yet met. . these notes being no part of the chord over which the suspension is held. by the sixth. as chords of the seventh.15° Harmony. 268 he has marked the 7. 349. we will only remark that the figuring of these inversions. If the student has accustomed himself to mark the roots before filling up his harmonies from the figured bass. will cause no risk of confusion. nor the \ [Chap. XI. 266 {/). they would be respectively iiiy. the 5 by the third. and We shall learn later that these chords \\\']d in the key of C. and 2. Supposing that in Ex. vcL'jb. giving the suspended note only half its proper length. 351. but that their treatment would be different. a suspenThis is effected by sion can have an ornamental resolution. r. X^^^^ Ex. We will now show the inversions of the 4 3 suspension seen at Ex. he will be able to identify these suspensions without any difficulty. m the progression would have been monotonous and weak. 354. because the The second crotchet of the quaver C is a note of the harmony. 272. 352. suspension at the last crotchet of the first bar. 273. lowing Ex. at the second and third. Though examples of this are not infrequent. the preparation of the suspension will be only of the same length as the suspension without its ornamentation. \^-n-. .. 274. 353. Occasionally in the case of an ornamental resolution of a suspension. 15' for the descending to C we had £z. second bar shows the somewhat rare and always ambiguous (§ 34^) suspension 6 5. Wfe have here some of the most frequently used suspensions. In the in fol- Bach. Our next illustration Schubert. Organ Fugue C minor." Handel.Chap. Messiah.] Suspensions. returned to D second quaver. XI. Ei. There is no 7 6 (the first inversion of the suspension 9 8). the method is not recommended for the student's imitation. Rosamunde. We shall now give a series of examples illustrating the Our first extract treatment of suspensions by the great masters. At the first crotchet of the bar is 4 3. Ex. will be a well-known passage from the " Messiah. 275. shows the root position of the 9 8 suspension. The last bar of this example also shows the rare first inversion of the suspension 6 5. The root position of the suspension 4 3 will also be seen in the last bar. XI we two inversions of the suspension 4 3 in the second bar. 278. St. 357. ^^ Mendelssohn. Ex. 277 the third crotchet is the second inversion of 4 3 compare Ex. gs g^r is ^ ^ r 1^ 1 2 — seen in the second bar the last inversion of the suspension 9 8. Ex. and the first the last inversion j inversion in the third. In the following example. P S 4- J i * J '-^r^. give examples of suspensions resolving up"Retardations". wards. in Ex. Ex. 355. 276 is the second inversion of 9 8. By far the most common upward suspension is 7 8 the suspension of the root of a chord by the note below it. see [Chap. 268. 277. ^A4 -I- I K±cn: sm Mass in D. In Ex. but there seems no reason for giving a different name to them. will The chord * — 356. their We shall now see the two suspensions 9 8 and 4 3 in second inversions. We now Some theorists call these — . Beethoven. 276. Paul. St. Paul. Mendelssohn. the third and fifth of the chord being at a distance respectively of the second and fourth above the ninth.152 Harmony. as be seen by reference to {b) Ex. 269 (^). 8 -|- Sonata. the eleventh (Chapter XIII. esting not only for the 7 8 in the second bar. Ex.7 8.Chap. 280 is interEx. 10. not on a triad. 279. i. but on a chord of When we come to speak of chords of the dominant seventh.] Sc/SPENS/OJfS.) it will be seen that this suspension might also be regarded as a second inversion of a dominant With the higher discords (the elevenths and thireleventh. Bach. ** show the first in- Gott der Vater wohn'uns bei. XI. 280. but because in the first bar we see the second inversion of a 4 3 suspension resolving. w Beethoven. as in previous examples." PC Ex. 281. .) we shall often find combinations which are capable of more than one explanation. teenths. 358. Op. No. ^ r £z. Ex. Bach. 7 6 5 6 The the stufirst of these examples is very rich in suspensions dent has already met with all of them excepting the one marked #. J J J-i f^Cr-h^-cT-o'^r I ^^ '' ^ £z. 279 is too simple to require explanation. 282. . The two examples next to be given version of the suspension . Organ Prelude in 153 E minor. that it is not so is proved by the preceding chord . 283. is suspended by a note a tone. for a second inversion of a dominant seventh never resolves on a mediant chord The C is therefore the suspension of the (see Chapter VIII) following D. Prelude 11. Ez.IS4 Harmony [Chap. Bach. the leading note in the upper The last inversion of the part being suspended under the root. 282 is rather different." Book 2. In the last crotchet of Ex." Book Prelude i. below it. Ex. 5 6. Though the 7 8 is the most common of the upward suspensions. 8. Wohltemperirte Clavier. 284. XI. •' show the other inversions of 7 2. same suspension is shown at Ex. 360. Before leaving the 7 8 suspensions. ** Wohltemperirte Clavier. 284 . we select a more modem passage. Ex. with an ornamental resolution. 230. . . Many examples our last extracts of this might be quoted from Bach . This at first sight looks like the triad on the mediant . 361. that it is rare to find this suspension with any otlier note than the tonic. it is by no means the only one. but as all have been taken from that composer. 362. The following examples Bach. It is not rare to find the suspension of a second under the third of a chord. in the first bar of which will be seen a series It has been already said of them in their first inversion. G. 283 the harmony is that of the chord of A minor in the second inversion. we would refer the student to Ex. instead of a If we had here a chord of the seventh semitone. and it will be observed that both the examples have ornamental resolutions. dominant chord. Here the root of the 359. the F of the alto after rising to G would fall to E (§ 239). PaiU.Chap." . 3. If two notes are suspended. and in Ex. Ex. 364. Two or more notes of a chord may be suspended at the same time. 7 6 Here the second of the chord is suspended over the third. 2 3 . Op. Ez. though somewhat more common in its first inversion. "Wohlcmperirte Clavier/' Book 2. Bach. 363. one part falling and the other rising to the note of the harmony.] SuSPENS/OIfS. if three or more are suspended. this is called a "Double Suspension" . 286. Quartette. 286 the suspension is a tone. Prelude h. Ez. No. 286. 287. it is usually called the " Suspension of a complete chord. . We give one example of each. The upward suspension 4 5 is extremely rare in its root position. St. 155 Ex. In both these examples the fifth of the tonic chord has the fourth suspended over it in Ex. The last bar of this passage shows a very curious doubling of a suspension . XI. the C is suspended both in alto and tenor. 288. 287 a semitone below the harmony note. Beethoven. i8. Mendelssohn. or a whole chord may be suspended over the following one. but the student would be more perplexed than assisted by the strange combinations which would be necessary. Cherubini. Here is a series of double suspensions. which : will require 365. these. No. The passage further a fine example of a sequence (§133)- 366. We conclude this chapter by a few exarriples of the suspensions of complete chords. further explanation. 4.IS6 JTarmonv. 290. in every case with an In the ornamental resolution which is frequently chromatic. Mozart. 291. and in the We have not figured fourth and fifth bars the two upper parts. [Chap. we shall find that the harmonic framework of the passage is the following Jz. the bass of this example. It will be remembered that unaccented If we omit all auxiliary notes are seldom figured (§ 329). first three bars the two lower parts are suspended. Ex. in F. is of course possible to figure them. After the explanations already . because no ordinary system of figured It bass will apply to such unusual and chromatic progressions. XL Mass in C. The following example is more intricate — Sonata. : We affords have marked all the suspensions. We no see here examples of double suspensions. Sonata. ^^^^m Bbethoven." Op. 367. No. 293. or the fifth of any chord to introduce provided that it can move by step upwards or downwards to the It will next note of the harmony. introducing suspensions at his discretion. 294. the third.] SUSPE^S/O^^S. this will probably save him many mistakes. XI. . he should harmonize melodies. 157 analyzing them Samson. 78. In working the exercises is now to be given. Ez. It may be well to remind him that when there is a suspension the root to be marked is that of f/ie chord on advised to mark his roots before When he has finished which the suspension resolves (§ 337). the student commencing the writing of the upper parts.Chap. able for this purpose. no difficulty in Handel. the exercises. Hellbr. (I) Moderaio. Op. " Promenades d'un Solitaire. In cases of doubt. 5. given. be best for him suspensions that resolve upwards very sparingly. No •^. £x. the student should have for himself. 14. Ezi 292. He will find chorals the most suit- and he should remember that it is possible to suspend either the root. XI. b una i'i no Aft nonce nee c 76 76 78 76 76 4— b 4— 6—9898 5 6 7 6 76 57 4- (VII) Allegretto.Harmony.8 7 76 6 5Jt4 — —#6 4322— 2— 5 4 1)6 —5 765—3 — 9 8 7 3 98 76 4 7 — (V) Andante. 4S96 43 45—5—7— 22—2—4— 2- 6 786ff76 76 8 7 6 7 S— 45 t . 3 6 9 6 4 $4 2 6 t6 4 3 7 — 6 76 4Jt 4 2 9. [Chap. ^^ ' =P=:e^ =i=tt ^t ^\A J IJ tst ^ (VI) Andante. Chap. XI. t]5 — 6 66 5 43 9876 J6— 4— 6*4 4 2 J5 6J5 767 — 7—76 — — 2 6 — 4 2 — 54 —— — 5 ( XI ) Moderato.] SuSP£NSIOJfS.) Trangtiillo. IS9 =t=t —8 —3 4 2 78 56 767846 4 — 4—432 112 — 4— 8 — 3 Prr^rH^-Jtpd^J^ J14 36 56565656 ^^ 47—8 S — — (VIII) Andantino. 76765—98766—6—786 — 5 — 54—3 4 — 4—2—6—4—65 4— — 2 3 98 9898 6—566—23 356767664 23 — 4 4 2 76 76 76 4— 7823 6— 67 4J1 54 2 6 5—43786 22— 235 22— 23 4 5-43781)6 4 9843985698 — 7 6—5— 4-3- • . 4ttl5 {IX ) 67 66 5 — — 6 4 — (6 — 4 3 6 7 6—4 7 4 J Moderato. 439 6 43 6 76 71161178 J6 '6—4 05 4 2 — — 5 2 — — 98 7 6 4 — 76t]5 (9 8 2345 2 34 2 6 J— (XII. ^— i^ r5 1 r6 :^=ff=?2: 7 ==t 6 .^4 d=^4Czn3=f^JLJ4^4 7 (XVII) Hymn 6 Tune. XL 3 6 4 2 —6 —4 2 8 3 6 '6—766667 4398 7666 4 — X X6— 67 4 3 5 4 2 5—5— 7—6 2—3— 4— — 2— 2 4 2 6 J43 9 J]5 8767643 6— 5— 4 43 43566—7- — 54—3 (XIV) F:W«. 4 4 (XVIII) Hymn 4(tt4 2 76 — 5— J6 4— 2— 7 6 2 — 764 4—2 76 6657 4—3 . [Chap.^ jc "" i -I -^ s) 9 7 gl 8 6 g 6 ^ 6 4 r~-^ r i I rJ - I r ^^"^ i*" ^ J> J J J *4 - ^^ 6 6 6— f 4 — Tune. i ^i'?i [- j-4ii4^ r 9 6 \- r 3 I f :3^=t= . 5 6 43 6 765—9878 — 4 3 6 4 — 4366 78 43 4 2 5— J6S7 866 2— 4 3 4 5 2 — — •43 6 4 2 76 66 6— 7 4—4 • 3 (XV) Double Chant.i6o (XIII) Moderaio. Harmony. 295. i6i CHAPTER XII. root position. and the chord thus obtained will be a chord of the dominant ninth. present in the chord. omitted 371. XII. and of a minor ninth in a minor key. We know that a chord of the dominant seventh is the same in major and minor keys but. It will be seen that a chord of the ninth contains fiveO As most music is written in four parts. is generally the fifth of the chord that is it but if the root be not in the bass. either major or minor. we add another third. THE CHORD OF THE DOMINANT NINTH. it is added when the ninth this chapter. . or. 369. "C: V9 c: V9 just as a A chord of the ninth is is marked V9.] Chord of the Dominant NmtH. — — Ex. sixth. it is seldom present at all. The Student has already learned (§ 36. The seventh is almost always either notes. this new note will evidently be at the distance of a ninth above the root. though its own progression will be largely affected by them.) that every chord is formed by the superposition of thirds. chord of the seventh indicated by V7. resolved. one above another. 368. and a minor key. . as the ninth above the dominant is the sixth of the scale one of the two notes differentiating the major from the minor key it is clear that we shall have a chord of the major ninth in a major. dealt with in Chapter VIII.) is v (See example 302 later in In the. The rules for the treatment of chords of the seventh given in Chapter VIII are therefore still to be observed. one note mustn evidently be omitted.Chap. If nO further * The only exception to this rule is the chord of the augmented which will be treated of in Chapter XIX. but its derivatives (§ 252. * If to the fundamental chord of the dominant seventh. if not. . and the only new rules to be learned will refer to the ninth itself. 370. The chord of g the dominant ninth in root position will 9 7 in be figured 2 in a major key. Inversions of the chor d of the ninth are therefore very rare.) are" more common than the root position of the chord itself. The addition of a new note at the top of a chord does not affect the progression of the lower notes. the figuring of the We next show the minor ninth resolving on Beethoven. the chord of the ninth at * appears in its complete form. 297. : Sonata. indication is given.) Ak 374. a dominant eleventh. 373. Ex. In that case the ninth mostly resolves before the rest of the chord. and frequently does. XII. and the fifth introduced instead (which rarely happens). P 372. a chord of the ninth can. Observe that in the second bar is a passing note (§ 317. Unlike a chord of the dominant seventh. We first give examples of these. the student will easily be able to and auxiliary notes. In such a chord should be as here shown. [Chap. The ninth may proceed to any other note of the chord . and the root position of the dominant seventh remains. instead of proceeding to the root. but by far the commonest progression is to either the root or the third. As this piece is for the piano. C: Ic The chord in the second bar of this passage. in which there is no restriction as to four parts. go to the third of the chord. it may either rise a second or fall a seventh. Op. V9V7 With the help of the distinguish the passing analysis. to. its root i. 296. this had better be shown in the figuring. case. Ex. as we shall see The first in the next chapter. the third bar is a dominant major ninth . the seventh and third should be added . Mendelssohn. thus. if either the seventh or third is to be omitted. No. 298. Fiist Walpurgis Night. resolve upon its own root. If the ninth. . minim of falls to its and V7 remains.l62 Harmony. is. the ninth root. Ex. Concerto in C minor.J^-4 Ez.299. In our next two examples. . and in the second bar the minor ninth rises an augmented second. (^^^ Ex. both taken from the same movement. to the third of the chord.] Chord of the Dominant Ninth. In the first bar of this passage the major ninth rises a tone. ^ ^_Beethoven. ''> 163 Beethoven. 300. 53. Sonata.Chap. XII. Op. . 378. or on a chord belonging to another key. it will frequently sound harsh in that position. provided that the ninth proceed direct to the generator while the third remains stationary. while the third and seventh move as in the resolution of the dominant seventh. The following examples show both the major and the minor ninth thus treated : . it will resolve either on the tonic chord. will As the major ninth if placed below the third of th be a major second below that note. spoken of recommend the student to restrict himself <^" ^i^" in § 266. It is therefore generally better to put the ninth above the third. first and second bars of the above will be seen in the soprano and tenor parts hidden octaves of a kind that are specially prohibited (§ 76). the passage therefore has some analogy with the change in position of the dominant seventh. third The be thus stated general rule illustrated in the above example may The major ninth should only appear below the : when the chord resolves upon its own root. £x. But to this rule there is one exception of some importance. A dominant major ninth can always be placed immediately below the third. 379. if not justified. When a chord of the dominant ninth does not resolve upon its own root. Stabat Mater. is taken by another part . If it resolve on the tonic chord. resolutions on the root and third of the chord.bar of this passage shows in the upper part the ninth At the moment of resolution the ninth resolved on the seventh. The second We 377. the ninth falls one degree to the fifth of the chord. by the tenor in the first half of the second bar imitating the first half of the soprano of the previous Between the bar. 304. as in the following example :— Dvorak. The infraction of the rule here is palliated. with all notes present. They are. "An den Sonnenschein/' Op. 36. No. 380. Ez. Dans les bois. When the fifth is present in a chord of the dominant major ninth. m ^^ ^•f r^z T^ i -g^rjrrr^ This extract shows the third inversion of the dominant major ^ ^^ Op. (See Exercises I and at the end of this chapter). Though seldom found in the root position. We give two examples. it will generally have the character of a dominant pedal (Chapter XX). 4. it must rise to the third of the tonic chord in the resolution. and is below the ninth. V — Ex. Impromptu. however. We shall see an example shortly.Chap. 306. Op. It was said in § 370 that inversions of the chord of the ninth are extremely rare. 307. 381. Schubert. Schumann. of a dominant held through harmony of which it is not necessarily a part.] Chord of the Dominant Ninth. 306. 308. go. No. Ez. this progression will often occur in the derivatives. somewhat more frequently to be met with when the ninth resolves by rising to the third. Heller. f ^ . When the root is found in any other part than the bass. 3. The student must remember that the C |} and in the bass are the real bass of the harmony. that is. 86. Here its B If is the first inversion of the dominant minor ninth. to avoid consecutive fifths. XII. No. Ex. i6s 4. In Chapter VlII we saw derivatives of the dominant seventh.) was no longer present. there will remain a chord of the seventh upon the leading note. We now give the inversions of this chord. The derivatives of the dominant ninth. " 6 . especially of the minor ninth. in § 253. like a chord of the dominant seventh. If in chords of the ninth the dominant be omitted. generator oi the chord. 307 the ninth resolved upon its [Chap.i66 ninth. the lowest note actually present became the root. 309. In Ex. Ex. are of great importance. and it was pointed out (§ 252) that when the dominant (the. the chords in brackets. XII. vii°7 vii"7 (V9*) (V9i) As explained indicate the harmonic derivation of This derivative is figured 7. own root j here resolves upon the tonic chord. from which it is easily distinguished by the nature of the intervals above the root. it Harmony. 382. we 383. Ex. and the rules given apply also to vii°7^. the student We first show the should be quite able to do this for himself.] Chord of the Dominant Ninth. instead of moving by step. just as is the case in the first inversion of the diminished triad (§ 261) . but we may also regard the B and G as accented auxiliary notes introduced before the tonic chord. 5. we shall no longer mark the roots under the examples . Kreisleriana. 167 inal seventh. both in major and minor keys. chord in root position. ) in the inversions. and in various positions. at the first crotchet of the last bar a modulation to F sharp minor is made by sharpening the tonic of E for the new leading note . its resolution is inWe may conteresting. sider the chord as resolved on IV^ . Te Deum. to save the fifths which would otherwise occur when E descended to D (§ 380). To save space. to leap a fourth downwards to the tonic. the vii°7 in the latter key . minor key." Ex. 312. Cantata. as in for y\\°b this the following: Schumann. 313.Chap. Graun. 311. because two explanations are possible. Our next examples show the chord Bach. ^nui i. . In the third bar we have the chord vii°7 . XII. vii°7f 386.) it is not uncommon for the bass. £z. 16. Op. — " Wahrlich ich sage Euch. in a 387. No. This passage begins in E major . We now give some examples of vii°7. But in the second inversion of chord (vii°7^. 82. 314. Op. the first (Ex. Adelaide. and the following chord as transitional dominants. and have the same which generator. 315. Ex. Both second and third inversions are shown in the fol- lowing: Ex. its resolution . Bach. ^^^^^^^S in the second bar here later. Johannes Passion. < '^ ^^f JL A.1 68 resolved Harmony. Ex. 388. The second chord which will be explained It is is a chromatic chord. in Ex. Mendelssohn. 315. In the following passages will be seen. upon a dominant triad on a dominant seventh is the more frequent.) and resolved on its own root. 316. unusual for a diminished . #_ * *_ Beethoven. is In the following passage. ^s. Paul. pfj^ B 1 ^ V In both these examples the resolution is on \b .) inversions of the chord vii°7. seventh to resolve. 389. as here. because they are both dominant chords of E flat minor. xu. taken as a transitional dominant We regard both this (§ 295. St. Variations. is in B flat minor. Mendelssohn. we see the chord of the diminished seventh (vii°7) of E flat minor. Ex. [Chap.) and second (Ex. 316. 315 the is delayed by an accented auxiliary note.317. upon the tonic chord. Mozart. The following passage shows all the positions of the chord of the diminished seventh. We shall therefore reserve the greater part of the exercises on the 393. seventh. we minor key. Like the chord of the dominant seventh (§ 266). only such notes are to be taken into account as are actually shall see this principle more fiilly present in the chord. Ex. here used chromatically in a major key (§ 510). If the root and third are omitted in the chord of the shall dominant minor ninth. and its most frequently used form. being resolved in the position in which they last appear. We illustrated when we come to chords of the eleventh and thirteenth. As the chord is a common chord. 318. and in considering the progression of the upper notes of a fundamental chord. like vii°. Ex. the chords of the dominant ninth. and do not mark it as a derivative. 320. As it is a dissonant chord. \\°b. 319. Ex.Chap. is. — (V9O (V9^). 169 390.J * ^ ' I 4 I ' I . it will be remembered. the chief derivative of the chord of the ninth. thus ii°. and ninth) form the diatonic chord on the supertonic of the major key. is more often employed chromatically than diatonically. I 391.] Chord of the Dominant Ninth. and especially their derivatives. we shall in future mark it as a derivative. the remaining notes (the fifth. King Thames. * * * I ! . a diminished triad. for the root and third are the only notes with which the seventh and ninth are dissonant. XII. This chord is now a concord . have the supertonic triad of the F^" # This chord. The chord of ninths A till in Chapter XVII we deal with the chromatic ninths. is a derivative of Nf)d. few exercises on their diatonic treatment are all that will . and a derivative of Vg^r. Its first inversion. \\°b. the diminished seventh. we take no account of its harmonic origin. If both root and third are omitted in the chord of the dominant major ninth. can change their position. 392. In many cases the diminished sevenths are inbe needed here. .170 Harmony. . ] i wh^^^. XII. troduced as transitional dominants.^-^ 3 6 5 4 6 — r ir> 6 6 — ri^?>7rr-J^4^^ — 7 966 74 436 I I 4 5 98 7 41 S j4 b 6 6 b b98 5— Jt— 6 43tl4 2 this 76 J]5 7 56— 6 is 5— . ( IV) Andantino.^-^vy^\i-M^^^ Moderato. m^~^-n. 8 (V) $ 4 (2 6 4 $4 3 6 {6 5 6 4 6 5 . (I) Moderato. . —The second chord of bar a passing chord and the unusual order of the figures in the third crotchet shows the progression of each part. 76 II NoTfi. [Chap. -f-v.Chap. ^] 9 . I I I 9 117 7 J15 6 6 4 4 2 6 S4 I 6 $4 3 6 8 7 (VII) Andante.4 6 — l?6 114 114l> 432 — 6 5 4 J2 — — — 6 bV l?5 JI6 6 6 7 5 J) 5 4 5 (VIII) Double Chant.^ . *=r 8 =f=F=t 16 —6 5 4 3— l=t: J4 3 6 S6 4 3 6 6 4t| 6 t{6 6 9 7 7 5 (? 5 240) 7 8 23 4 4 3I|2 7 6 Jl. J J i ^^r "r i r cr*- ru J -lj . XII.^ -W-44J 6 4 b I74 =^=b^ 7 87 4 3 6 6 98 7 b7 4 — m^ (X) Hymn Tune. 1.J 1 ^ i' -. ] Chord of the Dominant Ninth. and we have a chord of the dominant eleventh. 212. for a fourth is either the inversion of a fifth (§ 172. as in Ex. % Vll I I 395. As the eleventh is a dissonance. The bass would be figured thus 396. excepting occasionally when it is resolved on its third the eleventh may. spoken of in the last chapter. XIII.) or a suspension (§ 344). let the student refer to Ex. but the seventh is usually present. where the chord in the second bar is a dominant eleventh in its root position with the 7th and 9th. % C: 3. Unlike the ninth. The chord of it will therefore — — : Ex. S21. £z. this will be at the distance of an eleventh from the root. but the ninth of the chord. CHAPTER XIII. 394. being the tonic. It is sometimes figured 11. SE Vll b'^l. will be the same in major and minor keys . But the two notes are really quite different . occur at the interval of a fourth above its generator. THE CHORD OF THE DOMINANT ELEVENTH. tains six notes . which seldom appears at a less distance than a ninth from its generator never. It is by its treatment that we distinguish between an eleventh and a fourth. the third is mostly omitted in accordance with the general principle given in § 375. It has . Either the fifth or ninth of the chord is also generally omitted . The new note. the eleventh in its complete form conbe necessary in four-part writing to omit at least two of these notes. will be major or minor according to the key. fourth. 397. at the last chord of the second bar. indeed. 297. and the remaining figures of the harmony indicate the true nature of the chord. 322. but more frequently 4. and often does. a 3 — largest been already said that in figuring a chord the numbers are generally placed at the top. As an instance of this. the usual resolution of which is by descent of a second. another third be added. [Chap. If above the chord of the ninth.17a Harmony. if present. It will be noticed that the eleventh is the octave of the and we shall see directly that it is frequently figured 4. though occasionally this note is only added when the eleventh is resolved. No. Here. In this case the eleventh remains to be a note of the following chord. XIII. 8. in marking the roots. the eleventh descends to the third. which. ninth. 21. latter on a The passage : Schumann. with the third and ninth omitted. the chord of the eleventh may resolve either on its own root by which it is not meant that the eleventh leaps to the root. but only that it resolves on another dominant chord. at the end of the chapter. a minim later. to the third. But of these only the . e. usually a seventh or ninth or it may — — seldom occurs if the root be present in the chord of the eleventh . beginning with the highest interval. it will go either one degree down. chord in the next bar. Like the dominant. the discord often resolves gradually.Chap. This passage illustrates a point that is worthy of notice. which revolves on the tonic Such cases are of frequent occurrence. Novellette. we indicate by the letters b. which will be explained later (Chapter XVII). as here. Weber. J- '^ ' £x. or one degree up. elevenths. leaving a chord of the ninth . Here the third chord from the end is a supertonic minor ninth. 173 398. and rises to the third as below." 400. the higher discords (ninths. at the third bar. or thirteenths.] Chord of the Dominant Eleventh. the A in the bass being a dominant pedal (§ 381) the chord * is a dominant eleventh.323. c. at the third bar. as in the following resolve different root. 399. d. though even then it is possible to resolve it on a tonic chord. Op. When the eleventh moves. When in the root position of this chord the eleventh rises to the fifth. . to the fifth of the chord.) ^^ Ex. can of course have five inversions. Duet.) resolve. on their own roots. 324. (See also Exercise XI. " Se il mio ben. the ninth is usually also present. the ninth resolves on the root. When leaving a chord of the seventh. The chord of the eleventh. f. as it contains six notes. In the following example. the effect of an accented auxilbut if it were. [Chap.) that with the higher discords combinations were often found that were capable of more than one explanation. Bach. C. Owing to the harsh dissonance of the eleventh against the third. Fantasia in C minor. the B should be natural (§ 307). fifth. In the first The present is a case in point. and some are We first give a few examples of inversions. 403. of great importance. In Chapter XI it was said (§ 357. as auxiliary notes a tone below the harmony note were not unusual in the middle of the eighteenth century. 401. and remember that the figuring of any chord does not necessarily show its nature. for its preparation is too short. p. the first inversion of this chord is very rare. ^^^^^ Ex. and containing the same intervals as the chord shown above. bar of Ex. The eleventh here has much of iary note . the eleventh resolving on the third.) is often used. 280 will be seen a suspension bearing the same figuring. Eb: Vllf \^c the root. £. Organ Prelude in Eb. It would also be possible to consider the E in the second bar here as an accented auxiliary notej but its harmonic importance . though the derivatives of other inversions are very frequently met with. We give one example. but merely indicates the distance of the upper notes from the bass. Bach. seventh and eleventh of the chord are present. Our present example cannot be regarded as a suspension . it could be explained in either way.174 Harmony. It is probable nevertheless that the composer so regarded it. The second inversion of this chord is much more common than the first. 325. If the preceding chord were a minim. Observe the figuring. 402. XIII. second inversion (Viif. $ rS= ii7 ^^ ii°7 (VI I. which at unable to give an example of it.) This chord has a perfect fifth in a major. and a diminished fifth . The chord is therefore in reality a derivative (as we shall see presently. instead of rising. the B in the bass would have fallen. first sight looks like an example. falls a semitone. is clearly treated as a pedal note above the other parts Schubert had looked upon the note as a part of the chord.Chap. as in Here the ninth (the eleventh from the generator. 404. 327. It gives a chord of the seventh on the supertonic. vii"9 (Vii*) rising. Ex. but the student is not advised to imitate them. The E !> and D at the beginning of the last bar are chromatic passing notes. Ex. The derivative of the first inversion is as rare as the inversion itself. 406. employed.) instead of Ex. as here. for a special purpose . and we have a doubled leading note. The fourth and fifth inversions are also very seldom met with. Parsifal. Schubert.) (VI I.] Chord of the Dominant Eleventh. and for the same reason the harshness of its dissonance. 329. Rosamunde. 325. We quote a passage in which this very harshness is introduced for a special dramatic efiect. 405.) of the dominant eleventh below an inverted pedal. the root for if — Wagner. 175 makes it better here to look at the chord as a genuine chord of the eleventh. The derivative of the second inversion of the chord of the eleventh is much more important. Such violations of rule are sometimes to be found in the works of the great masters. Ex. and more frequently used. The third inversion of this chord is so rare that we are In the following. XIII. 328. being perfect. and the root of the chord either remains stationary. is free in its progression . nant is still the generator. the fifth. ^^ («) {i) {<:) (J) . xin It must be remembered that. or the leading seventh (§ 384). ) falls one degree to the leading note. or leaps a fourth or fifth to the dominant. Ex. like a chord of root (§ 252). 407. eleventh. but in a minor key both fifth and seventh are dissonant. major key. the supertonic has now become the The chord is simply figured 7. the only dissonant note is the seventh. This chord can be resolved upon either a dominant In the former case. the seventh (the original or a tonic chord. In a the dominant seventh. 330.176 Harmony. though the domiin a minor key. [Chap. Se C: ii7 (Viic) lb ii7 \c c: ii°7 \b ii°7 \c (Vllf) {b') (Vllf) (Vlif) The progressions at approaching a cadence Ex. Let us apply this test. latter either in the (a) (b) (. 121. and at . e. 323).) (^) E ^i^ Ex. ing a second inversion is not broken here. Ex. but may be first or second inversion. 177 must not be in root-position (see § 195). as the chord ii7 is not an inversion of another chord. — m^ ^ directly Vii°7 c: ii°7 (Vg^) (VI I. it will be necessary to look at its resolution.) In order to be sure of the nature of the chord in such a case as It must be this. trary —we shall see what this means —the common chord on which the discord resolves will be the tonic chord of the key of the passage. but only the derivative of an inversion. if resolved on a tonic chord.) that a a But if we dominant seventh by the nature of its intervals. will define a key as surely as the dominant In the absence of proof to the conseventh itself (§ 241). 333.Chap. and (rt^) are by no means uncommon in an example will be seen in Chapter VI. compare the two derivative sevenths.] Chord of the Dominant Eleventh. Note that the third rule given in § 188 for approach. 334.") and ii°7 in a minor key. In the last chapter it derivative chord of the seventh could be distinguished from that their intervals are identical. the seventh remains as the root of the tonic chord (Compare Ex.g. remembered that a derivative of a dominant discord. was pointed out (§ 382. {a) {b) {c) ii°7 \\\°^b ib ii°7 (Vllf) (Vgr) (Vilf) At («) the chord resolves on the chord of E flat major. In this case. xiii. we shall find 409. vii°7 in a major key (the "Leading seventh. it will suffice to give them in 411. as in Ex. as at (a) below. bass). Ex. fourth. It can resolve either on a dominant or on a tonic chord . 410. the third (the one degree. as at (c) proof. the chord in this position is commonly known as the ' Chord of the Added Sixth. and the fifth and seventh each fall one It is also possible to resolve it on V7(/. the is inversion. this case both root and third are stationary. the derivatives of chords of the eleventh. (a) latter will (i) Ex. and at (rf) by the chord of At {e) the chord is the diminished seventh in the same key. be seen that the bass of this chord is the subfrom the fact that the notes which it contains are those of the subdominant chord with the addition of a sixth above the bass. dominant ' ' ' the former. .178 Harmony. any position is possible for the latter. Both these passages are therefore in E flat But at (c) the same chord is followed by the first inmajor. is C minor. and the note above a tonic is always a tone above it. 337. G could still not be a tonic. rises 413. If ii7^ resolve on a tonic chord. is approached by a semitone from above . But here we have the followed by the common chord of G. XIII. most important. Here the root of the chord remains stationary. 412. Chap. 329 (a). which is followed by the tonic chord. as the progressions will be the same in a major and minor key. and fifth inversions of the chord of the eleventh. both in major and minor keys. that the chord for its root. the be generally in root position. is by one of the most frequently used of It will . and the key.] (^) on the dominant seventh of the same key. the fifth and seventh moving as before. Even if the A were natural.: i^ C: \qb first :g= iiji: EE iiyrf i ii°Jc ii°7rf c: ii°74 (Viirf) (Vli^) (Vu/) (VllflT) (Vll^) (Vli/) far the all Of and these. because it is approached by a tone from below. If ii7^ resolve upon a dominant chord. as at {b) . ii'jb. The three inversions of iiy will evidently be the derivatives of the third. referred to above. in degree. is not a tonic chord G. version of the chord of C minor. and (^). The G is a dominant here. ) « Ic . stationary often used as the antepenultimate chord in a cadence. in the last bar but one. their treatment is the same in major and minor keys. it is resolved on vi^r. here treated as a passing chord between two positions of iiy. tonic. Ex. except at (c) where the bass note (the seventh of the dominant. xm.) are much 415. resolves on the second inversion of the Mendelssohn. 122 and 186 it will be seen thus employed. The chord iiyi. 339. St. IV it iijd (Vil</) resolves on the root position of the less common than ii7^.Chap. In Ex. 121. {i) (. 414. and to give a few examples of their employment. 340. 338 (<:). now give two ex- is We amples in which it resolves on the tonic chord. 178 we find the chord (ii°7^) in a minor key. when it resolves on a dominant chord. As in other positions. Ex. 338. just as we saw it in the last chapter (§ 385) in the derivative of the third inversion of the dominant ninth. The second and third of Vii^ and Vii/.] Chord of the Dominant Eleventh. In Ex. As the notes have the same progressions as in the positions already described. it will be only needful to catalogue them here. 333) ] and the step. C: iiy* I* ii7i \c iiji I The seventh is now other parts move by (compare Ex. tonic. Beethoven. as in Ex. Op. Sonata. 53. 341. Paul.) leaps to the tonic. 179 Ex. In Exs. E: Vji: U iiy* Ic (Vii^) Here the chord In the following. inversions of ii7 (the derivatives {a) Ex. The resolution at (c) is the most common in this position. We Ex. Messiah. In our next illusthis volume. Cantata. which is also by Bach. J . wir gehen hinauf. give two examples. f ' ^' r' . very rarely resolved other- We g^ve two examples. one in a major. Ex. I F: V7(/ lb m\°b I (V7^) ^l^c (Vii^) We leave it to the student to discover the passing and auxiliary If he has carefully studied Chapter of notes in this passage. —" Sehet. Wtf 1 -^ . Cantata. [Chap.i8o Harmony." ! J-^J Ex. The last inversion wise than on its own generator. iiic has the character of a pass- X ing chord.) (ii?^/.) is 416. 344. MatthauS'Passion. — Handel. he will find no difficulty here. J J Ex. 342. tration. Bach. and one in a minor key." I-' Ex. Bach. XIII. 343. 1^'' J \ ^4- f ib I ^^p i b : m°b (V^c) ii°7* UV ' = Lj" 1 I p ivi ii°7<- u (Vii. 346. 346. Bach. —" Gott ist uns're Zuversicht. AH that is needful. when this is fixed. The rule is Every diatonic discord in any key is either a dominant discord. § 391). but. we do not analyze these chords as derivatives (Compare. perfectly easy to calculate the distance of the intervals above 418. therefore. ninth. (I) Allegretto. its 417. and to the chords of the thirteenth. with their derivatives. and eleventh give the triad on the subdomiriant. with their derivatives. and its dominant known. If the generator. analysis of these passages. XIII. free in its progression. and fifth of the chord are all absent. In the first bar. because will be very beneficial to the student to make his own. though both may contain exactly the same When in Chapter VI rules were given for finding the notes. it becomes it. it was said that.Chap. we shall see an illustration of this. (§ 409). is to determine the key. We therefore now give a new rule. 324. Exercises. third. the seventh. as explained in like : that of vii°7 § 409 . earlier in this chapter will be different. The figuring of the chord iiy in various positions (§ 383). will. to be dealt with in the next chapter. and the eleventh (the fifth of the chord) is now in the As with the chord of the supertonic major key. . which will apply equally to chords of the eleventh. for the discords above the ninth.) is in the bass throughout. it i8i We give no. root of a chord from the figured bass. 347. f^ IV ^hF As none of these notes are dissonant with one another. and the 4 and 2 of the figured bass show the eleventh and ninth of the chord respectively. the root (which is here also the generator. how to distinguish the derivative of a ninth from that of an eleventh. the rules needed modification. as with vii°7 the intervals of the chords We have already seen. Ex. or a derivative of one.] Chord of the Dominant Eleventh. the chord is a concord. If we turn to Ex. be the same as that of the dominant seventh. 8 4 2 6 5 {66—666 5 4 $4 4-2 6 4 3 S 616 606 §4 5 6 87 4J5- (VI) Andante.4 6J]6 7 6 6 7— 6 — 4 3 5 b — 7 6 6 7 { 5 4 (IV) * • / \ Allegro. [Chap. 6 5 4 2 6 J.I82 (II) Larghetio. ^1 4 J =1= c-j J If- r^'TT^r 8 J „j 4 J 157 6 4 43- (III) Moderato. . Harmony. XIII. I I I 6 6 6 7—98 4 3 7 — 3 6 5 7 6 4 4 2 6 — 4 3 6 4 9 7 6 4 7 g 4 4 966— 7t|6— b7 454b5 4— 2 :1=* — 3 — 6 5 6646 542 -i—r 793 7 4 5 (V) Andante. $4 3 6 9 7 4 7f5 4 t 117 7 115 S — - 4 2 6 5 6 5 4 2 6 4 3 6 7 6 S — — 3 4 3 6 6 6 7 4 . ] Chord op the Dominant Eleventh. 6 6 b9 % 4J J7 — 8 (78 {43 7 6 6 667V67 4— 45 6 t (VIII) Andante. ^=-f=- mS 3=t= jg=S2: 64 5 2 t=t: 6 i 2S 6$t4 5 2 6 6 j] I I 6S4 6 2 677 46 3 4 6 5 87 m (X) Hymn Tune.Chap. 183 (VII) Andantino.xiii. ^^^f^^^^^^^^f^ ^ ^^ J I I (IX) Double Chant. -f=^\r-nr-:a^u:^ 5 m= m . XIII.) Hymn Tune. 5 7 4 2 6 76 56 7 5 65 43 6 6 5 6 7 7 tl 6 7 s (XIV) Hymn Tune. [Chap. wtm f=j= 7 3t=5t 6 =t=!= 41 2 4 -1 — 117 = =t*: 1|5 J 4 3 J 6 4 Jir' 7 6 t . (XIII. Hymn Tune.1 84 (XII) Harmony. is in itself a consonance . we indicate by V131J. In actual composition. 348. one of the two notes which differentiate the major and minor key. Ex. As the chord of the thirteenth contains seven notes. the forms of the chord that we shall meet with will be various selections of four notes each sometimes only of three—from the possible seven. It will be seen that these chords contain every note of the diatonic scale a point on which we shall have more to say later in this chapter. 422. in marking our roots. This completes the series of possible dominant discords . P C: fe V13 c: V13 • 421. which. when the chord is in root position. that while the latter are all dissonant to the root. etc. for the next third above. This is partly because most music is written in four-part harmony . 419. partly also because the notes on which the dissonances resolve will generally not appear with the dissonances themselves (§ 375). Vi3^. the chord in its complete shape in both keys. frequently figured 6 than 13. we shall have a major thirteenth above the root in a major key. to confound the two This will become quite clear as tinguished by their treatment. and a minor thirteenth in a minor key. XIV. In analyzing his harmonies. ninth and eleventh of this chord is. 423. Another third placed above the chord of the dominant eleventh gives a chord of the dominant thirteenth.] Chord of the Dominant Thirteenth. As the thirteenth of the dominant is the mediant. 420.Chap. we it proceed. up to the last inversion. THE CHORD OF THE DOMINANT THIRTEENTH. the thirteenth will be the dominant itself. An important difference between the thirteenth and the other higher notes the seventh. they can always be disnevertheless. Vi3(r. he . . But it is extremely rare to find them in their complete shape. therefore. which has the thirteenth in the bass. exactly as we have We now show already seen (§ 368.. and the series will evidently recommence.) with the dominant ninth. can of course have six inversions. — — — — . A large number of and the student will find in derivatives are also to be met with his exercises and examples many combinations of figures that will be new to him. being the octave of the sixth. the thirteenth. the note is far more It would be a grave mistake. 185 CHAPTER XIV. It will be seen that the major and minor thirteenths are When.) . is identical with the chord iii^ (in the minor key III' (5). All the lower notes in a chord of the thirteenth. Here it will be not the fifth. This chord. Whether we are to regard it as a mediant chord or a thirteenth will depend upon the way it is followed.) or. comparatively few are in actual use. the thirteenth generally falls one degree to the fifth (see Ex. * We do not say "the second inversion" here. A chord upon its own — 426. I. which we have already met with among the diatonic triads of the key. (See Ex. and the treatment of the chord is far less complicated than might be imagined. account has only to be taken of such notes as are actually present. up to and including the eleventh.) that every diatonic discord in a key comes from the dominant of that key of the utmost assistance. while it is evident that the last inversion * of this form of the chord will give the root position of the mediant triad. rises to the seventh of the chord . 427. because the second inversion of a chord has the fifth in the bass (g 161). care must be taken in the resolution to avoid possible consecutive fifths four out of the seven notes of the chord of the thirteenth are possible. 425. The most -convenient way of dealing with them will be to take each combination sepaiatelyj speaking at present only of diatonic thirteenths. third. less frequently.xiv. thereperfect fifths above the major and minor ninths. as with other chords that contain dissonances. (§ 417. it may exceptionally leap to the third. obey the rules laid down for their treatment in preceding chapters. the thirteenth will mostly either fall a third to the tonic or remain as a note of the next chord. Root. 349. If it resolve on a tonic or submediant chord. though this form of the chord contains only three notes. P it will be seen. form of the chord. fore. but the thirteenth. If it resolve upon a dominant chord. that will be in the bass. will find the rule given in the last chapter — — 424. it being remembered that.1 86 Harmony [Chap. will be dealt with in a later chapter. 354. Other resolutions are possible . We shall begin with those most frequently used. is the simplest Ex. containing only three notes. upon another dominant chord —or upon a tonic or submediant chord. Though an enormous number of combinations of This 428. and thirteenth. (Compare § 380). 350 later. of the dominant thirteenth may resolve either generator that is. being chromatic. the ninth is present in a chord of the thirteenth. but these. Our first example will show the chord resolved upon a dominant seventh. as the thirteenth is itself consonant with the root. '. 187 If the next chord be the submediant. 3=^ p.br. Ez. In four-part harmony. r~l -I . No. though less good. But.Chap. . the thirteenth a third to the root . but if it be followed either by dominant or tonic harmony. the best note to double will be the root. c: i V13 i V13 falls i In both these examples. 6 Bb: I IV* Ic iiyi V13 B I Dvorak. - if V13 V7 g: Here the thirteenth descends one degree to the fifth of the chord. ^ | Ex. 362. and at the same time the doubled root in the upper part falls to the seventh. Verdi. It is not advisable to double the minor thirteenth. 351. the resolution of this form of the chord upon the tonic chord. as in the examples to be given directly. it is best to consider it as a mediant chord .] Chord of the Dominant Thirteenth. Stabat Mater. Waldscenen. of 431. Op.n^ 6. XIV.j^ | N. in a major and a minor key. Ex. In figuring this chord the thirteenth is almost invariably marked as a 6. p. 429. 82. next give examples. We Schumann. or a first inversion on the next degree of the scale.360. Requiem.| .n. because it makes with the third the interval of a diminished fourth. to double that note when it is major. 430. it is possible. such progressions will prove that it is employed as a dominant thirteenth. The root will here be the best note to double. The last inversion of this form gives. Harmony. This is the commonest and the most ^ form of the chord. while the other remains stationary . XIV. it is not a secbass. third. Mots et Vita.) falls to the (§ 429). we thus get another form of the chord. 353. it may indeed be laid down as a general principle that. inversion of this form of the chord is rarei ^^^ Observe that. than the root position. Gounod. Ex. seventh. («) Ex. Ex. because of the harsh dissonance of a second which it will make if below that note. This new form of the chord resolves in its second inversion.r I is the last inversion of the dominant thirteenth. .i88 of the tonic chord. .. as ond inversion .) as the In the second chord of the second bar third of the tonic chord. will therefore be wrong to double the in other chords (§ 190). 434. [Chap. 364. the thirteenth itself being doubled One of the thirteenths (that in the bass. II.365. that note should. It is also very seldom good to place the third above the thirteenth. unless it be in the last inversion. The first No further explanation will be needed. of which we shall speak presently (§ 438). when the thirteenth is in the bass. though it this inversion is figured ^. useful and (b) thirteenth. Our next exthe notes of the mediant triad in root position. fifth. G: vi V Vi3^Vi3.' ^ 7 6 3 7 6 J C: V13 It is c: V13 important to remember that the thirteenth should always he above the seventh. the thirteenth remaining (§ 425. ample will show its treatment as a thirteenth. 433. Root. as already said. upon the tonic chord. 4J2. i Chord of the Dominant Thirteenth.) that the higher discords can be explained in more than one way. orists who do not admit the existence of chords of the thirteenth many of would give this explanation. it is possible in each case to regard the thirteenth as an appoggiatura (an accented auxiliary Those thenote. 436. Op. xiv. 654 : Ab: It is clear that I Vi3iV7^I the chord. But this would not account for . not uncommon. We give a few examples in various positions. In our last three examples. Sonata. Beethoven. 358. 125. Sonata. be at the top of the chord. Op. If this chord be resolved on dominant harmony. Op. because the thirteenth would be below the seventh.Chap. 356. 189 with extremely rare exceptions. ~&1. 435. No. Schubert. the thirteenth falls to the fifth. 10. It has been said in an earlier chapter (§ 357. because there can be no second inversion of this form of it contains no fifth . ) to the fifth of the chord. Ex. Ex. i. 122. while the other notes remain. f^ Ab: I \^ l . Sonata. the third inversion is Sfohr. and in a major key.^ ^^d ' II V/} I Vi3fl' \b The last inversion of this form of the chord is unavailable. 367. which follows it. Our next illustration shows the first inversion of the same chord. in which the thirteenth exceptionally leaps to the third. x.190 Harmony. If this form of the chord resolve upon a tonic chord.. Cr f- . while the third and seventh are resolved as in a chord of the dominant seventh. Schumann. XIV such a passage as the following. \nf . [Chap. Schumann. No. 359. will suffice. ^^"^^^WW^W^ 437. One example Ex. 360. 99. the thirteenth will fall a third to the tonic. Bunte Blatter. Op. Ex. Faschingsschwank aus Wien. third. again. . few in if he remember what has been said in § 423.Chap. the seventh falls one degree to the fifth of the chord. Herr. it would be possible to explain the F ^ as accented auxiliary notes to the E and of the lowing chord. Notice that here.) on a dominant chord. The only note which is restricted in its proIf this chord is resolved gression is the seventh of the chord. ScHUMAHH. we shall defer speaking of them till a later chapter. our exercises . The . Bach. . Numerous derivatives of the chord of the thirteenth are in more or less common use but. 440. i £e c: C: IV7 (Visa-) IV7 original seventh of the chord has now become the root and the thirteenth is now the seventh above that root. There remains a chord of the seventh on the subdominant. (as is most frequent. are present (§ 391). The only important diatonic derivative is that in which the generator. with which they make dissonances. —" Nimm von uns.] Chord of the Dominant Thirteenth. N- £x. the student will have will We shall introduce a no trouble with them. Cantata. none of the lower notes. -1 191 Paradise and the Peri. Both the third and fifth of the chord are now consonances for. Ex. 361. XIV. as these are nearly all chromatic. one in a major. but they are not important enough to require to be dwelt on in detail. and one in a minor key. Various other forms of the chord of the thirteenth are occasionally to be found . as in the two following examples. 362. and fifth of the chord are all wanting." Ex. 363. and G D% fol- 439. though they are the ninth and eleventh of the original chord. Judas Maccabaeus. 418). 361. 4- * ^ m==r~'r~? J.) ^ ^^ Ez. The only example we have met with is in a well-known passage in the finale of Beethoven's Choral Symphony. are all consonant. in The chord in this form can also be resolved on the 441. we shall find that. Paul. [Chap. But. it can hardly be so in is D minor. quoted by Macfarren in his ' ' Six Lectures on Harmony " as a specimen of the its chord in complete shape : Beethoven. but as a diatonic triad. the seventh of the chord. T 442. 366. 365. when the seventh will remain as the third of the chord. It was said in § 421 that it was extremely rare to find the notes of a chord of the thirteenth present at once. and the root of the chord would being respectively the eleventh and thirteenth. at the top of the a seventh. As the note which was the thirteenth it is now longer always advisable to keep Ex. though it contains the same notes as a full chord of the thirteenth. . it is no chord . all 443.) of a chord of the thirteenth give the chord of the submediant. 354. The key be A D and F . resolves on F . XIV. we do not analyze it as a derivative (Compare §§ 391. (Compare Exs. eleventh. and the note on which a dissonance resolves may not (except the ninth with reality. The three upper notes (ninth. 9th Symphony. 364 it is in the tenor. whether in a major or minor key. St.192 Harmony. Ex. and thirteenth. G. But. As the notes of this chord. second inversion of the tonic chord. Ex. 364. when we come to examine the treatment and progression of this chord. Mbndslssohn. as we already know (§ 232). have also major ii7. though it contains a perfect fifth and minor sevSimilarly. Before we proceed. if we add a seventh to the supertonic triad of the major key. we shall have a secondary seventh the scale except the dominant. in the next chapter. for. above each of the triads of the major key given in Ex." but dominant seventh is also diatonic. perfect fifth. with a major instead of a minor seventh. For instance. By this term are meant all discords which are in accordance with the key-signature. are. it will be a secondary discord . ondary Discords. does not apply to auxiliary notes . 444. which have major thirds. the characteristic intervals of a dominant. iiy is a derivative of Viir (§ 406). we shall have a secondary discord. something must be said. 367. and vii°7 of Vg^ (§ 382). in accordance with the keysignature. the unusual feature is. root. third. XIV. Ex. when found together. 193 the root. which have minor sevenths. to meet with every note of the chord so accompanied. if we add enth. on every degree of ^ With enth. restriction. these chords is found in the complete chord of the dominant thirteenth (§ 421). and the simplest explanation of the passage is. are accented auxiliary notes to the notes of the tonic chord. or even two auxiliary notes employed in this manner . forming by themselves a chord of the diminished seventh. sevenths * . eleventh. about a class of discords to which much more importance was formerly attached than is These are what are known as Secthe case at the present day. B t} to the tonic chord of C major. This (§ 375. Notice also that in none of these chords the is the characteristic interval of a fundamental discord diminished fifth between the major third and minor seventh to — — be seen.) however. iii7. in connection with chords of the thirteenth. and contain any other intervals' from their root than a major third. and fifth. thirteenth. name "diatonic" instead of "secondary. to treat of the chromatic elements of the key.] Chord of the Dominant Thirteenth. thirteenth and root. The chord I7 consists of the elevseveral of these chords and third of the dominant thirteenth. with which they are sounded. root. I7 while and IV7. Some theorists use the is the latter term certainly preferable. as the . and minor seventh. and vi7 of the Every note of each of ninth. 62. it does not contain a major third. of the thirteenth. IV7 of Vi3^/(§ 440).) be sounded with the dissonance.* 445. or "fundamental " discord.Chap. that all the upper notes. together It is common enough to find one. iii7 ii7 iii7 IV7 V7 vi7 vii°7 we have already made acquaintance. which. vi7 and vii°7. If we place a seventh. that the seventh must be prepared that is.) and that it must resolve upon a chord the root of wluch is a fourth higher than its own. Joshua. For instance. that is itself restricted by the With all these secondary sevenths. on a chord the root of which is a fourth above its own. according to the old rule. though with differing intervals. Bir: I .194 Harmony. XIV. i^ Handel. and the dominant (the generator. It is also possible to resolve it on a chord the root of which is a second above its own. 332. Though it is by no means compulsory to prepare the seventh. as in a chord of the ninth (Chapter XII) . 448. presence of the root below. 446. or even of its being itself the generator. The following interesting passage shows a series of these secondary sevenths. have also minor thirds. which has now become the seventh of the chord. [Chap. 363. and each resolved. should be particularly observed with regard to these secondary sevenths. but only with their relations to one another. and resolved by step downwards. if the seventh has appeared in the preceding chord. — — — — Ek. But it is not the ninth which is restricted in its movement by the presence of the dominant. The old rule for the treatment of secondary sevenths was. 368. each in its third inversion. In speaking of the various discords. 337 and 344. in which the seventh above the root is always to be considered as the dissonant note. it has more than once been said that in their treatment it is only necessary to This rule take into account such notes as are actually present. it is the dominant. as in Ex. rule just given . the student has not to concern himself in the least with the relationship of the various notes of the chord to the dominant. the root of the chord is the ninth of the dominant. A similar series of secondary sevenths. like a dominant seventh. 447. 331. quite irrespective of its relationship to the generator. Notice that in each case the seventh is prepared by the third of the preceding chord. in the chord vi7. must appear as a consonance in the same voice in the preceding chord (§ 334. can also be obtained in the minor key.) is the seventh. for no discords except suspensions absolutely require preparation it will be advisable. to keep it in the same The best resolution in general is that prescribed by the voice. the student will find instances of it in the resolution of iiy in Exs. Chap. 195 4 .] Chord of the Dominant Thirteenth. XIV. (I) Moderate. [Chap. . between them and genuine chords of the thirteenth. XIV.196 Harmony. 6 S 1 — — 3 86 Irs 6 7 7 766 — 4 2 6 — 5 — — 4—65 6 7 2 3 (IX) Hymn Tune. 197 (VII) Double Chant. ^1*1 1% J f- wm— d ^ r I J * y I -t f I 1I r 6 7 4 (X) Hymn i Tune.] Chord of the Dominant Thirteenth.Chap. If- ^^yg^f^ r J 3= 6 3= I 6 i=i-isl 4 6 2 ^^ ^ I ---^ 9 7 7 ^ (4 2 5^ 2 - 6 6 7 4 J . XIV. § «5 r r yt f i L^4Bizm-r^ (XI) Hymn 5 6 Tune. one on each degree of the scale.198 Harmony. To make first this clearer. then. three chords as before. . As all music must be in some key. CHAPTER CHROMATIC TRIADS XV. all of which conform to the key-signature. as a key consists of twelve notes (§ 32. XV. But. 371. it follows that every chord must be either in the same key as the chords that precede it. Ei. it was key was effected by putting an acci- altered note thus dental before one of the notes of the key we were quitting. In the preceding chapters of this book we have treated of the whole of the diatonic material of a key. 203 the sharp before the F in the third chord of {a) takes the music from C into the key of G. consequently the chord i>: must be chromatic in that key. Now if the chords preceding any one chord be in the same key as the chords. if the chord have one or more accidentals before it. and chords that contain them are called Chromatic chords. The third chord {%) looks as if we were about to modulate into the key of G but the fourth and fifth chords absolutely define the key The chords preceding and following the chord of C (§ 241). the new key being established by the chords that follow. 454. Thus in Ex. will take the we will vary Ex. 203 {a). —THE 452. The first two chords are. But it was pointed out in § 278 that no single chord can ever define a key. When shown that a change of treating of modulation in Chapter IX. or in the same key as the chords that follow it. but will follow the We third chord differently. following that chord. CHROMATIC SCALE. .) there are five other notes remaining. Such notes are called Chromatic notes. it will be a Chromatic Chord in the key. 453. the becoming a diatonic note of the new key. and it has been seen that this is all obtained from seven notes. in the key of C. each of which requires an accidental. [Chap. as before. marked * are therefore all in the key of C . but which induces no modu- A D : —A lation. the first inversion flat is therefore regarded as diatonic in its of the chord of relation to the new key. They are. I I . XV. but that the suggestion is not confirmed but contradicted by what follows. The first question to be answered is therefore. chromatic chord. the note inflected by an accidental is regarded as belonging to the key in which it is diaBut if there be no modulation such note forms part of a tonic. From what keys do we borrow our chromatic notes ? The answer is very simple From the nearest related keys . 199 455. derstanding of the subject. by dividing A : — each tone into two semitones. of C minor. we could borrow both the chords of E major and of A flat major into the key of C. 0) At * of (a) there is a modulation to flat . 458. are enharmonics of one another can never be both used in the harmonies of the same key (§ 308). It will be seen that in both our last examples (371 and 372 {by) the accidentals introduced suggest a modulation to some one of the keys in which those accidentals would be diatonic notes. they are borrowed. If. Let us take another illustration. the fifth above (the dominant. Hence we get the following definition chromatic chord in a key is one which contains one or more notes foreign to the signature of that key. we Let us take the diatonic scale first deal with the minor key. For a reason that will be seen later in this chapter. tains only twelve notes. for example. and It will greatly aid our unViOt from which. if we remember that all chromatic chords are borrowed chords. To know which name to give to . and change it into a chromatic scale.) and the fifth below (the subdominant). as a key con457. there must be some limitation to our borrowing powers. borrowed from some other key. and in this latter case the fourth chord is a chromatic chord in C minor. 456.] Chromatic Triads. in fact. this time in a minor key. or we shall have more than twelve notes in the key. moment's thought will show us that. is followed by chords which define the key of C minor. that is. and here it is not considered to belong But the same chord (*) at ((5) to the key of C minor at all. and are only recognized as chromatic by their being followed by chords belonging to the key into which. we But two notes which should have both G ^ and A t? in that key. Whenever a modulation takes place.Chap. and is the same ascending and descending. # —^L =3 (=5 **- Y- ^ '1/= ^=Kg l|^_li_4i - This form of the scale is somewhat easier to read. we have only to remember that the keys from which we borrow are G minor and F minor. though more rarely. [Chap. and is also the same easiest rule for writing the : The following No ' and minor keys. with a different notation from that just given. At}. This form of the scale is called the ' ' harmonic chromatic scale. as it has fewer accidentals. As a matter of convenience. intermediate notes.200 Harmony. 460. b& tto !>= flg ' -' ' I f. This is probably the chief reason for its frequent adoption because we find that in the descending chromatic scale the correct notation is usually . D must be D \f. from G minor. borrowed. also. 373. P |. Between Al^and Bt) there will be two Fjf (from G minor). harmonic form : Ei. for example. the intermediate notes. the chromatic scale is often written.:^-^-'^ ' chromatic scale correctly is the degree of the scale has more than two notes upon it. G. and neither tonic nor dominant can be chromatically altered.chromatic scale of C. sometimes. A |f is written instead But F jt is almost invariably retained. 459. 376. Ex. without key -signature therefore The note between C and neither F minor nor G . especially in rapid music. xv. The scale of of B t?. and G \ are often substituted for D 1?. We first give the scale of C minor. t?. — : Ei. which The whole scale is is diatonic in both F minor and G minor. and from these keys we borrow only the diatonic notes. we show the chromatic scales of he should compare with the scale in Ex. especially in ascending passages. which ij and of in major A A 374Ei. and Bt?. 375. borrowed from F minor minor contains C \. . In the. C will then appear in the following form. C jf. E t* and A b . That the student may see the application of the rule just given. Between E b and F we shall have Et[ (from F minor) and between F and. 374. to write it correctly. because it is a note of a nearly related key. How is the suggested modulation to be First averted ? There are three principal ways of doing this. as it is not uncomform to find the flattened fifth instead of the sharpened fourth. if therefore in every key the tonic is the most important chord we follow the chord containing an accidental by the tonic chord of the already established key.! IV jvi of which would be destructive of the true character of the key. It is impossible to include any keys less nearly related than the dominant and subdominant in the borrowing keys withIf. XV. for instance. . the mediant and submediant are only found once. and render the tonality obscure. we should introduce chords which would destroy the special character of the minor key.) that the introduction of a chord containing any chromatic note always suggests a moduand lation to some key in which that chord would be diatonic the next question is. The form of the scale just given is called the " melodic chromatic scale " . for inout bringing more than twelve notes into the key. the feeling of tonality is not disturbed.] Chromatic Triads. the leading note of G minor. we borrow for C minor from D minor. its submediant. we shall introduce C sharp. the chromatic scale is written in four different ways.. — in this 461. which they seem to write in many cases on no system at all. the great masters are often extremely careless in their notation of the chromatic scale. major keys. and all the other degrees of the scale twice . Thus from F major we should have the following chords : («) Ex.* 462. thus saving an accidental. cannot co-exist in the key of C minor with F sharp. it is the same as the harmonic scale. In Beethoven's concerto in G. . at the foiu'th and fifth chords. stance. 201 adhered to mon ^most likely for the same cause. An example of this method has been seen in Ex. the next sharp key after G minor. G flat. 372 . * In actual practice. if on the flat side we go beyond F minor to B flat minor. all 464. we borrow only from the minor keys a If we borrowed also from the fifth above and a fifth below. It is important to remember that in borrowing chromatic chords for a minor key.Chap. 463. It was said above (§ 456. . {b) (c) IS. (Ji). it must be remembered that in ascending. claim. while in descending. But we already have D flat as a chromatic note . and the latter has the prior Similarly. The manner in which the root of the third chord is marked will be explained directly. 377. Ex 379. neutralizing the suggestion. be contradicted. on the other hand. and what chord it is in that key. it is neceswhen the root is itself the chromatic note. to indicate the fact by an accidental placed before the Roman numeral. The bracketed figuring below shows the key from which the chromatic chord is borrowed. We now give a complete list of the chromatic common chords in C minor. The student need never confuse the bracketed analysis of chromatic chords with that of derivatives (§ 253). not I5II. we prefix a sharp. way of averting modulation is by the immediate contradiction "of the Thus. the position is also always different. or vice-versa. even though the note may actually be a natural as in Ex. the position of the chords is the same . sary. varied from that given in Ex. like that of the One suggestion balances the other. to follow one chromatic chord by another borrowedfrom a different key either a chord borrowed from the dominant by one borrowed It is. c: 1 wi II III V (g: *-*. is immediately followed F sharp which suggests the key of by F natural. in derivatives. bvii (f:V) (f:VI) (g:V) (g:VI) i) (f: iv) . Here the I'll shows that the second degree of the scale is lowered a semitone. as the root is different. 371. that the suggestion of the second chord should. 372 {!>). because here D \ would be the flattened supertonic of the key. The second. as in the fourth chord of this passage.202 Harmony. 377 (c). needful from the subdominant. The third method of averting modulation is. In marking the roots of chromatic chords. in Ex. [Chip. will illustrate this method of treating chromatic chords. The the feeling of the original tonality remains unimpaired. the root be a note of the diatonic scale chromatically raised. and first. of course. 465. If the passage were a semitone higher. If. in C sharp minor. 468. XV. if he only remembers that in the former. following progression. and the chord in question were that of D jj instead of D I?. G — Ex 378. V7f \b hWb \lb ic V7 (f:VI*)(g:V*) 467. All the diatonic material of the neighbouring keys can be borrowed for chromatic chords. 466. and perhaps the most obvious. the chromatic note in the following chord. it must still be marked bll. it will not be needful to consider them at present. and the rule for its treatment. as we know. The following will be a modulation to the subdominant key. Calvary. and in this case care must be taken not Evidently. ) the chromatic chord has the character of a passing chord. and. 379.) as the final chord minor key. only the first three are The chord at {a). which we deduce from the . m^ ^' n^F^=^^ ^ ^ I \b Kb II vii°7 VI V) \\°b {e:Yi) (f»:V) (Vgb) (e : (Vgd) third crotchet of the third bar is the chord (c) of Ex. The Spohr. It will be seen that in both these examples (and many more might be given. In a minor key I is seldom used in any other way . we have already met with (§ 229. the second inversion of the tonic major chord. ivb Ic \c Vll V9 V7 I {Vgb) (e:V. As But it can also be used chromatically. Exi 381. Our next example shows of which we shall speak presently. 203 triads of F minor and G minor can also be borrowed ." at *. 380. examples will show how this is to be Avoided. derivatives of dominant discords.Chap. b: Vb 111 vii°7 i — ' . in the such. it the so-called "Tierce de Picardie " is — not considered a chromatic chord. the tonic. Presto Agitato. being a major chord on often employed.) Here we see the chord first as "chromatic. The diminished and augmented — 469. and comparatively seldom used. XV. but these chords being. Ex. at the end of the passage as the Tierce de Picardie. 470. if followed by the chord iv there to leave the key. Mendelssohn. Of the chords given above.] Chromatic Triads. There is no rehowever. in Ex.note of the subdominant key. Organ Prelude in C minor. if only there be no modulation. [Chap. 379. because it is a prinaary note in both the which and into which it is borrowed. keys. 472. 471. Ex. v\\1b vP'Jc (Vgf) it is (Viif) followed by a chord of the diminished seventh. and proceed to the semitone The third must never be doubled. because it on the other side. The second chord (b). This form is frequently met with than the root position. Bach. here the chromatic chord is followed by V^. to double either of the other notes." a name for difficult to give a satisfactory reason. and in its first inversion one of the most frequently The root is here the chroemployed. The first inversion of this chord is generally it is which much more the "Neapolitan sixth. Sonata. S. It is possible. In the following passage.) must be approached from the semitone on one side of it. 57. XV. that the third of the chord (the leading. is the leading -note of the key from which the chord is borrowed. from Ez. and the third of the chord will be generally the best note to double. of the chromatic triads. 383. striction as to the chords which shall follow this chord. is one of the most important. practice of the great composers is.204 Harmony. Here as known ^ . Op. 382. matic note. J. Beethoven. g: i vii° vii°7ar u i bll Vb The Student will easily recognize the auxiliary notes . The second inversion of this chord is also sometimes. the student to his make Handel. 387. and 388 by the second inversion of the tonic chord. It will be here used as a transitional dominant in A minor. . Mass in Bb . Schubert. £x. though more rarely. The analysis of these passages being very simple. XV. illustrating most usual progressions. the chord * is followed by the diminished seventh of E minor. merely saying that in Ex. Messiah. 384. At Ex. Haydn. 387 the chord is followed by a dominant seventh. seen that these three examples illustrate the three methods of averting modulation explained in §§ 464-466. 388.] Chromatic Triads. 473. 386. Op. some of minor. 141. Sonata in C jt Ex. Ex. 385.Chap. we leave it to own. 205 its follow three examples of this chord. £z. at Ex. to be found. chord is subject to the same rules as regards its third as in the root position. If. before the chord * because none of the keys in which this chord is diatonic are "borrowing keys" for B flat. both third and fifth being chromatic. being the leading-note of the key from which the chord is borrowed. if this note rises. [Chap. more usual. as in Ex. It is very seldom that II is followed. as marked in our analysis. either upwards or downwards. it should be followed by some position of the tonic chord. may never be doubled (Compare § 470). 371. Der Fliegende Hollander. though this passage begins in B flat. {c) in our list of chromatic triads. Bb: I ^'\ d : iv J &-'b ' ^^ (a = W\i°b\b \c V7 i V) Observe here that. either the first or second inversion is much . or there will be a modulation . as its third is now in the bass. as we shall see when we speak of the chromatic chords of a major key. Wagner. frequently also the 9th is added to it. it may be followed by any chord of which the subdominant is one of the When used in its first inversion this notes. It is comparatively seldom that this chord is found in the simple form we are now describing. . 379. It is a Ex. If the third falls there is more choice. major chord on the supertonic. 474. Generally the 7th. to the subdominant of the key. XV. 476.3o6 Harmony. The third chord. the third fall a semitone. is no less important than that last spoken of. it is clear ttiat it cannot be followed by the dominant chord. and is the dominant chord of Here the the dominant key employed as a chromatic chord. It must always move a semitone. there is evidently a modulation to D minor. The second inversion of the chord is very rare. and special care must be taken with its treatment. on the other hand. I Lthe thj rr] pf tViTs r. We now give a few examples of its employment without these dissonant notes. it should be followed by the second inversion of the tonic chord. The third.liflfd risp a spmitrtnp (to the dominant). as will be seen in the following chapters. as here. 475. by the root position of the tonic chord . root is the only diatonic note. Obviously. i II* vii°7ir (Ct: Vi) (Vg^ i* the third of the chromatic chord note of the following chord. Wagner. 31. though possible. illustration of the "balancing" spoken of in § 466. falls a semitone. and the resolution of this minor. minor. last example of this chord Ex. . 379) {e). Tannhauser. used in either the major or minor key. if the key were D minor. and B i} is a (a?) («) and (y") 477.) in A.5) ' ' u (d:VW) (Vg^) (d:VW) The second chord of this passage is clearly the Neapolitan sixth" (§ 472. Op. The remaining chromatic chords of Ex. which also belongs to both keys . a chord borrowed from the subdominant key is followed by one borrowed from the dominant. Ex. No. Beethoven. We give a few examples: — — Ex. latter chord on the chord of E flat proves the key of G 478. 6. 392.] Chromatic Triads. 379 are very rare. the C Here at * we see an excellent in the first chord would be sharp. Mendelssohn. 391. 207 2.Chap. a: i bll* iv \\i°Tc \b — bll* \U (e: V. Op. 390. which last is followed by the tonic chord In our of the key in which both the preceding are chromatic. we shall see shortly that it can be It is followed by V7. r u I g: (di nib V7 VI \U) In this beautiful passage the chromatic chord III^ is approached from the key of G major. The minor chord on is the dominant (Ex. Sonata. Sonata. the rarest of all when it is used the minor . XV. 2o8 Harmony. [Chap. Dvorak. xv. Spectre's Bride. third of the chord will rise a semitone to the leading note. / . No. Brahms. Spohr. provided always that they are followed in the same key from which they are approached. The Sun. progression marked under each a.] Chromatic Triads. 398< Goring Thomas. Deutsches Requiem. 209 Ex. Ex. C: I \Nc I 11 IV Ic (G: V) Ex. Mendelssohn. i. 395. We now further explanation will be give examples of some of these chords.Worshippers. the — — 481.Chap. J . hA Ex. C: V last five \i bill (g= Nc^-jd^cVb V7 arpeggio of Vy. \c (e: \c ic) V The minor chord on the dominant Ex.n. ) js subject to same restrictions as regards its third as in the minor key (§ 47S) . 397. the remaining chords are free in their progression. 396. 120. VI) (The chords may also be analyzed as an . XV. Op. (and we do not advise the student to use it. 394 (/) if used at all. The major chord on the supertonic (f. No needed than is furnished by the rootpassage. Idst Judgment. ) should be similarly treated. (bl7: VW) Jagdlied. XV Mass in D. G: I lb Ic (g: frVI \c \b I IrVIf \b \c \ VI) p. (g: VI. 400. Sonata in B. 54. 399. . Concerto in A minor.n. Beethoven. [Chap. Op. Op. £z.) Exi 401i Schumann. (f: \yb) Ex. Schubert.Harmony. 147. Beethoven.Chap. Sonata Fathetique. . -^ We will give Exi 403i one example of each method.] Chromatic Triads. XV. (VII) Moderato 8 Be 6 bB 56 tl 6 4 14 2 76. [Chap. XV.6 b5 6 5 6 as 4 4 6 4 b7 pg^^^^^§Jm^ 6 Jtfer^ ^ 6 «4 2 6 } 6 86 f5 % 6 {6 65 J 15 4t (IX) AlUgrello.Harmony. . .. jj . — 6 6 t — 5 .. 213 ~ 6 4 6 5 7 b 8 7 (XII) Andante.. - 7 i a allegro.. XV... 6 ^ 7 i -^^ *e=^ r - 1 f-^^r It I J fl -3b5 6 I75 86 4 3 I75 _ ^ 4-43 J 6 — 7 — eF=F=B . 64 b be b— 7fl6 7 5 116 6 6 li'S 667 — 5465 2 3 ^^S 8 7 (XIV) Larg-ketto... J4 2 U 5 2 .. ^-b J — r 8. ^^^ (XIII) Un poco 6 t{4 J* 6 He i|6 4 6 l>6— 6 2 5 —/ 116 i ^ I 6 6 6-:. — 6 J4 6 4 ... _ 6 7 6 5 (XV) Moderate.] Chromatic Triads.Chap.. 3t=P= t=t= 6 6- |4 2 6 ^^ 4 It if eiwi:e=^ Jg-U-U Jt —6 ^^^^m J6 6 7 4 4 8 5' 4 3 . XV. (XVII) Hymn 6 Tune. (XX) Hymn \&.%it4 r — Tune. tt* B * 4 2 6 7 5 6 6 V ^ =t tI6 117 6 6 4 4 $ m. ^^T"rr^rtvT^rT"tp¥ 6 5 6 i . . 7 ' (XVIII. [Chap.214 (XVI) Double Chant Harmony.) Hymn Tune. -y—ri< *6 7 ^ US 6 be I.j 7 ^ 8 7 i virFf^^^ ¥56 J 6 {4 2 5 6 4 4 4 2 6 6 4 8 7 3 — (XIX) Hymn Tune. ) it is to be omitted. as being much more frequently used. *J 7 7 tt5 % C: (G: II7 c: (g: t II7 V7) V7) third of this chord. being the leading-note of the dominant key. but that they are borrowed from neighbouring keys. We will take the former of these first. Just as we can borrow all the coromon chords of these neighbouring keys for chromatic purposes. and more important. 379 (c) and 394 (c). and become chromatic only when they are not followed in the key from which they are borrowed. 483. and gave rules for their treatment. nant key is the supertonic.] Chromatic Sevenths. The Supertonic Seventh. and the dominant of the subdominant key is the tonic. with the addition The third of the chord is chroof the seventh from the root. and must be marked in the figuring. being the dominant seventh of the dominant key. and examples of their employment.) it occurs in the supertonic chromatic triad should either rise or fall a semitone . for a minor key. the chromatic common chords of both minor and major keys. CHROMATIC CHORDS OF THE SEVENTH. will be the same chord which we saw in the last chapter at Exs. £x. As the dominant of the domionly of their dominant sevenths.Chap. XVI. we can also borrow In the present chapter we speak all their dominant discords. the chords with which we have now to deal are usually described as chords of the supertonic and tonic seventh. The progression as when It (§§ 474> 475. and the three minor keys with We saw in §§ 468. 479 the derivation of all the same tonics. It was shown in the last chapter that the chromatic notes and chords in any key do not belong to that key in the same sense as the diatonic chords. and for a major key its domi-f nant and subdominant majors. the minor keys of and subdominant. . 215 CHAPTER XVI. for the dominant 484. is subject to the same restrictions as regards its 486. matic in both the major and the minor key in the latter the fifth is also chromatic. It was also pointed out that the only keys from which we can borrow chromatic chords are. unless (as not infrequently happens in root-position. in the . 485. 405. — ** Ach. and in the by some chord of which the subdominant of the key But we occasionally find that.ai6 former case latter Harmony. as in the following example in one of Bach's Cantatas: Ic. in the first informs a part. version of this chord. by when the third rises. wie manches Herzeleid. Gott. not but by V7. XVI. Cantata. 406. — Bach. [Chap." /[#^ Ez. . it should be followed by the tonic chord. it is followed. 410. The fourth chord from the end of the passage. Ex. used as a passing chord (§ 480) . Notice also that at the beginning of the passage we have three consecutive chromatic chords . 490. We have here in the second bar an excellent exa'mple of a modulation effected by taking a chord as diatonic in one key. 8th Symphony. . 411. in Ex. * E.Chap. looth Psalm. In the first bar is seen the rare chromatic chord i in a major key. 4th Mass. XVI. (Compare Exs. 491. ! . Peout. and the other being free. or to its Here the seventh octave. ^M Ab : "fWWWT < 5^ C: II7 *r :3=^ V^b V7- ^ bVl| (G: V7) fifth of the dominant chord. while in the second it falls a second to the third of the dominant seventh. bar is a tonic pedal. We next give two passages in which the seventh leaps. but the fifth of the chord proceeds to the note which was the seventh.] Chromatic Ssvenths. . J I J- J^-^-^^—A T' ^ Bb: is A ?==^ II7 (F: V7) doubled. shows the seventh rising to the The A flat in the first Haydn. 395 we saw the chord in its second inversion . More frequently the seventh is not doubled. because no two adjacent chords are borrowed from the same key. but in the first the seventh remains as the fifth of the next chord. will be explained in the next chapter. 194. 217 bi II7 the third falls a semitone . 404 in the last chapter).) one remaining as a note of the next chord. here it is in the first. Our next example Ezi 409i Beethoven. the feeling of tonality is not obscured. 195. and leaving it as chromatic in another (Compare Ex. marked itiv°7. 4-JEx. 361. but because the bass moves to the note on which the seventh would usually resolve. is [Chap. Schubert. also .* . Ex.413. '*. wahr'r Mensch und Gott. J J. Die Zauberharfe. c : I Il7^ Yjd \l> vii°7 V7i5 i (f:V)(g:V7i) (V9. -I j^^-i-^js= vis^- Vi3^ (b: II7 vii°7 (b: vii°7f) V7) (V9*) first two bars of ^his passage have been already quoted in Ex. here so simple that it is superfluous 492. Our last example of the root-position of this chord given for a different reason. 409. N i^*^ H . chord. 414.2l8 Harmony. The next extract. to prove the key. to The harmonic progression mark the roots. We now Few give some examples of inversions of this explanations will be needed. Cantata. in a dominant seventh the leap would be wrong. We have here an illustration of the seldom used progression spoken of in § 240." . The 493. 412i is Schumann. We repeat them here.}) see an illustration of the freedom of the seventh of the chord. first inversion. _r I Paradise and the Peri. In the third bar of this example we see the seventh rising to the fifth of the following chord. showing the second inversion. -. XVI.. Ex. we 494. —" Herr Jesu Christ. which here leaps to the root of the next chord (§ 487) . I I Ex. ' ' '^ In our next example of the Bach. Overture. not as in Ex. •^ ^S= «iv° (II7*) °i fiv°. dominant. so with those now treated of. while the second is borrowed into as a chromatic chord. I bVI VI) In our next example. Il7</ V7* V7«') 495.] Chromatic Sevenths. Op. 219 illustrates Ex. for it is followed by the chord of E. it is therefore quite . No. A A V7 A. 418. as the student knows that II7 is V7 of the dominant key borrowed. the following of one chromatic chord by another. it would complicate the analysis too much to add the keys from which they are borrowed . 416i Deutsches Requiem. it is possible to omit the generator . we then obtain derivatives. As with the dominant seventh. Our example of the last inversion of the supertonic seventh needs no explanation.Cbap. Brahms. XVI. -J- ^ A BIT: ii A^^^ (blr: A^ (F: y^c) Schumann. Ex. :(D: Vyi) IV I<:(E: Vyr) V \j<i{D:Vj6) IV If Il7f V7 (E: V7^) the student notice the different treatment of the two chords They are both E Vy^/ but the first is a transitional *. let marked : A Athalie. Novellette. 416. Ex. it would also be superfluous. Evidently the derivatives of II7 will be the fol- lowing : Ex. 6. 21. {lljc) ^^8^=1^ fe fiv° (ll7i) ^ tHv°c $iv°i tiv"c (1170') {U7d) (II7O In marking the roots of these derivatives.417. Ex. 497. One example of its emtives of the ployment will suffice. The Tonic Seventh is the dominant seventh of the subdominant key the seventh in the major key.) that Handel almost always Similarly. the former being the more common. has been already said (§ 262. being the leading. and the third and seventh in the minor are the chromatic notes. iv° [Chap. the and seventh of this chord are the two notes the progression of which is subject to fixed rules. ) those of chromatic ninths are very common.note of the dominant key.220 clear that ft Harmony. XVI must be vii° of the dominant key. as the tonic is essentially the chord of rest in the key. latter. we omits the generator in 'V'jc. The third of the chord. the feeling of tonality is easily disturbed if it is changed from a concord to a discord. third . 420. Handel. though (as will be seen in the next chapter. Note the apparent irregularity in the treatment of the Ajf here. the probable reason being that. and E in the upper part is interposed between the auxiliary note. B. 419. here find |f iv°3 in place oill-jc. though the . Ex. No new rules will be required for the treatment of |fiv° . must never be doubled. a similar progression to the resolutions already met with in chords of the seventh and It ' ' ' ' suspensions. 496. The Ai} in the third bar appears in the middle voice at first. Messiah. and the A which should ornamental follow it. The practice of the great composers is therefore to resolve the chord either on a dominant or on a supertonic discord in the same key. The tonic seventh so strongly suggests the subdominant key that special care is needed its resolution. The derivachromatic sevenths are rare. it must be remembered that the root. requires no accidental. in fact. It is. C: 17 (F: V7) c: I7 (f: V7) Tonic discords are much rarer than supertonic. to contradict the suggestion in As with the dominant and supertonic sevenths. using \i\°b instead. ] Chromatic Sevenths. C: (F: 17 vli°|. as will be explained in the next chapter. S-h n. the third will usually rise a semitone to the seventh of the next chord but it is possible. may If the chord resolve on a dominant discord. 221 being (as in other chords of the seventh. being a chromatic dissonance. 422.7 V7) (c: yii°7) . dominant discord. ) for the third to remain stationary. rh-^. or rise a tone to its third. the third will a chromatic semitone to the minor ninth of the super(*) tonic. 424. the latter in Exs. the seventh of this chord may never be doubled. XVI. At ((5) we have taken I7 in its last inversion. because this progression could hardly be used. the seventh will fall a semitone to the fifth of the chord. The former progression is seen in Ex. . . when the tonic seventh resolves on a derivative of a minor ninth. for it to fall a tone to the fifth of the chord. Unlike the seventh in the supertonic seventh. 421. which is here chromatic. . even in the derivaIf the chord resolve on a tives. as here. Ex.Chap. if a supertonic discord follow. Ex. 421 . or to fall a tone. ^ C: (F: 17 V7) (F: V7) If the chord either fall be resolved on a supertonic discord. though less frequent. It would also be possible (but only in a major key.428. 422. ninth (§ 382). ) a leading note. this note will rise a semitone . if the chord were in root-position.-. c: I7 jiv°7c V715 (f: 17^ Il7<r \c (f: V7) (g: vii°70 ^id) (g : V7f) Both these progressions illustrate the "balancing" spoken of in The second chord at (a) is a derivative of a minor § 466. never be doubled. : Ex. It is also possible for the seventh to fall a tone. Ex. 423. C: I7 (F: V7) tiv°7^ vii°b7 I (G: vii°7^) (c: vii°7) N^b 117a' I7 (F: V7)(G: M-jd) 498. 59.222 499. and the seventh In our next example. 3rd Symphony. rises a semitone. 426. 426. Bach. give [Chap. No new rules are required for the As with the supertonic seventh. 423 (a) where. Ex. the chord is resolved on a derivative of a supertonic discord. IV (Bb: V7<r V7*) We have Ex. Prelude 2X. Here the third is stationary. we positions. 426. ii I7 (F: V7) third of the tonic seventh falls a tone. inversions of this it in all its 500. Wohltemperirte Clavier. 501. The first inversion of the chord will be seen in our next extracts. Ex. 3. Beethoven. however. Book i. Harmony. and the seventh falls a semitone. as in Ex. Quartet. No. XVI. 42 1 {F) Here the . 428. 427. Op. examples of the employment of the tonic and with various resolutions. I7 IV7 tiv°b7 II7* (Eb:V7) (Vl3^) (IIb9*) V7 the chord resolves upon a derivative of a dominant discord. Ex. We now give seventh in all its positions. Mendelssohn. to show the correct figuring. chord. Ex. as in Ex. here the same progression of third and seventh seen in . g: i VI (c: 17c \n°^c\b Ylc) (Jgd) i is the second inversion.n-> ^^^ ^^^ Bach. Handel. XVI. Fugue 16.Chap. we give for the last inversion two passages in which it resolves on the derivative of a supertonic discord this resolution is oftenest met with when the tonic seventh is in the last inversion. p . resolved on a derivative of the dominant ninth . third and seventh of the 502. Ex. as in Ex. 223 Fugue 33. 429. V/a' lb \\°^ J-jb \\°']b - (Vll^)(el>:V7^)(Vil</) Here. in all the examples yet given. 424). Boqk x. V7 1 (Eb: V7f) (Uhgb) The F in the bass is a pedal note. 421 The (l>). the third and seventh have the same progressions Here as in Ex. tonic seventh move as in Ex. the chord resolves on a derivative of a dominant discord. Bt: V7 ic T IVi ^^ Ijtr Yyc ^r" (iv°7 . As this chord resolves. Bach. 430. 427. on dominant harmony. Wohltemperirte Clavier. hb: i . and the seventh falls a tone (Compare Ex. Wohltemperirte Clavier. Organ Toccata in F.] Chromatic Sevenths. Bach.. The third rises a semitone. Hercules. 429. Ex. Book i. Ex. 42. 434. But | is not a note of that key at all.*/ %\y°1b life \\°-]c (eb: vii°7) (Ab: V7^) (IV) (eb: Vll^) three of the five chords are derivatives of chromatic ninths or elevenths. (Compare Ex. vii°l>7 Vlb I. Ebr. the thirds is that shown in Ex.) given will present teresting ' ' 503.writing. The analysis here little difficulty to the student. Here the chord § 495. 422 (Jb'). If the student will play the passage. The part. is [Chap. We give two examples. as Schumann. 423) (a. resolved on the derivative of II7 explained-in is very often the case with Handel. XVI. The minor seventh of the tonic is E t*. No. Schumann. The derivatives of the tonic seventh are even more rarely to be met with than .224 Harmony. The note is . 435. Ex. Op. 2. " Er.those of the supertonic seventh. the thirds of the chromatic chords being doubled in the arpeggios of the upper part. The derivatives of the tonic seventh will evidently contain the same intervals as those of the supertonic seventh In fhe minor (§ 495)) but the root will now be the mediant. This example is instructive as the first instance yet met with of incorrect notation. borrowed. der herrlichste/' Op. he will feel at once that it is in the key of F. 433. 99 Ex. which will be explained later. key the root is chromatic. and its D enharmonic cannot belong to the key (§ 457). is rather free.°c [ijb) (l^d) (17/5) {iid) be seen that all these chords are different positions of vii° of F major or minor. 504. Bunte Blatter. and we mark the chord If iii°. We now give the derivatives. C: It will iii° c: #iii° {\^c) %m°b {\^c) VvS. Here is an inexample of the third in the chord of the tonic seventh remaining stationary. in which the progression of In our next example. (§467). as the seventh in the chord of the leading seventh V of the dominant key. the chord being chromatic in both keys. p. We give a fine example by Bach. The chord # is taken as the second inversion of the tonic seventh in that key. Obviously If a of in this chapter can also be so employed. 436. 506. £z. 505. or the root of a transitional dominant. but it is extremely rare with chords of the seventh. p. as end of the second bar can either be considered an we have marked it. XVI.Chap. The second inversion of this derivative is exceedingly rare. supertonic or tonic seventh be quitted as a dominant seventh. 437. 225 is therefore really E t?. and left as the second inversion of .n. £z. but as diatonic in the new key (§ 455). But a supertonic seventh may be quitted as a tonic seventh. and the chord marked ^ properly being the first inversion of the derivative of the tonic seventh.n. The reason Schumann has used the incorrect notation is because the seventh is resolved a semitone upwards. V73 in F. as it brings together two unrelated keys (§ 273). as in the following example. or vice versa. g: V7i5 B|r: i\ Bfcr: kPc YTb I vi (F : vii°7) V (I7rf) The C at the anticipation. In § 482 it was shown how a chromatic concord could The sevenths treated be used for the purposes of modulation. Wagner. Matthaus Passion. but it is occasionally to be met with. it is to be regarded not as a chromatic chord. We shall see in the next chapter that this false notation is very common with chords of the minor ninth . This method of modulation is not common.] Chromatic Sevenths. Bach. Die Meistersinger. G: V7 V9 F: ll^c Here what precedes shows that the first bar is in the key of G major. as with the secondary sevenths. and quitting it as a supertonic seventh. 507. quitting it as a dominant. fourth above series of Ex. and so on indefinitely. Exercises. 439.326 the supertonic seventh in Harmony.V7 * 7 F: II7 • I J . 3 6 {6 3 6 7 » B7 s . the root of which was a The same plan can be adopted with a its own. can either be analyzed as C: V7 F or as C=V7)f. or (which comes to the same thing. that chord will be the dominant seventh of F. If. if we continue the sequence. V7 / Bb: I7 Eb: V7 1 etc. the chord of fundamental sevenths. each resolving on another seventh.) taking it as a tonic seventh and Thus the simple progression. F major. it was seen that a chain of secondary sevenths could be written. A modulation is often made by taking a chord as a dominant seventh. instead of resolving on the triad of C major. which may in its turn resolve on a dominant seventh of B flat. resolves on a chord of the seventh on that note. XVI. In Chapter XIV (§ 449. J In such a passage it will be necessary. [Chip. to omit the fifth in each alternate chord. we Such modulations are frequent shall have £x. C: V7 C: 17 F: V7 \ F: 17 Bb: 1 . the dominant seventh in C. 438. ( I ) Andante. for example. There is another way in which chromatic sevenths can be used for the purpose of modulation. Chap. jt'6 4 3 — - 6 7 6 t4 2 6 J15 S5 » 4 6 5 6 4 (4 2 6t6 4 J 6 J5 H . gMf^-Jf^^^^l^^^E^^^tpiJiCU^ 6 4 b 6 5 6 Jl6 6 4 4 3 b5 (V) Larghitto. 4 2 6 I77 (6 4 3 6 6 6 #6 4 4 3 1)7- Andante. XVI.] Chromatic Sevenths. 237 ^ ^^^^^^^^S (III) Mcderato. =SCijg: 6 6 4(4 65 6 |4 2 6 16 * 6 $6 *4 3 ]]6 if Jt5 6 J ' 6 16 4 5 Jt4 2 t 6 6 tS 6 8 7 4 J- (IV) Andantino. j l t^^Rrh^fc^^^ri ^^'tea^^lr r 6 6 f4 6 6 6 1)6 '-^ -^Ir 65 f ^ 1)7 6 t]6 4 5 tt 2 JS 5 B 4 3 4 B 6 I |6 6 US (VII) Sidliana. 3 l76 8 7 6 7 5 It 4 J 2 4 3 98 4S 46 J4 2 116 l>6 b S4 2 6J|6 b6 flS 6 7- 4 3 4 5 11 4 H- { X) Allegretto.328 (VIII) Andantino. 6 4 87 43 . XVI. Harmony. [Chap. ] Chromatic Sevmnths.«=- t=f=: g 0= 4 2 5JP=: ::t=l 6 1^331 (6 65 43 TS--p. a^Hr^^g?4^=i^t^.Ch«p. t=P 6 Jl S^ 6 7 Jt ^^ 5 6 4 2 t6 6 US 6 5 87 (XVI) Double Chant. t=T ^ J^^-dj:gE^gt5Jw1. . 6 Jt6 5 6 5 6 5 4 2 6 6 4 ^ 7 3 mn (XV) Double . XVI.^^ ^j -r!l?3^ — =t=t |- fl 6 56 4 3 5 4 — — 6b7 U6 4 3 J14 16 116 7 6 7 2 11 4 6 fl - 5 ^^ (XVIII) (XVII) Hymn Tune. -f '^ II* ^^ i=t 7 It 1)7 ^^ 6 4 d^=3=?n^=fd:^^j:=i 6—6 6 6 4 4 2 6 6 t|5 5 4 — ^E^ $6 4 6 ^^-i4J—j=t=fi 6 6 4 (5 Hymn Tune.J:J:^J^^U^U^^ 4 2 6 -tChant. 6 «6 6 6 4 4 t|6 5 J 6 4 7 t (XIV) Mcderaic. 229 (XIII) Lento. b r. XVI.230 (XX) Hymn Tune.y' J 4 4 2 6 Uj 6 6 j if- g 96 4 3 6 4 b5 5 65 43 '- — 1^ II I U I ' I S6 6 {6 4 ^y>. IChap. 6 7 S 6 5 6 J? 3 4 ' jg I I I ^j -^ J I ^ T 6 I r I ' vj 76 7 «4 « (6 B65J4 S6 S4 3 3244t 6 6 6 5 6 117 (6 f5 IJ 6 (XXII) Hymn Tune. -^ Harmony. bH^ 4 2 3 3 ir r 1^' I f- P^ 6 4 6 D6 449 6 b7 p t^ — r tr .. g4''i>fi J J \ ^J rtr 6 r . i rif7iti-'. In speaking of chromatic triads. the third chord here is marked II t'g but its derivation is only g Vg.9 I9 IW (f: V9) (G: V9) (g: V9) (F: V9) V9) . for C minor. Thus. It must also be remembered that. of course. in our last chapter how chromatic chords of the seventh were only the dominant sevenths of the neighbouring keys not By resolved into the keys from which they are borrowed. XVII. CHROMATIC CHORDS OF THE NINTH FALSE NOTATION. marking their harmonic derivations. also of the supertonic and We also tonic sevenths. . while in a minor key we could only borrow from neighbouring minor keys (§ 463). this must be shown by an accidental. W Ez. because in G minor E The chords . we could for major keys borrow from either major or minor keys (§ 479). 508. — We 509. dominant ninths. 231 CHAPTER XVII. when the ninth is itself a chromatic note. the fifth is mostly omitted in rootposition. know that this is not the case with the chord of the dominant ninth.Chap. (^) M ¥) W (/) (^) C:Vi.-ENHARMONIC MODULATION. similarly borrowing the chords of the dominant ninth of neighbouring keys. in indicating the roots. and its treatment illustrated. 440.] Chromatic JVintj/s. In Chapter XII the chord of the dominant ninth was have £ilso seen explained. Thus.9 (c: 119 111. it was shown that. It will be remembered that the chord of the dominant seventh (and therefore. : flat is not a chromatic note. We give a table of all the chromatic chords of the ninth. the only chromatic ninths available are minor ninths on the supertonic and tonic but in C major we can employ the minor ninth on the dominant. to show them complete but. and a minor ninth in a minor key. and either major or minor ninths on the supertonic and tonic. provided always that we do not go beyond the neighbouring keys of the dominant and subdominant. which has a major ninth in a major.) is the same in-major and minor keys. as with the are given in five parts. we obtain chromatic chords of the ninth. comparatively seldom employed thus except in its derivative form as a chord of the diminished seventh. in in its second Symphony D. but a pedal note in a middle voice. 318 will be seen all the positions of vii°|.) we saw in Ex. f=F= sf * ^^ D: I p f^ vib ivi \c (d:iv^) I vii°b7f (d: vii°7<r) D in the fourth chord is not a note of the harmony.441. £z. The minor ninth of the dominant is In treating of the chromatic the minor sixth of the scale. it will be most frequently followed by the tonic chord of the major key. (§§ 382. is 512. XV. however. The progression of the bass The illustrates what was said in § 385. 299. As being the simplest in its treatment. and not of C minor. When the chord is used chromatically. 440 {a) ). as here. An example of its introduction in in which it is very common. In Ex. though the chord of the ninth frequently resolves first. It is. [Chap. but the fact that it is so is proved by the chord following our extract being that of C major. 510. derivatives of the minor ninth. give an example of the same chord Beethoven. The We now inversion. upon its own root. ii°. 392. =3= Ex. it is equally available as a note of a chromatic discord on the dominant. vii°|?7 and ii°. Beethoven. as said above. Symphony S^ F: I \c I^(c:vii°7f)V ii°* ii° \-jc (f:ii°* u°) V7* V7 I The chromatic chord at the sixth crotchet is a transitional domi- . passage The other : seen in the following in F.) are. In our quotation it is its root-position will be seen in Ex. 442. not seen to be a chromatic chord .7 in the key of C major. derivative. XVII.232 Harmony. very frequently used chromatically. used as a chromatic chord in a major key (Ex. the last resolving on the tonic chord. 511. triads of the major key (Chap. 394 {b') ((?) and {g) how this note was available in the concords . we first speak of the dominant minor ninth. The occasions for its suitable introduction are very rare. the notes up to and including the seventh of the chord follow the rules already given in the last chapter .Chap. the ninth will mostly fall a tone or a semitone to the root . 298. and the resulting dominant seventh is followed by the tonic major chord. like tonic and tonic sevenths. ) far oftener as a derivative than with Only the supertonic minor ninth can be employed in minor keys (§ 509). is the more frequently used. though (like the dominant ninth. 513. the supertonic seventh.] Chromatic Ninths. It is. XVII. it will mostly resolve upon either a supertonic or a tonic discord — more frequently the former. at the end of the second bar is an A if. the progression would have made a passing chord. just as we saw in the last chapter was the case with the super- Of these the supertonic ninth. 443. The minor ninth in the derivative seen at # is resolved on its own root. If the chord of the supertonic ninth resolve upon its root. the root present. but both major and minor ninths As with the dominant ninth. which is there explained The movement is here Prestissimo. Double Quartet. in slow time. we leave the student to make his own we simply point out that derivatives of both the diatonic and chromatic dominant ninths The . Op. all are available in major keys. are only two chords in the bar . *33 nant. own example : Spohr. 516. 136. Ex. however. where the third inversion of the diminished seventh in B flat resolves on a derivative of the supertonic ninth in the same key. and there as a passing note. of this will be seen in the second bar of Ex. . The chord of the dominant major ninth in the minor key is only possible as a •' passing chord " (§ 310). illustration An 515. it is only now needful to give rules for the treatment of the ninth itself. 317. it is possible also for it to rise to the third of the chord. much rarer for a supertonic than for a dominant The following is a good ninth to resolve on its own root. If a chromatic chord of the dominant ninth does not resolve upon its own root or upon the tonic chord. analysis of these harmonies being by no means difficult. The supertonic and tonic ninths are simply the dominant ninths of the dominant and subdominant keys borrowed. 514. In Ex. («) {!>') Ex. When this chord resolves upon a chord having a different root. [Chap. 518. it will be resolved upon a dominant discord. it ceases to be a true supertonic ninth. 422 (a). if the third of the supertonic chord rises a semitone. the ninth of the supertonic chord will fall one degree to the fifth of the — dominant. and' that the second bar shows the derivasupertonic major ninth resolved upon its own root.234 are to be seen in the Harmony. 423 {a) and 433. The student should observe that in every case it is derivative of II9 that is found . will be seen at the fifth bar of Ex. If it resolves on a dominant triad. a either the common chord or a tonic discord tonic chord will follow if the third in the supertonic chord falls a semitone. in its original position the chord is rare. 323. 444/ . These different resolutions of the chord will be seen in Exs. and becomes a "transitional dominant" (§ 295). first bar. A 517. — — . similarly resolved. tive of the same chord. 408. When resolved upon a dominant discord. 287. XVII. will 522. and any natural than a flat. The sharpest note of any scale. Thus. 235 Ez. in its G and C sharper note than F. Naturals. it is only necessary to is or (which amounts to the same thing. flat. and ascertain which is the sharpest note. Fjf. It will be seen that each note is a perfect fifth above that which precedes it. C F. The same procedure applies with flats. Sharps. ) enter into the question in some little detail. or of any chord. DJJ is the sharpest note of the first chord. naturals and sharps follow each other in the same order. G is flat has six flats. give a table of all notes. We now and take a few chords of the seventh and without their generators. E E. is a sharper note than C. 447. As this is often perplexing to students. D b. If we compare two notes. in Ex. Thus at (3) of Ex. ninth. B in the key-signature. It will be first necessary to explain what is known as the Law of the Sharpest Note. and F flat eight flats. Gf. remember their key-signatures to find which is the sharper. flats. 446. having the fewest the sharpest note of the chord. B#. t'. £#. a Obviously any sharp note is sharper than a natural. 520. F >.Chap. we must (See § 504. 521.) while Fjf would only have six.XVII] Chromatic Ninths. G I'. beginning with the flattest. is that which. excepting double double flats in the order of sharpness. C#.) the fewest Thus key-signature.446. A}}. flat has two. Sharpes" ) n C:V7 g:V7 -D b: V7 e: yi\°b G: V9 a: vii°7 Eb: vii°7 F« A« DJ Ft GS D . if regarded as a tonic. G. B B. Therefore B D flat five. for it would have nine sharps in its signature (§ 56. both with C. 1?. and that flats. A. sharps and We now Flats. D#. 1?. j?. would have the most sharps. C: tlv°li7 tiv°i»7 (c: Jtiv°7) (c : Jiv°7) Here we meet again with an instance of False Notation. both of which are sharps or flats. A D. In the present case D jf must be enharmonically changed to Eb. [Oap. which is the dominant of E. but only when it rises a chromatic semitone. guidance is. written. those derivatives of fundamental chords in which the third is not present. given will enable us infallibly to detect false notation of the minor ninth. We now chromatic chord. ii. Ftt is now the sharpest note. 449. this rule will be found extremely useful. the chord is therefore derived Jf But its resolution on the from B. such as ii°.236 It will Harmony. and that the dominant.. as we already know (§ 417). or IV7 . but for these it will not be needed. with the same resolution. give some examples of the use of II9 as a These will all be derivatives. tonic chord of C proves it to be chromatic in that key (§ 464). Look again at the first chord in Ex. and not always then. The irregularity of its notation is well shown in the following passage : £z. because E is not a "borrowing key" for C. proves false notation.* But with chords of the seventh and ninth. - shall now show how the application of the rule 523. from which. every diatonic discord is derived. The sharpest note is always the third of the original It must be understood that this rule does not apply to chord. just We D G 524. Whenever false notation occurs. it is always the sharpest note which needs to be changed. comes not from F or but from E. a supertonic minor ninth in C. because here false notation is not likely to be met with. The false notation of which we have been speaking is never employed when the minor ninth falls. and then directly afterwards with the notation. 446 (3). as for C are F and G. as in Ex. is a The simple rule for our major third below that sharpest note. and we have a derivative of the dominant minor ninth of G. that is. first false 525. and the only keys from which we can borrow chromatic chords The fact that the chord in question. XVII be seen that in every case the sharpest note is the leading note of the key. 446 {a). is written with the correct. Here is the sharpest note . it has been . Here the same chord. key of a passage by observing the auxiliary and passing notes. the It ninth therefore remains as the third of the chord (§518). it further proves the key of the passage to be It is often possible to decide the major. A 526. will We now show the inversions of |iv"7. Israel in Egypt.Chap. XVII. tiv°7 (E: vii°7) the supertonic major ninth resolves on the tonic chord. and the chord In resolves on the third inversion of the dominant seventh. Our Ex. Op. 527.] Chromatic Ninths. our next quotation. E: V7 V7/5 \b «iv°7 \\^b V7 of the dominant (B:vii°7){Vll</) Here j(iv°7 is resolved upon a derivative eleventh. Our next extract shows a different resolution Schubert. 451. 460. ^ ^^_3. D tf. 164. £z. Hercules.g_C^S e: i ^ )tiv°7 \b V7</ M \c V (b: vii°7) Here the minor ninth (G. first Handel. : Sonata. is interesting to note here that the auxiliary note.) falls a semitone. in the third bar makes no false relation with the DJ| in the bass (§ 323) . Hanuel. its 237 root -position already said that the is rare. most of which need no further explanation than is furnished by their . employment of the chord in examples are by Handel. £z 452. not E major (§ 307). 238 analysis. Ex. Ex. (d : vii"?*) Mendelssohn. but vii°7 in the key from which they are borrowed. [Chap. 466. We purposely use sometimes one. ^. No. Octett. (a: vii°7c) Mendelssohn. ninth. . Quartett iu G. 453. Das Rheingold. as hitherto.^^ Jtiv°l>7</ V7<: V7 (f: vii°7</) It will be seen that in our analyses we mark below the derivatives ^iv°7. Ex. Ex. D: \c Jiv°7* vii=b7 : I (A: n\°^b) (d vii°7) Here jf iv^y^ resolves on a derivative of a chromatic dominant Wagner. not the II9. and sometimes the other analysis. XVII MoeART. 464. 14. Harmony. 455.^txj^ Bt: I* y. S Elijah. that the student may accustom himself to both. the tonic ninth. Probably to save accidentals in the The false notation at method shown in § 523. 469. when the chord is seen to be the diminished seventh in F minor. 528. Like the supertonic ninth. This must also be changed to Dj?. or upon a different root. If the ninth resolve on its own root. the progression at (c) Ex. if it next chord.Chap. form with the generator present even rarer than the same form of the supertonic ninth. XVII. which will also require resolution. indicating the key of B minor To it will be needful to apply here the sharpest for —not a borrowing key A^ is note to B t'. resolve cord. is often thus find the true nature of this chord. or its derivative. showing D minor. and we shall have a tonic seventh. {b) {c) "C: iii°7 Y^d iii°b7 V7d iii°l77 V7</ (F: 530.. upon a dominant disbe major. resolution. («) W W l^6 {d) w I7* c: Ibg (/) iii°b7 I7 iii°b7 l^b If a tonic ninth. it can Kiii°7 resolve either upon its own. and if it The former progression is rare . will rise a chromatic semitone.) should resolve either on a dominant or supertonic discord. iii°7 (in the minor key compare § 503). will remain as the fifth of the be minor.) the tonic ninth. like the tonic seventh (§ 496. C. When we change this 53 1.) is often employed. generator. so also is the minor seventh. the law of the sharpest note twice. 467. as the case may be. note. The chord of is. the latter is common. the latter — (tf) and {g) in its original — shown 440 (<j?) — being by far the more common. borrowed as iii°t. 529. 468. Ja) Ex.e. If not resolved upon its own root {i.] Chromatic Ninths. It is almost always found as the derivative. the rest of the chord will remain. C |j remains the sharpest note.7 in C major or minor. If the chord of the tonic ninth resolve on a supertonic . (Compare (^) and (f ) of the following. vii°7) (f: vii°7) (f: vii°7) (r) can be detected by the But with this chord it is by no means uncommon to find that if the minor ninth is falsely noted. and in this case the same false notation already seen with the supertonic minor ninth (§ 519. ^39 in Ex. the ninth. Ex. is Here in § 53°The Aj^and C^f are chord to be really Bj? and Dj?. although the original position is possible. 465. Schumann. [Chap. 460. —E Jj for F !>. actual composition. We resolution of the latter first show iii° 77 and on a dominant seventh. Ex.240 Harmony. it is so seldom used that we are unable to give an instance of it in give We now by the great masters. It is." Op. Our next illustration shows the second inversion of iii°t?7. discord. Fall of Babylon. for. 7. XVII. the ninth will fall one degree. The last inversion of the same chord following: * For an instance. Ex. C: 532. see Ex. within is seen in the . No. iii° ^^b. 461. * however. 48. Song —" Ich groUe nicht. 462. 435 of the last chapter we saw a derivative of the tonic seventh (iii°i5). 5 VHb iii°|>7<: V7* I (f: vii°7f) seen an instance of the double false notation spoken of proved by the resolution of the In Ex. with the Spohr. rare for a major ninth to be so resolved. false notation. very Ex. tonic ninth iii°b7 «iv°b7</ iii<Tj7^ tiv°lr7 examples of the employment of the These will all show derivatives of the chord . in which Schumann had also written the minor seventh as an augmented sixth from the generator. 634. V7 iii°b7 iii°b7^ V7 (ab: vii°7 vii°7*) Note here the 533. which has been seen in' all the passages yet quoted.] Chromatic Ninths. 5. the derivative of the major ninth. the derivative of a chromatic dominant ninth. at Heie we have not only the derivative of the tonic ninth.Chap. Op." * JL Op. that We EXi 465. Spohk. 241 Ex. the root not appearing till the change of harmony at the second quaver. Observe again the double false notation in iii°>7. The tonic major ninth and its derivatives are rarer than the minor ninth. This is its most usual progression . Fall of Babylon. 164. I^ (ab: vii°7a') (Vi. 463. V7 II vii°lr7 iii°7<r tiv°b7* : ii°7<^ (e: vii7)(A: vii°7<r)(b vii°7i5)(e: ^7 Vl If Here are seen all the chromatic ninths in turn. J —" Schone Wiege. No. now give one example of iii°7. . Song. Schumann. 'I I I V^Tii°b7)F:tiv°t>7 F: iii°b7i V7 This is effected is instructive. 26. In all the examples hitherto given the tonic ninth has resolved upon a dominant discord. because it shows a modulation by means of the diminished seventh. where B |7 is written bar . but its resolution shows passage it is quitted as the derivative of a tonic ninth in F. we now show its resolution upon a supertonic ninth : Spohr. Nonctto. 535. £z. S36. The third chord taken as dominant harmony in B flat. but the end of the first bar. Notice the very unusual false notation at the fourth quaver.9«') also. XVII. The second is over a dominant pedal the first chord is an incomplete chromatic triad on the supertonic. 31. all the sevenths will be diminished. — — Exi 467i Beethoven. it would be vi° and v° respectively. 18. this resolves on the second inversion of the derivative of the tonic minor ninth. as in our last example . was said for Ajf. [Chap. In order to make the progression of the harmony in the second bar easier to the student. we have omitted the usual analysis of this passage under the bass. is very seldom used except for dominant harmony. then the series (dominant. generally. which again is followed by the first . 442 thus employed. We give one example the only one we can recall of the latter. As a derivative of the supertonic and tonic ninths. Meyerbeer has written them in a very promiscuous manner. we have given each chord with its correct notation. To save space. however. 3. Bfe: I V7*I \ Vic v°cy^c (e|>:ii°f) Ic li «iv°l>7flri3 F: IVi ) F: V7 I J Here is seen again the double felse notation already more than . as in the following passage : Ezt 466i .inversion of that of the supertonic minor ninth . tonic. xvn. but each time in a different position. ^ Meyerbeer. No. The first diminished seventh is the derivative of the dominant minor ninth. Binorah. Op. We have seen it in Ex. 538. The music continues in A minor throughout. It is not uncommon to meet with a succession of sevenths over a bass ascending or descending chromatically. The second derivative of the minor ninth. and compare in § 460 on the notation of the chromatic scale.242 Harmony. * Quartett. ii°. because it is resolved downwards. supertonic) recommences. what 537. for instance. 540. If. being in the key of F| major. ^s^E?^^^:zf[^-=^ Even an experienced player might stumble at first sight over such a passage. that is. The chord of the diminished seventh is of great importance from its use in modulation. It has been already said (§ 308") that two notes which are enharmonics of one another {e. B (?. It is evident that it may -be taken in any one of these keys. is now perfectly easy to read. as follows A Ex. to avoid the use of double sharps and double flats. 469. can never both be used in the same key. understand A its little explanation is necessary to enable us to further use. 243 once pointed out. 468. We have already seen (Chap. and substitute for the key of | its enharmonic.g. it would make the music difficult to read were it written ' ' ' ' thus £z.] Chromatic JVinths. and quitting it as a diflferent chord of another key. and left in any other of the six.) how to modulate by taking a chord as belonging to one key. the chord derivative of a dominant minor ninth in C major or minor. IX.Chap. XVII. It must be especially noticed that here the change of notation makes no difference whatever in the progression of the The passage harmonies. It is therefore much more convenient to mark a change of signature. But its utility for the purposes of modulation by no means ^ may be the G ends here. Every chord is exactly the same as before. If the . 541. it was also mentioned (§ 49) that. For instance. of a supertonic minor ninth in F major or minor. and At*). 53^. especially in extreme keys. Clearly we can apply the same method to the chord now under consideration. or of a tonic minor ninth in major or minor. we wish to modulate to the mediant of that key (A||) which would have ten sharps (three double sharps) in the signature. an en- g| harmonic change of notation was not infrequently employed. keys with many flats or sharps in the signature. as at (f). by enharmonic modulation in every key. Gj| as at (3) the nature of the chord is I? we substitute changed. student will transpose the above passage a semitone higher or have here lower. If. the chord is the third inversion of It now belongs the derivative of the minor ninth of A Jf. E^. We 542. A[?. we get an enharmonic modulation . by enharmonically altering one or more of the notes of a chord we change the harmonic origin of the chord. Now take E^ instead of Fj. and tonic in E major and E minor. to the keys of D |f major and minor. therefore simply an enharmonic change of notation. B major and minor. [Ch»p. Again changing D f} to C x. it is usual to write the chord in the notation of the key which is being approached. We A — G — G A A D D 543. It is no longer derived from G. rather than . supertonic in minor. their enharmonics. but it is the first inversion of the derivative of the minor ninth of E. (*) (0 K) (') have already seen that the chord at {a) is the derivative of the minor ninth of G. and minor. It will thus be seen that any chord of the diminished seventh can be used. and belongs to the keys of C major. If now for minor. C major. and evidently belongs to the keys of F ft major and minor. beingtaken in its relation to the key quitted.[. being em- ployed instead. and gives it a new generator. F major. there is only an enharmonic change of notation between {d^ and (^) as the generator A^ of (aT) is the enharmonic of the generator Bb of ((f) and every note of the chord is changed. or tonic) in the new key entered. and the chord of the minor ninth lends itself to this process more readily than any other. supertonic. G | major and minor. (</). 470. and is domimajor and nant in major and minor. xvii. the chord is for these keys written as at {/) where it is the last inversion of the minor ninth of B k It should be noticed that while between each of the chords {a) {F) (^) and (^) there is an enharmonic modulation.. we can change any of its notes enharmonically each change alters the nature of the chord. so that its altered notation induces a different progression of the harmony. _W Ex. and Cj( major and minor. and resolved (as dominant. and A^ major and minor. As these three major keys are very rarely used. he will find that no change is required. If. F minor. for instance. When a modulation is thus effected.244 Harmony. we take the chord given in § 539. however. and B1?. and the chord becomes the second inversion of the derivative of the minor ninth of C %. 544. . The analysis given below it will require. u V7* vii°7 Jtiv°7ar"l a: vii°7 (V9i) a: J n°^ci (-(Vg*) . The passage marked as being in B flat major. One point more must be noted. showing how enharmonic modulation can be used to connect two very remote keys. XVII. could also have been regarded as in B flat minor . 245 at the which is quitted. Observe that the progression of the different parts is.] Chromatic Ninths. We will now give a more modem example of the same method. 546. Ex. very free. very close attention from the student. 471.Chap. J Bach.Vi3^ Bb : vii°|?7</ ( {IMc) V7 Jtiv°|r7*\ d: iii d: YlZg] Few remarks are needed. in that may be adopted 545. we have considered it as in the major key. 472. but will also repay. One of the most magnificent examples of enharmonic modulation by means of the chord of the diminished seventh will be seen in the following passage by Bach. In every modulation the diminished seventh is written in the notation of the key which is being approached. because this is so much less remote from the keys that precede and follow it. but quitted as a note of the harmony in D minor. it is taken as a dominant pedal in B flat. In the last chord but one the F in the bass is no part of the Jfiv°|77^ in B flat. as often with Bach. though either pleasure of the composer. Chromatic Fantasia. Ei. The ninth resolves on its root in the following bar. then by the enharmonic change from D|? to CJJ the generator changes to A. While the chord under consideration offers an easy means of modulation to any key. A modulation a remote key can often be quite as well effected by some other means.% f ^ T \ . it is well to warn young comit too freely for this purpose. after several changes of position. It is a " German sixth. vktf." which will be explained At *^ the first chord is taken (with D I?) as in Chapter XIX. a derivative of the supertonic minor ninth in that key (generator C) . (I) Moderato. XVII The fifth chord has not yet This passage begins in B [? minor. almost exclusively by this chord would show great poverty of posers not to use to invention. [Chap. 547. and the chord becomes a derivative of the dominant minor ninth of D. and the too frequent use of diminished sevenths To modulate soon becomes monotonous. and palls on the ear.246 Harmony. on the tonic chord. and the dominant seventh which remains is resolved. been studied. "7 U 3 6 b7 1)6 l>7 116 66666667 6 6 7 4 4 6 S ^. I I 5 46 47 3 J? 6 12 $ 6 5 t6 6 6 4 \\ ' 4 s? 95 s 3fclIP 1(6 I I $4 4 6 D6 6 T7 6 6 7 3 4 (v) Unpoco allegro. XVII.'7 f 97 6 S 4 6 ' 6 7 6 fl6 117 6 17 6 II7J6J7 II6S6 44 S7 } 7 987$ t2 t- (IV) Allegretto. 3 6 6 65fi6 l.Chap.] Chromatic Ninths. 347 (Ill) Andante. J J J J . |f4_j]7 6—98 K .5 66 — 45_ — ( B Te^ ^4 J12 6tt4 6 7 4\.|. (6 ^^ 4 6 11 =]= 4 lli4 II 2 6 4 b 376 5- 114 116 l.4 B ipt 116 US - ^rrr — — 116 "r 6 .24S (VIII) Larghetto. [Chap. Harmony. (6 — 76 5 4 6_ 6 4 2 — — — 6 5 654 4 3 t 6b5l?7 \l |76 b* 3te 44 116 3 — — — b? m. 7 r-r I- ^^HG -J4 ^ Allegretto. XVII. ^^ — rfir 1 rift°-^ I I II t 5|4 4« b 6 6 tl4 6 |77 1)6 b 4 7 3 (XI) ^MY\v 5 r 5 nr 6 r r 6 ir 117 f4 S 4 J! nj^Mr^T^^^ 6 5 7 116 116 175 J » a pgii =p5^ te b5 tf —(6 -b5 S He 114 ^ 9 117 4 b 1. Tune. xvii] Chromatic Ninths. 7 5 J — - 6 6 119 4 8 7 — t- ^^t:^TT^ (XV) Hymn Tune.Chap. =F4.-t^=g5^^J"r^ 6 6 V' 6 4 ^^g^ ^hj" s 6 6 7 7 6 5 J 4 S 4 2 6 4 5 3 6 6 — 1*7 5 OS . 249 (XIII) Hymn (XIV) Hymn Tune. We already know (§ 406. ing to the more elaborate chords of the thirteenth. 548. Our next illustrations show the second inversion of the Haydm. CHROMATIC CHORDS OF THE ELEVENTH AND THIRTEENTH. Ex. 474. so rare that they may be almost said to We shall deal first with these. before proceedbe non-existent. are much less frequently employed than the chromatic chords of the seventh and The elevenths indeed ninth treated of in the last two chapters. \\°ic taken in a major key . In Ex. [Chap.) of which we have now to speak. xvin CHAPTER XVIII. 473 Air: ii I*ii<>7* V IV* (ab: u°7i) 550. and in Ex. are. 274 will be seen ii°73. as in the following example : Spohr. zst Mass. used as a chromatic We saw in the last chapter (§ 510. 465. ^^ ¥=F= . But it can also be substituted for the diatonic chord. and the chord resolves . The one exception mentioned just now is that of the dominant eleventh with a minor ninth.250 Harmony. how the chord of the minor ninth was often employed in this manner . and. like that chord. Mass in C. chord. ii?. The higher chromatic discords (elevenths and thirteenths. 549.) chord in a major key. Bb: I falls i 'r ii°7<: ^1 Vy (bb: ii°7') Here the chromatic note a semitone. in both cases the chord is treated as a passing chord. the present is far more frequently found as a derivative than with the dominant present. Ex. with one exception.) that the derivatives of the dominant eleventh in the minor key are ii°7 and its inversions. " A Ex. to be found excepting as derivaand the derivative of IIii. and not D minor.] Chromatic Elevenths and Thirteenths. D: V13 V7 v°7 (g: "°7) Let the student paris instructive. like all other chromatic chords. S. 342. analysis of this passage ticularly notice the The D that the derivative of IIii. Wagner. according as the ninth We show both is major or minor. The chords of the tonic and supertonic eleventh are so extremely. 477. They tives. which a moment's thought will show the student must be vi7 or vi°7 that is ii7 or ii°7 of the dominant key. 552.Chap. but it must of course be resolved. 476. semiquaver of the second bar is evidently an anticipation of the following dominant harmony. he will see the diatonic chord II7C with the same resolution. — 551. in the key into which it is borrowed here. rare that very few words need be said about them. a: V VI \ 0:117* I^ ""7^ C: IV/(G: Vyi) (c: u". Bach. ambiguous in its very nature.^) \c V7 If the student will look at Ex. is. as will be seen directly. the derivative of Iii. is in its nature ambiguous. —" Ich habe meine Zuversicht. Cantata. C: vi7 vi°7 . if ever. forms of the chord in the key of C. No new rules beyond those given in Chapter XIII will be needed for the treatment of this chord. Die Meistersinger. Observe that in the last bar the F ^ proves the key to be major. it 351 on V7. are very seldom. The fourth passing and auxiliary notes. in a major and not a minor key. on Ic. In the following passage J. We first give an interesting example of v°7. It was said just now — ('^) (*) Ex. resolves P-Hj.xvm. 476. The note characteristic of supertonic discords the leading note of the dominant key is evidently unavailable here. seventh. This is more particularly the case when the vi7 resolves upon a chord containing the leading note of the dominant key. or as the fifth. has already been given as a rule (§ 417. Mass in £b. be noticed that the first of these two chords is diatonic. eleventh. ninth and eleventh of the supertonic chord. fag^'l ^ J ^ -' ^J 1 . XVIII. The chord {b) might also be a chord of the minor thirteenth in C major (V|7i3^). as in the following passage — — : — ^ Exi 478i Schubert.252 It will Harmony. The chord (a) above may therefore equally be regarded as the ninth. as well as the derivative of a chromatic supertonic eleventh. Yet occasionally progressions are found in which the mental effect produced is decidedly that of supertonic rather than of dominant harmony.) that every diatonic discord in a key is derived from the dominant. because that is the note on which the eleventh would resolve (§ 375). [Chap. thirteenth and generator of the dominant chord (Com- and it pare § 445). Beethoven. when chromatic in a major key. 481. Op. rises a chromatic semitone to the third of In the last chapter we saw (§ 519. The false notation can be detected. («) (*) Ex. 434. resolved in the same way . minor thirteenths in our as augmented fifths : last In precisely the same way. 483. By far its most common resolution is on the tonic chord. xviii. No 2. 253 seen in §§ 428. £x. both with and without the seventh. the example are almost always written Ex. above the generator. Sonata.Chap.] Chromatic ELEysNTHs and Thirteenths. Unlike the diatonic chord. instead of a minor Here the thirteenth ninth. a chromatic dominant minor thirteenth never resolves upon its own generator. as explained in § 523. in a major key. of the supertonic. 30. by applying the Law of the Sharpest Note (§ 520). 555. 482. A: V V7fl'(fJ|: V7) vi iii ii V9 Vlri3 I . and resolved on a tonic chord. P C: (c: i=3= Vbis V13) Vl7l3 (c: V13) 554. Ex. 480. and it was pointed out that the chromatic note was often written as an augmented octave. The following passages show the minor thirteenth.) the minor ninth the tonic. Our next illustration shows Ill?i3. are much less frequently found with the generator present than the dominant thirteenths . [Chap. A A which the dominant minor on a tonic chord. 486. the T. both major and minor. ) were resolved. A: W9 Vg V7 V1.I3 (T.P. in which the part-writing can often not be shown clearly. Vbi3 bVIpg V1. the thirteenth will fall a semitone in this case. In the last two bars of this passage is seen the usual resolution on the tonic chord.I3 bVIyg Vbi3 \c In this passage the chord Vt»i3 resolves at its first and second appearance on a chord of the . dominant thirteenth. XVIU Ex.) I No further explanation will be necessary than is furnished by the analysis of these examples. B 1?.254 Harmony. but is a " Tonic Pedal " (see Chapter XX). The minor thirteenth.) which will be explained in our next chapter. as well as the . In the rare instances in thirteenth resolves otherwise than . in the very large majority of instances it will be the derivatives of these chords that are employed. in the first chord does not form part of 485 indicates that the the chord. 557. as with the minor ninth. whether major or minor. The tonic and supertonic thirteenths. it would not remain stationary while the lower notes of the chord (the third and seventh. Die Meisteisinger. in the second bar of Ex. Jessonda. Wagner.P. its apparently also rising to C j} is simply due to our extract being taken from the pianoforte score. We give an interesting example by Wagner 556. falls to A . If the were here the eleventh of the dominant chord. 486. : Ex.augmented sixth (marked bVIjrg. Spohr. false notation will not be used. This extract also illustrates what was said in § 357 as to the possibility. 255 Tristan und Isolde. it will be derived from the dominant. 487 above). In the third bar we mark the B^ as changing notes.] Ell 487. where the presence of the augmented fourth together with the minor seventh shows the chord to be supertonic. The only exception is the rare supertonic minor thirteenth (See Ex. because if we had here a derivative of and a Hominant ninth it could not resolve upon iib. but these are so excessively rare that for practical purposes they may be disregarded. for both dominant and tonic discords contain the subdominant of the We scale. in bar 2 and the On the other hand. before enumerating the chief of them.xviii. its notation would D G D beCf. or supertonic chords. as it is rising. of more than one explanation. it will obviously be by noticing how the * In a few of the higher derivatives of a supertonic discord the third is absent (See g 552). If a discord contain neither the augmented fourth. have now to speak of the numerous derivatives of 558. Chromatic ELEyENTHS AND Thirteenths. needful to ascertain the key with certainty. seventh of the scale.Chap. Ilbia (bb: V9 V13V7 Ic V13) Notice in the second bar of this passage an example of the false notation spoken of in § 554. if it were. we shall. Before applying the above rules. 559. The distinctive note of a supertonic discord is the augmented fourth of the scale. . the |? in bar 4 can scarcely be considered as a passing note . give a few rules which will help the student in deciding whether they are derived from dominant. nor the minor ninth of the key. Either of these notes is sufficient to prove the origin of the chord. Whenever this note is present. the minor seventh. As the identification and analysis of these may be found somewhat difficult. I. The Fjj. there can be no doubt as to the nature of the chord . tonic. the chromatic thirteenths. Waghbr.* II. in bar 5 might be regarded as auxiliary notes. — III. The distinctive note of a tonic discord is the minor sometimes also the minor ninth. with these higher discords. submediant.) resolve by rising a chromatic semitone (§ 519). We shall see later other derivatives of the thirteenth. Ill (Vi35^) VI (Ii3^) VII (III35*) the Law of the Sharpest Note. while at ((5) and {d) the ninths and thirteenths are borrowed from the minor and major keys of F and respectively. combination by figures thus analysis needlessly —V13 but [79 this would complicate the we shall indicate the in. XVIII. it will these chords as noted are the dominants of A. this must be practical application of the rules will be seen in the analysis of the various derivatives now to be shown. which is almost invariably used in a major key. By applying be seen that and E. This chord. and put (as we have done above. The minor ninth of the chord is. At (a) the note E be1? is borrowed from C minor". 488. The derivative we are now discussing is very seldom seen with the notation given above. 561. this 3 in all such cases A G 562. in which the ninth is major and the" thirteenth minor. although it does not (as in other cases of false notation.2S6 discord first Harmony. 489. longs to C major. as common its last inversion ^ Ex. of which is a "borrowing key " for C. and in 560. tolerably I. version by the letter following the 13. none . and leading note respectively. which is a derivative of a dominant discord. there be any false notation. it must be pointed out that form of the chord. Such chords we call False Triads. Third. if rectified. is mostly found with a minor ninth and a major thirteenth. Ex. resolved . The chords now look like major triads on the mediant. Before proceeding further. similarly. D. is only partially chromatic. ('') (*) (4 Vl3^ 113^ 1113^* It will be seen that here the notes of the chords cannot be It would be possible to indicate the exact arranged in thirds. ninth. ) an asterisk after it to show that we have an irregular selection from the notes of the chord. The and thirteenth. almost invariably written as an augmented octave of the generator. in this combination. is [Chap. xviii] Chromatic Elevenths AND Thirteenths. decisively proves that we Our next illustration the final cadence have here a false triad. 1 42. 257 563. |(if) —rh— 1 J J J. 491. J^. but the resolution of the fourth chord on the chord of which is the final chord of the piece.Chap. F: I ^—d^-- ^^ ^ i *n 1 1 1 III Five more bars. Here the resolution of VII on Y^b proves it to be a false triad. Die Idealc. (Vi3^) There is clearly a modulation to B minor at the second chord . Liszt. give a few examples of this chord. II Ex. (. 490. D of one of Liszt's symphonic poems is perhaps even clearer. . major. 1. Ex. Ii3Schubert.J. Op. containing only the chord of F. AuBBR. We now Le Dieu et la Bayad^e. 492. for here there has been no previous modulation to the relative — — lix. We now give examples of the derivatives of II 13 and Sonata in A minor. 564. conclude the work. as in our last example. and becomes a False § 562). xviii. Ex. 494i Beethoven. II. fifth. thirteenth are both minor. both ninth and thirteenth being. but it is more usual to write the minor ninth (as in the form of the chord last shown. [Chap. minor. than the form last shown. Third. Tristan und Isolde. and the chord is in the first.858 Harmony. which it resembles in generally containing the minor ninth with the major thirteenth. Ex. is over a dominant pedal. as an augmented octave of the generator. 493. —a chord of four notes built up by thirds. . Ex. The chord * is the fourth inversion of a derivative of the tonic thirteenth. not in This is the last inversion. In this passage the chord appears in its correct notation . This passage Less common 566. blr: VI V IIl3^* Here the ninth and a somewhat different example. 565. Op 13. It then looks like a Tetrad* (Compare * Tetrad fundamental seventh on the mediant. ninth. Spectre's Bride. and thirteenth. Here is seen at the third crotchet an instance of the thirteenth resolving upwards on the seventh (§425). 495. Dvorak. The following is a good example of its employment : Wagner. Sonate Pathetique. Our last example of this chord shows it as a derivative of the tonic thirteenth. Third. 259 is 567. Op. Mazurka. 480 (Ji).^5=^S=. C^ must therefore be enharmonchanged to D t* . XVIII. kVIII. by the substitution of the ninth (generally minor^ for the generator. An instructive example of the chord with this notation seen in Mozart's great Fantasia in C minor : £z> 496i Mozart. in the third bar is taken in that key as b VII 177 a derivative of the tonic thirteenth which will be explained later in this chapter (§ 575). 22. and thirteenth. Here. as in so many 569. III. seventh. 497. ninth. No. Fifth. 3. cation of one of the commonest forms of the thirteenth (Ex. A One example will suffice. The rare example of this form here shown Beethoven.Chap. but with that it is the thirteenth. The chord ically quitted in that key. instead of the ninth. and thirteenth. Bb:Il3'* l>9 . its resolution on the chord of F minor in the next bar proves — f:Vl3^. 498. seventh. modifi568. Ab: Vl3i* I Vl3^* I V13** I similar cases. in the bass. 17. and we then see that we have the same form of the chord as that just quoted from Wagner. Chopin.^^5^ Ex. Fantasia in C minor. IV.? ( This passage begins in B major. it is possible to regard the thirteenths as auxiliary notes or suspensions. Ex. S=F. Sonata.] Chromatic Elevenths AND Thirteenths. ninth. Op. effect. and that the chord is the last inversion of a derivative of a dominant major thirteenth. with the addition of the fifth. The key of first major. the root position of the dominant minor ninth of B minor. Fifth. with a chromatic D D auxiliary note. I ^7 Ii3^Ii3(f*V7(/I* V7^ Dvorak. 570. ninth.26o requires is Harmony. XVIII. and thirteenth. VI. Exi 499> Brahms. ninth. eleventh. Deutsches Requiem. containing only the minor ninth. and thirteenth. and major thirteenth.eoi. 571. this only given for the first half of the passage. The chord * in bar 3 is the second inversion of the same chord. of which the second is an exact repetition. C: Ex. but shows that the its resolution in the third bar on the chord of B i? of the tenor is the minor ninth from A. of a very striking examples. 600. Ex. no explanation beyond that given in the analysis . in the last inversion. It is curious to notice that. I Stabat Mater. eleventh. The first bar gives the this passage is The second bar sounds like inversion of the tonic triad. Third. G: le 113^ N^d In the first of these examples we see at the last crotchet of the second bar a very unusual form of the chord of the thirteenth. We give two Die Meistersinger. V. A rar6 form of the chord. [Chap. Wagnbr. The chord in the third bar is \b. while the effect of the two examples here . ffthy seventh. both 572. nor the minor ninth of that key . 604. C: iv7 IVb7 (VbiS'/) (c: iv|>7 Vl3rf) The form (a).Chap. like most of those we have been showing. The Daughter of Jairus. The notes of the chord are those of the dominant seventh of B flat. and thirteenth. the first time the thirteenth falls a third to the root of the tonic chord . which. Ex. The form (i5) of the chord (Ex. XVIII. of the practical value of the rules given in § 558. We Ei. is Here the chord (a) Ex. Stainer. ) is more common. is. contains a minor ninth and major thirteenth. We have already seen this form in § 440. chord. 573. Seventh. which its resolution proves to be in the key of C. ^ (*) =b5 EiSE =Sg= Here is an illustration cannot possibly be a chord in B flat. when resolved on the tonic chord. is but rarely met with. but if either the ninth or the thirteenth be chromatic we have the chord now under notice. the chord of the thirteenth and resolution. 261 given is in position entirely different. the minor seventh. as the only important diatonic derivative of the thirteenth . (only one note being borrowed from the minor key. is often written with false notation as D |. The chord. eleventh. like (a) only partially chromatic. give a good example of its employment. PP r T p.] Chromatic Elevenths AND Thirteenths. 503. but if resolved on the tonic chord of C. which is most often met with as a derivative of the dominant In this shape it becomes a seventh on the subdominant. 502. the E ). it . contains neither the augmented fourth. identical in both. m r iiyi is m I I mm F: I U iv7 li uji rv'j I (Vii</) (Vbi3a') (Vila') (Vbi3«') seen twice . VII. ninth. It should be mentioned in passing that.n. 502). it is therefore derived from the dominant. the second time it rises a third to the fifth of the chord. which. As all fundamental discords can be derived from any one of the three generators in the key. Rosamunde. F«: IVb7 ivb? I (Visrf) {it: Visa?) b9 shows both the forms (3) and (<:) of Ex. J>VII|77. Ex. 496. however. it is evident that the chords of the thirteenth can be used for the purposes of modulation . and vice versa. and thirteenth present last if (^) "g \ may. 6. 575. become the inversion of a similar chord derived from instead of this change or we substitute C^ for the chord will thirteenth become a first inversion of a minor on E|2. and quitted as derived from the tonic or supertonic. 43. the root will now evidently be t'VII. Lyrische Stiickchen. For example. as with the chords of the ninth. XVIII. In these cases the chord can be quitted in . Harmony. and the chord We have already seen it in the third bar of Ex. 506. Ex. 502 the latter has evidently the character of a passing chord. for they can be taken as derived from the dominant. where. it was enharmonically changed before resolution we now give an example in which it is resolved in the key to which it belongs . S B: ljVIIb7 (IlMS'^) 576. 606. with only generator.262 574. Schubert. No. the dominant minor thirteenth in the key of C. But their use may be still further extended by enharmonic modulation. The following passage E. third. [Chip. by changing E I? to D \. Op. The same derivative of a tonic discord can also be used. Grieg. we now add a few others which will repay careful study. supertonic or dominant. Fantasia. a: i (d: V7i/) iv4 VlF6-tC:I C: IVb7/ : This passage begins in A minor the chord # is the augmented sixth (see next chapter) in that key . the seventh in the bass leaping to the generator of the tonic chord. 1. Ex. in that now to * Exercise VII at the end of this chapter has been composed specially enharmonic modulation by means of this form of the chord. the third crotchet of the second bar is taken as lie in that key . made the chord 579. No. since in making a modulation there will always be a connecting link. the chord becomes the derivative of V13 in D major seen in § 560. is effected in the same way.Chap. two bars later. We have already met with one instance of an enharmonic modulation by means of this chord. but it is resolved in the key of C . Mendelssohn. as in Ex. 16. In the passage just analyzed the enharmonic change into a chord of the thirteenth . The two passages from Wagner next to be quoted are Tannhauser. 263 any of the keys in which the new generator is either tonic. i yb nc\ D: g: I- V* lie D: Vl3^*/ V I J F: I F: V13** Here. and the chord itself thus becomes the form of the thirteenth shown in § 568. 505. 496 . Op. beginning in E minor. more curious Ex. It will be observed that here the general rule as to writing the chord in which an enharmonic change is made in the notation of the new key is not observed. by the enharmonic change of A|| to Bj?. 607.] Chromatic Elevenths and Thirteenths.* 577. to illustrate . Ex. and here written as a "false triad" ( § 562). The Djf of the chord * is quitted as an El?. Wagner. The modulation to F major. XVIII. 578. the last chord but one must therefore be in the key of C. 608. it At * the iifth rises to the minor thirAs it resolves in the next bar on the . bar of this passage the chord is the derivative of the dominant eleventh (the "chord of the teenth of the same chord. XVIII be given the process is reversed. 509. and the chord being quitted as an unusual form of the augmented sixth (§ 610). introducing the various forms shown in this chapter as naturally as he can. dominant seventh of G. [Chap. the student will probably find We the present chapter the most difficult in the volume. 580. to analyze very carefully all the exercises now to be given . it will be of great advantage to him to compare his own analysis with that given in the Key to the Exercises. After working the exercises here given. never to leave his tonality doubtful. ^Tr}—TZt}A^ bb: ii°7* ^ i f II Vi3rf*\ G: V7 (Vii</) G: bVI^el At the first third inversion of the added sixth") in Bb. bvt not before. a chord of the thirteenth being changed into something different. Die Meistersinger. Ex. He must be careful to resolve each properly. strongly urge him. When he has done this. -^- 1 — l- . (I) Moderata. and. Exercises. Owing to the almost inexhaustible varieties of the chromatic chords of the thirteenth. it will be profitable for him to try to compose short pieces of eight or sixteen bars in length. in which every chord is fully analyzed. Wagner. in this he will find the three rules given in § 558 extremely serviceable. above all.264 Harmony. if he would master the subject thoroughly. is clear that there must be here a double enharmonic change G b and D i? being changed into F tt and C jf. ] Chromatic Elevenths AND Thirteenths. wtf-rTr^=^=^t^^=^ ^6 3 6 =p I r-=i»^=ig= I -t-t 6 6 5 6 4 (4— 7 6 f5 6 6 5 6 6 5 4 ( m -f—^sr I I I 6 J 7 6 P^^FF^^E^^^ — 766 766 67 Vje 7 je . 5 t b4 6 3 jt J4— 2 4 8 (V) PasioraU. XVIII. 6 6 — - 616 ][6 6 14 3 7 a? —6 9816 4117 6 6 115 J17 J5 t 4- 45- (VI) Larghitto.Chap. 4 SJ142 76tl4 6 6 5452 6 7 fl4 16 1.5 6 45 6 6 7 9 7 8 7 5- 1] (III) Andanti. 7 (4-115- 2— 4 . (IV) Andante. 265 (II) Larghitto. =t2=U S 7 ^m 6 6 4 3 b'7 43 662 —4 6 — 55—3 6 4 6 t] 1?7 6 3 t|6 6 6 4 3 S . [Chap. Of. iB 6 4 6 B be b5 B — T5S4 — J2 S 6 7 4 (VIII) Mcderato. m. ^ (VII) Andante. XVIII.p .266 Harmony. ] Chromatic Elevenths AND Thirteenths. r' I i.7 bS « 4$ (5 3 J 4 3 ^%^faj:^gi^ {6 — 56—6 M^^j=. XVIII. 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This is the Chord OF the Augmented Sixth.Chap. and that the upper notes are the two sharpest. in other words. whether major or minor. there is one chord of great importance and of fre- quent use still to be noticed. whether in a major or a minor key. 582. In addition to the series of fundamental chords already explained. or of one of its "borThe differrowing keys. 581. and which contains an interval which we have not yet met with. which is formed in a different manner from any of the chords yet shown. given in Ex. It is 584. Aj? also being chromatic in C major. is chromatic in both keys. 583.) of the same tonic ." the fifth above or the fifth below. The only possible augmented sixths in the key of C are above the minor second and the minor sixth of the scale. 269 CHAPTER XIX. We already know that every discord in a key is derived from the dominant. at {a) D^is a chromatic note in both C major and C minor.(§ 520).) In both these cases all the notes of the chord belong to the scales (major or minor. XIX. or in which the major ninth was combined with the minor thirteenth (§§ 573-575. that it is derived from two keys and therefore from two dominants at once. must always be chromatic. but the chords now to be explained are derived from two tonics. ence between the augmented sixth and all other intervals is. THE CHORD OF THE AUGMENTED SIXTH. for no diatonic scale. we shall find that only two of the notes thus obtained will be in the key. contains the interval of the augmented sixth. while at (^) Fjj. We saw in our last chapter certain forms of the chord of the thirteenth in which some of the notes belonged to the major and others to the minor scale of the same tonic . either of that key. Such were those chromatic thirteenths in which the ninth was riiinor and the thirteenth was major (§§ 560-571). If we take the chromatic scale of C. the notes of the chord were taken from different modes.] Chord of the Augmented Sixth. It must further be observed that the interval. 374. {a) • (*) Ex. 510. and put an augmented sixth above every note of the scale. P ^^^ important to notice that the lower notes of these intervals are the two flattest notes in the key of C. and the chord containing the interval has a — — — . though rare. 586. the minor sixth of F minor. f: V9-I-C: V we c: V9 + g: V We shall . (a) „ The (b) __ ^ „%J —J b (c) %J —J b (d) . analysis general tendency of the notes of an augmented inmost frequent resolutions which the two notes move apart. for both to approach ((/). augmented fourth.) a "double generator. XIX. minor ninth of C and the major third of G while {b) contains the minor ninth of G and the major third of D. in being derived from two roots. the of the augmented sixth are those in It is even possible. not only. is combined with the and at (Ji) the minor sixth of C minor is leading-oote of C combined with leading-note of G. octave. as at (a) below. "double root. 512. and in the latter of the dominant and supertonic. at the intervals seen in Ex. or one remains stationary while the other moves a semitone toward it. The chord of the augmented sixth differs from all chords hitherto met with.) of the key a perfect fifth above. We have at present only seen the interval itself. [Chap. each other by step of a semitone. and perfect fifth of the lower note of the interval.student will see are the major third. 511.?7o Harmohy. as at {c) 585..) l Itg J- Ez. as we have just seen. one or more notes must be added within the interval. These notes will be the seventh. 510 may be marked thus . The usual forms of the chord of the augmented sixth are made by adding either one or two notes belonging to the upper of the two roots. . More rarely each descends a semitone. 587." or (more accurately. There are three forms of the chord in genei:al use . The That at (a) consists of the . In the former case we have notes of the tonic and dominant fundamental chords. but in the fact that it is not made by placing thirds one above another. which is always formed by combining the flattest note of one minor key with the sharpest nois (the' leading-note. : {a) (6) Ex. as at (tf). as at {b) . 511. and minor ninth of the upper root. (. Look once more . which the . terval being to diverge (§ 234)." At (a) Db. to complete the chord. see presently that this use a simpler formula in our one is given to make clear the nature and origin of the interval. we have first to show how they are made. each a semitone in contrary motion. The minor sixth of a key is and the roots of the the minor ninth of its dominant chord intervals shown in Ex. " Instances (that is simply "Augmented Sixth") thus i?VlA6of these analyses will be seen in Exs. : analysis. but this will cause no confusion in practice. F. which occurs in no other.Chap. may be added. Ex. 589. it is clear that the letters. G.above another. by placing thirds one. These three forms of the chord are usually known by That containing only the third is called the Italian Sixth. it mark the three chords at (a) with 588. A. German the natuof service. gives the initial letters I. the figurings of these chord." * As to "aid memory" dreenish. that containing the third and fourth is called the French Sixth. The order Italian. French. or G6 below the root. mart ^W ^ W would of course be necessary to ft6. Sixth* 590. instudents are apt to confound these names. containing third alone. g. XIX. The positions here shown are the root-positions of the Owing to its peculiar construction. usual forms of the chord have major thirds above the root. 513 {b) is not chromatic. 478. As these chords are not made. third and fourth. 486. 614. and S°959 1. If the key were C minor. ral order of the chords. 513. as the augmented the chord can be instantly identified by the interval of sixth. and that with the third and fifth the German distinctive names. {b) C:l7VIn6 bVIpg WIgs c:viit6 vip-g viQe In the rare cases. these are indicated by "A6. 472.) may be — . In marking the chords of the augmented sixth in our we indicate the roots by )7ll and 7VI in a major key. we show the exact nature of the chord by adding It6. F6. we use capitals for the numerals . third and fifth. 495.] Chord of the Augmented Sixth 271 third will always be present. We ^ and to it either the fourth or fifth show the three forms of the chord. the following artificial (for which the author is indebted to his friend Dr. root-positions resemble the figurings of inversions of triads. like all others. : — («) Ez. J. ing the figurings. in which irregular forms of the chord are met with. in the latter key the root As all the of the chords seen at Ex. of the three syllables " I ForGet. or chords of the seventh . to be mentioned later. just as we show the dominant discords e. and by \fll and VI in a minor key . always a major third above the root. and in the German sixth the The examples shortly to be given will make of the chord. This is because the interval of the diminished third (the inversion of the augmented sixth. but Wlf will show that the next note above the third is in the bass. We have seen in § 584 that the augmented sixth on {'II composed of fundamental harmony of the tonic and dominant. We now give this chord with its principal resolutions. neither of the dissonant notes of the augmented sixth can be doubled . . as contains only three notes. it is therefore not surprising that the chords of the augmented sixth on l?II are much less often met with than those on i'VI. in the regular forms. This is the simplest form. French sixth the • this quite clear.272 Harmony. The chord is figured like an ordinary first inversion of a triad . As with other discords. and bt Jt4 the latter extremely rare.VIit6V7bVIit6vii°lj7'/bVIit6ll7r!. We is already know that tonic discords are rarer than supertonic . 592. Y^lb or |?II^ will indicate that the third is in the bass . commonest progressions first. in which form it is tolerably common. XIX. and that on bVI of dominant and supertonic harmony. 515. We now proceed to speak of the three 593. the third from the bass note therefore appears in two parts. putting the Ex. I. Ex. fourth. note above the root is. [Chap. Evidently one note must be doubled in four-part harmony. but the sixth being a chromatic note in the dominant chord. C: bVIn6 V tVIiigl. 516. will require to be indicated accordingly \ 6 or jj 6. |. As the first dicating the inversions will bear a new meaning. . This form of the chord susceptible of two inverfirst is 5^5^=^ be. Of these the infrequent.VIjj6m is 594. The Italian Sixth.) can hardly ever be used with good effect except in the last inversion of the German sixth. in the fifth In the Italian sixth this will be the sixth itself. it usual forms of the chord. Hercules. : Ez. and (as will be noticed. analyses are so simple that. C: IrVIpg This chord is figured like the second inversion of a chord of the . 20. we omit them. — ^^VI to V. II. 620. 596. to save space. Fall of Babylon. The French Sixth r gg? :. 617. Schumann. ^^ Prometheus. ^ ' M'.] Chord of the Augmented Sixth. Spohr. Ez. Here is seen the commonest resolution Handel. Op. ^^m — -*I . 516 (^r) ) is rather rare. the most usual progression for this chord. XIX. 518. '^I^ B ^i"£:J ^^ Here we see the chord on bll resolved on I. Ez. The passage looks like a half cadence in E flat minor . but on another part of the scale. 619. Here follow a few examples of the use of this chord. Ez. This resolution. 521. Ex. Beethoven. Humoreske. on V7 (Compare Ex.Chap. that it is really a cadence in B flat major is proved by these being the final chords of the movement. ) the same as ^VI-V. ill The 595. seventh . 523. though possible. a: VIC Vb (d: vii°7^) IV/5 VIpg Symphony \c Mozart. it is seldom used (See It is needless to show all the 594). 625. the student will understand the progressions without difficulty. bVIpg V IrVIjrg \c bVIp-g vii°fr7</ bVIpg H?^ With the aid of the analyses here given. Susanna. I . but the chromatic note must of course be indicated when not in the bass. as the progression of the dissonant notes is governed by the rules with which the student may be reasonably presumed to be by this time quite familiar. The following examples of this form of the chord will last inversion is so sufficiently illustrate its use IiXi : 524i Handel. § resolutions of these inversions. 622. in V7 G minor. 599. : C : bVIp-g* IfVIps' I'VIk6'' The harsh in effect that. XIX. 598. There are three inversions of this chord Ex.The principal resolutions of this chord are the following: Ex. [Chap.274 Harmony. V Ex. 597. and the progression is Vlpg^r \b and in Ex. *' Paradise aud the Peri. p. ' — — Ex. 527. on the tonic chord.e29. it is almost always a major chord. 628. Mendelssohn. which The major chord on the subdominant in can be nothing else. first i Vlp-gVIie 1?II resolved on the tonic |?II resolves on the tonic chord." Ex. 520. the French sixth on When an augmented sixth on We Wagner. 524. on the second inversion. is the entry of a new part. on the root-position in Ex.n.Chap. on the the G in the bass on the last chord first inversion in Ex. The examples now to be given illustrate other resolutions. Athalie. tr Die Meistersinger. 525. of the augmented sixth taken in succession in this way.] Chord of the Augmented Sixth. 526. 600. 27S In Ex. 525. XIX. The analysis of Exs. In the following bar we see the French sixth on VI changing to often see different forms the Italian sixth before resolving. 526 is so simple that we leave it to In all these examples the French sixth resolves the student. 524 we regard the F in the alto as a suspension by analogy with the B flat in the treble of the following bar. ^II7WIf6 Here we see minor chord. and the chord resolves rather irregularly on the first inversion of the dominant seventh Schumann. the second bar can in a minor key only be a " passing chord. f: iv* VI16 Vlpg VI G: bVIpgr V* G: ivi This interesting passage shows in the first bar the Italian sixth . vipg ^r^b Here the D and F ft of the French sixth are suspended by E and G. tr Ez. as in Ex. XIX. Ex. and in the second bar the second inversion of the French sixth irregularly resolved on the first inversion of the dominant (Compare Notice that G. changed to the French by the addition of the fourtn . The resolutions of this chord are the same as those of the other two forms. Ex. III. (Chap. 527). The chord in the passage now under notice resolves on \\ic. third and fourth crotchets of the second bar as chromatic passing-notes in two parts by contrary motion. Verdi. and . 531. rises because A Ex. Here are shown two positions of the chord. The German Sixth. an illustration of the rare progression mentioned in § 240. with a diminished third above the bass The last chord of this bar is clearly an auginented sixth. Here is falls to the note on which it Would regularly resolve. We find first the rare last inversion.because of its resolving upwards. 602. 601. like the minor ninths and thirteenths which have been already met with.276 Harmony. 530. We Here the fifth of the chord (the minor ninth of the upper generator) rises a chromatic semitone in the major key. the D]? is incorrectly written. 512 {e). where they approach each other by step of a semitone. the derivative of the fourth inversion of a dominant eleventh. to remind the student of the difference in the figuring. Ex. b5 C: tVIr have given the chords in both major and minor key. Observe also that it would be possible to regard the second. the seventh of A. The passage is further interesting as furnishing an example of the rare progression of the notes of the augmented sixth shown at Ex. 532. for eft is not in the key . The last example to be given of this chord offers some new features. Requiem. excepting that when the bass falls a semitone it usually resolves on a second inversion. note. resolved direct on the dominant. fall fifths French fe= sixth. Evidently. are not always objectionable.Chap. (as will be remains stationary in the minor.] Chord of the Augmented Sixth. if 277 the chord is a semitone. Like the three inversions. 603. the fifth will making consecutive fifths with the bass. Such seen presently).be- is: i =«&= be 1 . this form of the chord has . XIX. Ex. 640. 638. In the following passage the chord were a dominant seventh in E flat. the minor ninth of the upper generator. Its resolution sixth shows it to be the last inversion of the German on the minor sixth of the key of D. 537. The commencement of gives Schubert's fine song "Am this an excellent example of the first inversion of chord. "Am Meere. resolved on the root-position of the tonic. Vebdi. [Chip. — — . Beethoven." £z. In this Tcey Aj? is . 536 shows the resolution of the chord on domithe score. show some other Colomba. resolu- tions of this chord. Meere ' ' Schubert. 607. 639. 512 (^) . and moves in consecutive fifths (§ 468) with the bass. The passages next to be given Mackenzie. Requiem. Ex. it 605. . The dotted lines show the progression of the separate parts in Ex.Mozart. its true notation is G j|. XIX. and which we do not recommend for the student's imitation. # is written as if Symphony in D. in the part writing by no means usual with . £z. is written as E^.278 licence JTaxmonv. nant harmony in this case on a dominant eleventh the two notes of the augmented sixth move in similar motion (Ex. not a note 606. F V. Ch^. XIX.] Chord of the Augmented Brahms. Sixth. Schicksalslied. 279 Ex. 641. Ex. 539 gives the chord on the minor second of resolved on the chord of the dominant seventh, the upper note of the augmented sixth remaining to be the third of the following chord. At Ex. 540 is the last inversion of the chord (compare § 605), resolved on the dominant chord; and at Ex. 541 the chord on the minor sixth of the scale (here written as B^ instead of €[?) Ex 542 is somewhat similar, is resolved on a supertonic seventh. the augmented sixth being resolved on the supertonic chord but here it is taken above a tonic pedal, and the minor ninths G from both the generators are written as augmented octaves The real notation of the chord * is of course (§ 5^9)- this 608. Schumann's music is full of interesting examples of select a few typical specimens. chord. We Schumann. Novellette, Op. 21, No. 7. 1 ^ r ! i * I I Ex, 543. Ex. 544. Schumann. Kreisleriana, Op. 16, No. 2. -1- At Ex. 543 the chord # is the augmented sixth on the minor 38o Harmony. [Chap. XIX. The notation is evidently inaccurate, second in the key of A. The as B band Ett cannot possibly belong to the same key. E jj is really F J^, and the resolution of the chord is unusual, Ex. 544 being on the first inversion of the submediant triad. in which, to make the progression clearer, the distribution of the first chords between the two hands has been altered is another illustration of false notation. C| and Gl? cannot belong to the same key. The whole passage is in B [>, and the C | in the second bar is really D t?. The chord * is the second inversion of the augmented sixth on Gl? (with a diminished third), resolved on the root -position of a supertonic seventh. — 609. The following passage Schumann. " Bunte Blatter/' Op. 99. Ex. 645. probably unique, as containing four chords of the augmented many consecutive bars. The first two bars are on a "double pedal" (see Chapter XX.). The first chord of the second bar is the second inversion of the German sixth on the minor second of the key resolved on a minor tonic chord. (Compare Ex. 528.) The third bar of our present illustration shows the last inversion of the German sixth, resolved on the dominant of C minor, as in Ex. S4° > the fourth bar gives the secofid inversion of the same chord on the minor second of C minor, here resolved on a major chord ; and the fifth bar contains the first inversion of the chord on the minor second of G minor, the minor ninth of the lower generator rising a chromatic semitone, and the chord being thus resolved on the third inversion of a dominant minor ninth. is sixth in as 610. The three forms of the chord of the augmented sixth already explained are by far the most common, but by no means the only ones to be found. We give a few of the rarer forms. Haydn. Creation. Ex. 646, Chap. XIX. J Chord of the Augmented Wagnhk. Sixth. 281 Tristan und Isolde. £x.B47. Verdi. Requiem. '^^= Ex. 548. Hi^^kk^^^ E. Prout, Overture "Rokeby." -Jg : M - £z. 649. In Ex, 546, B jj, the third of the lower generator for C, the seventh of the upper. The chord is the of 'i^ is substituted first inversion is — Another position of the same chord seen in Ex. 547, though here it is simpler to regard the chord as a French and to consider the G|j an auxiliary note. At Ex. 548 a beautiful effect is obtained by the substitution of the major for the minor ninth of the upper generator. Ex. 549 shows the chord on the minor second of the key, with the minor ninth of the lower generator, and the octave, third, and minor thirteenth (instead of the seventh) of the upper. It may be said in general terms that any combination of the harmonies of the two generators is possible for this chord, so long as .the minor ninth of the lower and the third of the upper generator are present, and that no false relation is induced between the notes employed. sixth, 611. Like other fundamental chords, the chord of the augsixth can be freely used for the purposes of modulation. As it can be taken in either a major or minor key on either the minor sixth or minor second of the scale, it can evidently be taken in any one of four keys and quitted in any other of the mented same four without an enharmonic change. But it is also largely When thus employed, available for enharmonic modulation. the upper note of the augmented sixth, being enharmonically changed, becomes a minor seventh, of which the lower note of 282 the interval is Harmony. the generator. [Chap. XIX Ex. 660. This change evidently converts the chord into a fundamental seventh. 612. thought will show the student that it is only be thus converted ; for the French sixth contains a note which will not be a part of a chord of the seventh at all ; while the Italian sixth will be impossible as a seventh in four-part harmony, owing to the doubling of the little A the German sixth that can third. 613. This enharmonic change of an augmented sixth to a dominant seventh, and vice versa, is mostly used when a modulation is desired to a key a semitone up or down. If, for instance, in C the chord of the augmented sixlh on Af? is taken, and the F ^ changed to G t', the chord becomes the dorhinant It might also seventh in D \l, and can be resolved in that key. be quitted as the supertonic seventh of GJ?, or the tonic seventh of A t?, but these resolutions, the latter especially, are seldom, if ever, to be met with. Conversely, if we take the dominant seventh in the key of C, and change the F to E |f, the chord becomes an augmented sixth in B major or minor possibly, even, in F ^ major or minor. We shall see directly that some other enharmonic changes are possible; but the above are by far the most usual. 614. We shall conclude this chapter with a few examples of enharmonic modulation by means of this chord. Our first extract — Schubert. Sonata^ Op. 164. what has been said in the last paragraph. At the and fourth bars is the. chord of the dominant seventh in F major. In the fifth bar B is changed to Att and the chord becomes the last inversion of the German sixth in E major, in illustrates third 1? CKap. XIX.] Chord of the Augmented it is Sixth. 283 which key 615. follow ; resolved at the seventh bax. illustration will Our next be found more full. difficult to we therefore give the analysis in Exi 552i Bach. Chromatic Fantasia, it: V9 bar of this passage is clearly in B > minor ; as the note F ^ in the bass of the second bar is not in that key, it is evident that there is here an enharmonic modulation, the chord being The chord in B b minor written in the notation of the new key. will have Eft, and will be the last inversion of the German sixth. The modulation, as proved by the last half of the secIn this 1? minor. ond and the first half of the third bar, is to I?, nor key the chord * cannot be dominant, because of the supertonic because of the D b ; it must therefore be the last in- The first A G minor thirteenth (§ 575). 616. The progression of the harmony in the fourth and The chord * in the fifth bars is the same as that just analyzed. version of a derivative of the tonic fourth bar flat is taken as the last inversion of a German sixth in (the notation of three notes being enharmonically changed), and quitted as the last inversion of a derivative of a tonic thirteenth in F sharp minor, which is resolved in the next bar on At first sight the chords the dominant harmony of that key. marked * in the second and fourth bars of this extract Iook A like third inversions of dominant sevenths in C I? and A ; but 384 Harmony. [Chap. XIX. they cannot be so regarded, because these keys are never estabThe chords in question must therefore be taken in their relation to the keys next following. 617. One of the most beautiful and novel harmonic progressions ever written will be seen in our next example. lished. Ex. 653, Spectre's Bride. V Db This passage commences in IV1 Cb: I bVI(j6| C minor, and passes rapidly through major, whence by a simple, but most unexpected, enharmonic change, a return is made at once to Ct} major. The chord * is taken as the augmented sixth in C I?, its notation in that key being D i? to C I' If the chords in the third and fourth bars be written in B 1^ major (the enharmonic of Ct^), the student will follow the progression more easily, as then only one note will need to be changed for the key of C. It will be a useful exercise for him to do this for In this passage himself; we shall therefore not do it for him. we see the converse of the modulation shown in Ex. 551. 618. Our last example is chosen to show the student how to overcome some of the difficulties arising from false notation in the extreme keys, as well as from incomplete, or merely suggested harmonies. Ex. 554i Schumann. Romanze, Op. 28, No z. The first chord, being a chord of the diminished seventh, can be (as we already know, § 544), in any key. We look at the next bar to see what key the music goes into, and we find C | minor clearly indicated by the A {j, B and F x. The fourth |f, quaver of the bar is an outline chord of the augmented sixth, in its last inversion, with the diminished third ; for this interval Chap. XIX.] Chord of the Augmented Sixth. 285 The occurs in no other chord. x must be of necessity a because of the E jj in the upper part at false notation for t[, the beginning of the last bar ; for no chord which contains E G A notes can possibly also contain G x. The chord at the end of the bar is therefore the augmented sixth tt, C fi, F x; the last note is enharmonically changed to Gjl, the change being exceptionally written, and the chord is left as a derivative (t'VTIl;;) of a tonic minor thirteenth in B major, and resolved on the dominant of that key. The enharmonic change is the same as in the passage from Bach given in § 481 ; and the G X was evidently written by Schumann instead of {[ because of the note resolving by rise of a semitone as we have so often seen to be the case with the minor ninths and thiras ^ one of its A — A teenths. 619. The student will no doubt find the analyses just given Such passages require, but they will certainly repay, careful study. It must not be supposed that we have given all the possible examples of such modulaThis our space will not allow ; we can only give a few tions. somewhat difficult to follow. representative specimens. Besides this, the resources of art are not yet exhausted ; new combinations are constantly being discovered, and it is certain that whenever such combinations are good, they will be capable of a satisfactory theoretical explanation. Exercises. (I) ms Vivace. ^Ejzt^^^T^r—b-j-iTb^^^^jg ae6 t|6 P^p f=^"r^ tl6 ^ ira 4 4 3 fl- II6-— m tl6 t5 (II) Larghetto. 2 |g>:J r" J 1 . XIX.286 Harmony. [Chap. 5=1=1= (6 je ' 6 6 7 7 (XII) Larghetto. b5b44 jje 6 6 6 116 s 6 S6 He 6 jje 4b5 3 — b7 3^ 465 fle 3 (XI ) Moderato.] Chord of the Augmented Sixth. 8 — 6 46 3 6 6 b4 2 4 5 S 6 b7 b4 b5 2 3 b5 b b5— 6 5 tl Jl 6 6 }6 4 3 J6 4 6 4 3 6 $6 87 4 S 1 s- b . 5 ' (6 t6 4 6 7 Jtt4 t 2 $5 6 761t6J6 6 4 t1 6 987 5 {6 5 Jt6 US 4} f (4 2 6 J6 ' 6 be 6 5 b5 4 t (X) AlUgrttto. 6 J16 J6 be 4 S 4 3 J5 4 7 6 3 5 (IX) Andante. 287 b7 US 6b7 4 6 6 S6 t|6 )(4 I. iTF=t= 5 614 ]] 6 6 6 6 2 4 1 US je— e 34 4 3- =t=t: 6 ^ 6 6 7 6 H6 U 6 mrrrtE^^^rrtr-r:r4^^d^j4^^^^ 6— He S6 b5b7 6 b7 IT 6fl6b6 6—46442 6 6tt4 7 6 J16 7 46|f J 3S2 (XIII) Andante.Chap. XIX. Modtrato. I ^\ V f^ riT^^R-^' ^ f6 4 3 6 j-4i^ J6 IfI 4 4 2 ^ 6 St S7 f ::t 4 P^ P-i^PP n^^H^^ f^ \ir-> b7- T7116 t J . Vii/ace. xix 5 6 $6 (XV) Hymn Tune.288 (XIV) Double Chant. 6 6 Ir4 7 9 117 8 3 Tt 6~ 6 S5 ( J2 4 I- 7 6 • «- (XVII) ' Hymn I Tune. i m^iT-1 j_ j J 6 M^r^fir^rrf^ 4 2 6 6 '? =F ztz 6 6 5 116- 6 6 4 4 3 4 5 ' - 6 4 7 If ^ ^ ff=ffF=rr^B ^ 6 6 I. ^grfagfe. ]]4 6 1]6 Fe %\ 2 4 6—ebS 31 9 7 tj i 3 4 2 it 5= l77 ne'e 4 6T 3 1> (XIX) Hymn Tune. [Chap. ModeraU. 7f6 5 3 4 115 6 7 S 6 7 \> 6 4 *S 2 b 5Jt4 II |6 t| 6 4 6 7 I? 7 6 2 7 I] 7 \n - b6 J 6 4 7 US $ f . Unto.u-fj^ 9 7 6 7 4 4 5 ( XVIII) Hymn Tune. 6 6 b7 16 (9 6 4 7 I? —6 —4 7 65 (XVI) Hymn Tune. Harmony. XX. the dominant pedal almost always comes first." 623. III). pedal is mostly found toward the end of a movement. — — . but a root-position. and is not allowed to move A jljl in a way in will which it could not move were it a bass note. A Pedal is a note sustained by one part (generally. for then the chord # would be. the note next above the pedal is considered as the real bass of the harmony for the time being." 621. But the progression at (3) is (§ 189. as at (<r). however. In marking the analysis of a " Pedal point the pedal note is to be indicated passage containing a pedal. At the third crotchet of (a) is the second inversion of the dominant chord over a tonic pedal. 555. the tonic pedal very good example of this may being reserved for the close. stance of this is the opening of the Pastoral Symphony in the "Messiah. the bass for the time being. The name is no doubt derived from the pedals of form a part. may not leap to A quite correct. the passage at {a) were over a dominant pedal." 622.Chap. The pedal note is not a therefore D. 289 CHAPTER PEDALS. It is not unusual for the same piece to contain toward the end both a dominant and a tonic pedal . The note used as a pedal is invariably either the Tonic A tonic or the Dominant. though not invariably. the bass) through a succession of harmonies of some of which it does. Pedals. When the pedal note forms no part of the chord above it. An example make this clear. though A well-known init is sometimes met with at the beginning. as is evident from the fact that what we call a pedal is called in France and Germany an " Organ-point. because the pedal note is the root of the chord. the organ. when this is the case. XX. Ei. which are used to play the bass of the harmony. the latter being the more common. be seen in the last ten bars of the great five-part fugue in C minor in the first book of Bach's " Wohltemperirte Clavier. " that is a 624. 620. and of others it does not. it would be quite correct. part of the chord . not a second inversion. If. x:&. But at (r) the first two chords are marked I and \b. At (a) the second chord is marked I (not W). (dominant pedal). The chords above the pedal. Ex.. 560). [Chap. because in both cases the pedal notes are the roots of the chords. Mass in F.except those of which pedal note is itself the root. with the analysis marked below them. is not the root. 557. though a note of the chord. or T. 555. (tenic pedal).P. we shall not mark the roots. are to be marked without reference to the pedal at all. to save space. by D. 666. (not I^) . we give (a) and (f) of Ex.ago Harmony. . excepting in one case to be seen presently (Ex. and at {/) the third chord is marked V (not V^). The following examples of dominant pedals require explanation. £z. Cherubini. even though the pedal may be one of the upper notes of the chord. little 625. The student should by this time be so accustomed to analysis that. because the dominant pedal. 558.P. pedal the £x. placed under the roots and followed by a line continued as long as the lasts. To show this clearly. In such a case it is called an " Inverted Pedal. ii* lb I IVi Quartett in D minor. similarly treated. 560." or " Inv. Mass in C. 56O1 Beethoven. r At Ex. is Though a pedal note to by no means unusual ' is most often found in the bass. voices (or parts). of which the voice dominant in z is seen the the upper part of the harmony." Book i. whether in an upper or middle part. In our analysis. both in three and four-part harmony. sustained as a pedal note.Chap. D. ending with a "Tierce de Picardie" (§ 229). and at Ex. is indicated by " Inv. ' ' 626. " placed over (not under. " Wohltemperirte Clavier. XX. ' El. Ex.] Pedals.') the other roots. Sometimes a pedal parts only are given. also in the upper part. 561 is the tonic. note is found at the same time . -J- IV lb ii V Mozart. but the pedal note itself is not reckoned as one it will be seen that in the last bar of the extract there are three parts exclusive of the pedal. it meet with it in an upper. The end of the eight gives an excellent EZi 559. This is a case of very frequent occurrence. T. 628.P. or (more rarely) in a middle part. This passage illustrates a point of some importance which must The fugue from which it is taken is for three here be noted. Fugue 2. Bach. 2gt second fugue of Bach's "Fortyexample of a tonic pedal. 627. we give the analysis of our next example.P. To show this. 661. an inverted pedal. . —^ f • f f • student will remember what has so often been insisted upon broken chords (as in the bass of Ex. 27. An example has already been seen in Ex. 562 we see a dominant pedal. and at Ex. the pedal note is also in the middle. Mozart. : [Chap. At Ex. on the piano they are very .292 Harmony. Sooata in D. XX above and below. 563 a tonic pedal in the highest and lowest part of the harmony at the same time . with different qualities of tone. No. and the B is a dominant pedal. In the orchestra. 664. as in the following examples Ex. pedal note in a middle voice is somewhat rarer. We add another — The that A of a somewhat different character. The special interest of the passage arises from the fact of the pedal note being so close to the other notes of the har- mony. 562) are harmonically the same as if all the notes were struck together (§ 228). 629. i. The fifth quaver of the second bar is here evidently the first inversion of the chord of F minor. J. Beethoven. in this latter passage. such combinations are common enough . rare. Ex. 441. Sonata^ Op. 662. Beethoven. 14.* but it is by no means invariable. A pedal point often begins. 293 630. Op. 666. Sonata. 2. No.Chap. and generally ends.] Pedals. /fi^ . as the following passages prove : £x. with a chord of which the pedal note itself forms a part. XX. This has been the case in all the examples hitherto given . Op. 569. with a distinct modulation to G major in the continuation of the passage. 83. 633. Tariatioiis. 20. Paradise and the Peri. Schumann. Mbnsblssohm. a further modulation is made to E minor. We have here a dominant pedal in B minor. Ex. On this dominant pedal in B flat is a modulation to the very . Humoreske. be instructive.294 will Harmony. Ezi 570i Schumann. Our next passages more curious. Ex. [Chay. and the music continues in that key are to the end of the extract. XX. . at the third bar a moduminor. Op. Here we lation is see a dominant pedal in to made G E flat . 668. 295 remote key of of E minor. the restriction appears unnecessary.] Pedals. Two examples by living composers will conclude our Dvorak. to the keys of Ei. 571. with a modulation in the third bar to the key of F. In this passage there is a dominant pedal in D. on which is a modulation Jason. It is possible. and towards the close of the finale of his symphony in A. In his organ fugue in D minor in the Dorian mode. 634. . Here is seen a tonic pedal in D minor. the music returning at once to the key B flat. A * Some theorists strictly forlSd any modulations on a pedal except those referred to in § 631 . Beethoven introduces a pedal E alternating with an auxiliary note. XX.Chap. LudmUa. illustrations of this point. A. is . Mackenzie. C and B flat. to introduce omameptation on a pedal note. jg^^^^^^A ^ J J. St. but. tained. though rare. Bach has a shake on a pedal . 572.* 635. double pedal. otherwise the fourth above the 636. with both dominant and tonic sussometimes to be met with but in this case the tonic must be below the dominant. Ei. provided the modulations are properly managed. In many (see. and XIII. bars i this is done. The last exercise is written for five-part harmony throughout. as numerous combinations not hitherto met with will be found. . of a double pedal.] (I) Allegretto. it indicates that there is to be four-part harmony." Exercises. 5 4 7 5 2 8 4 87 4 l?7 944 5 4 3 3 6 6 7 S 5 B^=g—r t|7 r I r r t|4 r fi ^ i^ t|6 -t- ^ t|7 8 3 6 b7 6 6 7 4 2 4 4 h6 4 — (II) Madtrato. VII. 2 of Brahms' s " Deutsches Requiem. A will be found at the end of No. 3 9 7. ent voices. 8 7 4 2 6 4 5 4 7 5 3 ¥6~~5~S6 J4 B (4 h |J 7" fl4 2 b?^ 4 3 -iff. where four figures are placed under a pedal. 545.--^ [The figures of these exercises will require very careful attention. which is unfortunately far too long to quote. XX An example will be bass will produce an unpleasant effect. 3 — 76 4 6 9 . for instance.396 Harmony. very fine example of which neither pedal note forms a part. With a double pedal it is rare to find chords seen in Ex. it is to cases the figures are placed in an unusual order and 3 of the first exercise). exclusive of the pedal note itself. When show the student the progression of the differIn a few passages (see exercises V. [Chap. 897 ^^ 3 2 6 (IV) Andante. 5 4 6 76 46 4 65 4 b'5fe 5 7 t)6 2-— (a) «4 5 S 897765 4 6t|4 5 6 m 3 a From this point put four parts J4 above the pedal. 9 .$6 44« 7 J16 — tl3 4(7 4. XX. 7 1^ 6 Ik J7 117 6 7|4 H 6 b%b 4 3 4 4 b 6 1|4 6 6 7 7 8 $2 4 4 4 2 ^6 4 5 3 2 2 (VIII) La rghctto.] Pmdals.Chap. 3 6 5 ^1^^^^ 6 4 6 b S4 be 12 B l77 t] J4 5 «2 3 — — B7 6 J7 5tt4b4 2 ^^ 6 3 6 6 2 5 43 565 (7 £7 2 9 S 8 $6 4 6 J15 6 5 " " 7 4 8 5 £8 — 9 7 6b6 3 4 3 5 B6 4 3 3 6 137 4 3 7 4 2 8 3 ! 6 4 3 6 ($7 6 J Jt4 2 J2 4 S6 b7 115 3 —45 6 6 6 } 8 6 7 45— f.- 3 (VII) Moderata. !737t|7J7 ]|6 367 45444 2 3 2 2 =p: 4 8 3 7 d— 44 5 9 7 i j J 3 ir 6 4 3 986 4 r^^ 7 6 5 »54 3 6 4 5 3 4 =t= — — 46 8 3 ^ (V) 4f4 5(5 |7 6 Modcrata. . H6 5 115 1 — — 6 5 6 6 5 7 11 64II9 J16k6 5 1|7 bS 4 JS ]]6|76 6 7 1] 8|7 B 5 117 1. 4 2 5 4 4 2 3 — .19 1.298 Harmony. XX. „^UiJ^'-J 117 6J * 2 — - 3 t' 4 2 ga^J.J^n ^^^g^^-4jj^^jjjJ -7 3 — 6 — 74 2 ___-_-j1-_—iP Mjjl^ 6 6 IJ 6 J J J J7 B7- P —0^ 5 3 .9 8}7 (IX) ^^^f=t^^ 6 r r * rlJ. [Chap. •—» 1 » ^ 1"^—"F--^ . . Double Chant.Chap.] Pedals. XX. 299 (XII) . we shall have consecutives . if the root be present. both being in root-position. to introduce all the notes of the triad . For instance. as at {a). and with the third of each chord at the top. and in a derivative of the ninth both these notes should be retained. Thus in a chord of the seventh. one and sometimes two. however.Ml I If the chord of C be followed by the chord of A minor. it will therefore be necessary to double either the root. as at (3). Even in a quartett. it is clear that if we introduce the fifth in both chords. We shall therefore conclude this book with a chapter explaining the general principles by which a compioser is to be guided when writing in fewer or more than the four parts part. in the second chord. XXI CHAPTER HARMONY 637.part writing is justly considered the founda- tion of harmony. so as to keep the third and seventh similarly. 638. Not seldom. there are never more than three notes sounded at once but the middle part being in arpeggio. where practicable. one of the parts takes two notes of the harmony in succession.300 HaRMOHY. it is clear that if all the notes It is advisable. and even more parts. This is not three -part writing in the sense in which we are treating of it now. n Ex. the fifth should be omitted. e. . 197 where the upper part moves from the seventh to the fifth. while in instrumental compositions we frequently meet with passages in five. 639. In writing in three parts. there is practically four-part harmony throughout. often have rests . FEWER AND MORE THAN FOUR PARTS.g. . and the middle part from the fiftji to the third of the chord. . as in the first bar of Ex. Though four. it is very seldom that a composition of any greater dimensions than a hymn-tune is found in which the harmony is in four parts throughout.. hitherto treated. as at (f). the most characteristic notes of the chord should be retained. but it frequently becomes needful to omit the fifth. In chords containing more than three notes. [Chap. W. 640. three-part harmony is often virtually in four parts because of one of the parts moving in arpeggio. 360. . . in a root-position of a chord of the ninth. or the third. THREE-PART HARMONY. 573.W| I I . of a triad are present none can be doubled. In instrumental music. six. in Ex. IN XXI. either the third or seventh. 574.^^^ fifth given illustrates another important principle that the part-writing should have special regard to the motion of the separate parts. Mendelssohn. El. give two examples. St. the tonic appears without either third or ^ — ^ ^ ^ . In a full cadence in three parts it is desirable that the penultimate chord (the dominant in its root-position). El. This passage is the opening of the unaccompanied trio in the . 95. Paul.Oiap. the purity of the part-writing would have been impaired. should be in as complete a form as possible. 264. Robert le Diable. 301 641. The fewer the parts. But in vocal music the compass of the voices may render it necessary to break this rule. XXI. Had Mendelssohn made his tenor leap to A I? for the sake of having the third in the last chord. and bass . The parts should either be at approximately equal distances. the more clearly each is individualized. — tenor. Thus in the following cadence. We now. The rules for the position of the chords given in §§ 94. as in Ex. apply no less to three-part than to four-part harmony. Cherubini's first mass is written for three voices soprano. and in many passages it would be impossible to place the tenor nearer the soprano than the bass. 575. 643. even if this involves leaving the final chord incomplete. or the largest interval should be between the bass and the part next above it. 642.] Fewer and More than Four Parts. close of the just The example 644. Meyerbeer. one vocal and one instrumental. to illustrate the principles laid down. Harmony. XXI. . Trio. 576i ^ ^- .^^-. and observe the reasons for the exceptions. 87. how the chords are mostly comBeethoven.^^ I^J^^.302 third act of the opera. Ei. . Notice [Chap. Op. -^ . plete. V/^ No. V^ (7 ri ^^11 .Chap. XXI.] Fewer and More than Four "15 Inventions" . 677. Inventio. i. Farts. 303 first written are Bach's is the opening of the Bach. given here. Ex. 650. Judas Maccabaeus. We now give two examples of vocal two-part harmony. 45 1 duet the two voice-parts. being a cadenza is indicated in the original by is The its fact of its being printed . [Chap. let the student refer to the extract from the Here The Lord is a man of war quoted in Ex. The passage just thirds below. XXI. |tlff-_ a cadenza for unaccompanied solo voices. The first Ell B79i Handel. 580. though not necessarily A progression of two voices complete harmony by themselves. Wagner. are The rule in such cases as this supplemented by the orchestra. in fourths thus would therefore be incorrect. is that the voice parts must make correct." omitting the lowest voice part. is the and tenor commencement of a double fugue given The second voices.304 Harmony. Der Fliegende Hollander. the harmony will be correct. an example of this. which are printed on the upper staiT. even although an instrument played If another voice adds the in thirds below the lower voice. ' ' ' ' . out by the alto £z. given is taken from the trio "Lift thine eyes" in "Elijah. to go. It will readily be understood that every part above four to the harmony increases the difficulty of the task. the fifth voice is voice is the new one. Thus. and even for twenty-four voice parts. because of the danger of incorrect progressions. and more parts is by no means uncommon in the works of Bach. Among modern composers. XXI. 653." and the Kyrie and Gloria" in 48 real parts by Gregoriq Ballabene. and many similar instances might be given. if possible. Beyond this number it is not needful seven. consecutive octaves and fifths by contrary motion may be used freely . the general rules already given (§ 97). HARMONY 651. while of our own countrymen the place of honour in this department is probably due to the late Rev. and therefore the difficulty. even when both voices leap . etc. one. added 652. the stringency of the rules relaxes. Orazio Benevoli. we even meet in the works of the great masters with examples of a doubled leading note. 654. There parts in IN MORE THAN FOUR PARTS. Sir Frederick Ouseley.Chap. it is immateHal which In five-part harmony. but harmony in ten. usually either a second soprano (as in the examples to be given . and eight parts. But the most astonishing feats in part-writing are probably Tallis's "Forty-part Song. composed many masses and anthems for sixteen. In adding to the four voice parts. which it is needful to avoid. but this does not invali- date the general principle.] Fewer and More than Four . No new rules need though it is better to avoid this. twelve. six. be given for writing in more than four parts the practice of the best composers will be most clearly understood by a careful study of the examples now to be given of harmony in five. The opening chorus of his cantata " Herr Gott. will be found most useful. Such pieces are merely ingenious curiosities . an Italian musician of the 17 th century. increases. Brahms and Wagner are especially distinguished for their skill in "polyphonic" (many part) writing. It will be seen that the outline of the harmony in this passage is perfectly clear. Many cases will doubtless be found in which it is necessary to double a secondary note . dich loben alle wir " (founded on the choral known in this country as the 100th Psalm) is mostly in fifteen real parts . hidden fifths and octaves are allowed. Farts. . consecutives. But in proportion as the number of parts. that in general it is better to double a primary note of the key than a secondary. time of the 303 first in small notes this also explains the irregular three bars. In writing for more than four parts. is hardly any limit to the possible number of which harmony may be written. instead of the upper. the two trebles and the alto being on the upper staff. had he arranged the upper parts in the third bar thus As this would to see have been a more usual position for the chord. could not well be omitted. G. This is not the case in this particular passage. lines on the lower staff indicate that tenor parts cross each other. We have placed the alto part on the lower staff. In the fifth and sixth bars first tenor has B throughout. because it makes the passage clearer to read. EZi 582i Mendelssohn. He might. is and the The dotted the and sometimes even with five. ' ' ' Ex. In more than five parts. ' Acis and Galatea but instances may also be found of a second alto or second bass part." This passage is for two trebles. " Tu es Petrus. Our next illustration will be in six parts." It will be seen that in the last bar but one the A and G on the upper staff are printed in small notes. Bach. as in the five-part choruses of Handel's . 581. Cantata. alto. alto. as he had left no voice available. XXI. The third of the chord. Our next example is arranged in the usual way. it becomes needful to cross the parts in order to avoid consecutive fifths or octaves. where the crossing seems to be . [Chap. This passage bass. and bass. and Mendelssohn has therefore added it in the orchestra. written for two trebles. Belshazzar. two tenors. have easily managed it. tenor. Exi 583i is difficult Handel. 655. below) or a second tenor. it why he did not adopt it.3o6 Harjuony. as usual. however. —"Wer weiss wie nahe mir mein £nde. 656. Handel. J PI I _ -J J J J yj JS-j which is n. 2. had it been condensed on two staves. to show clearly the progression of the different voices. In the 658. The following extract. £Xi 684f * 1 Brahms.] Fewer and More than Four Parts. as it would have been impossible. example we give we have printed the passage in score. XXI. Parnasso in Festa. and the other falling to E in the following chord. written for treble. t Gesang der-Parzen. At the third crotchet of the second bar is an instance of a doubled leading note (§ 652) .Chap. and in the last crotchet of the following bar is a doubled seventh. affords illustration of Notice in the first chord the crossing of the tenor below the first bass to avoid consecutive octaves with the first alto. but in the passages in seven and eight parts to be quoted shortly. Observe that the F is here 2. primary note (§ 653).4 4^4^4^-4:4: two some other altos. a. Seven-part harmony is comparatively rare. tenor. points. such a procedure often becomes absolutely necessary. ' ' ^ ^ ^ * ' —="*—*^ ^^ ^"^"^ ^-^^^ Alto x. B85. 657. Ex. Sop. one F rising to G. . 307 the result of a wish to give melodic interest to the second tenor part . J* I*. and two basses. i. " (§ no). Chbrubini. 659. — . but with all the voices divided. . we find We give one only one choir. [Chap. Credo i 8 Voci.368 Harmony. Choruses in eight parts are much more common than Sometimes they take the form of double choruses. In this passage will be seen numerous crossings of the parts and the leading note doubled in every bar at the end of the fourth Between the last chord of bar it even appears in three parts." at others. as in Handel' s ' Israel in Egypt and Bach's "Passion according to Matthew . course a slip of the pen. example of each arrangement. Here we have printed each choir in in " short score is previous examples. XXI. ' Handel's " Athalia " and Mendelssohn's 114th Psalm. as in in seven. ' that is for two separate choirs. the fourth bar and the first of the fifth are found consecutive This is of perfect fifths between the first tenor and the bass. probably the result of the haste with which it is notorious that Handel composed but such slips are by no means uncommon in his seven and eight-part writing. The part-writing and will repay close study. as remarkably pure. Mendelssohn. if the priticiples underlying the science of harmony are thoroughly grasped. when all are employed at once some of the parts This can be seen are mostly doubled in the octave or unison. 661. Though in the quotation given from this work in Ex. so as to allow himself more room for the additional voices. Even in the strictest writing it is frequently expedient. z. 3. . himself proficient in five-part writing before trying to work these. Sop. becomes tedious. if too long continued. some of which eight notes. XXI. to give rests to some of the voices. to the student. but not all.Chap. as great fulness of harmony. Farts. 309 660. It will be seen that after the first two bars the harmony is only in seven parts. there are parts. He will also find it useful to with a larger number of voices. *' Am Himmelsfahrtstage/' Op 79. endless instruction is to be gained from the 663. he will sometimes find it expedient to take the first chord in a higher position than that indicated for four-part harmony. the voices are therefore arranged differently.and three-part four voices. for the sake of variety and contrast. In concluding this work. I ^^mm Bass x.] Fewer and More than Four . In our second illustration Ex. the are harmony 662. Much of what is called eight-part writing is not really For instance in Mendelssohn's Octett for eight stringed instruments. The student can now experiment for himself in writing For two. In this case. is not in more than five doubled. we have only one choir instead of two . B87. such. No. we offer one piece of advice Much. can be learned from a textbook . in for fewer or more than the accompanying parts need not be treated as voiceFor more than four parts he can hardly do better than the harmonization of the chorals of which he will find a large colHe should of course make lection in the book just referred to. 456. parts. harmonize for more than four parts some of the exercises given in this volume. harmony he will find the National Airs given on pages 20 to 30 of the Additional Exercises to Counterpoint very suitable . is impossible to make any text-book absolutely exhaustive . xxi. "Prove {i. while founding his practice mainly on the example of the acknowledged masters of the past. hold fast that which is good. from wheresoever it may come . not neglect to acquaint himself with the more modem developments of music . It is from their works that the volume have been deduced . and let his motto be. test) all things. masters. therefore. let him welcome what is excellent.e. ' . [Chap. Let the earnest student.3IO study of the rules laid grea^t Harmony. the best It theory is that which agrees most closely with their practice. for down in this art is always progressing. Appendix A. 665. Any now say. With the Ecclesiastical Modes. and it would be impossible to place a common chord. in which he treats of the twelve church modes." was changed. as a '667. he altered all their names. 3II APPENDIX A. We now which were known give the six principal ecclesiastical modes. when we speak of the major and minor modes" of the same key (§ 37). and minor. ) excepting B.e. no two of the old modes have the same order of tones and semitones. At the present day any major or minor key differs from every other one only in its pitch.* 666. borrowed from the Greek scales. on the other hand.] ThE ECCLESIASTICAL MoDES. As soon as the tonic or. By writing an octave of notes. and using natural notes only. the "Final. . G minor as C — note could be taken as a Final (or. either major or minor. Each of these was known by a name. though differently applied. superior modes. we obtain the various ecclesiastical modes. as it was then called. commencing on each note of the scale except B. and when only seven notes were employed within the octave. tones is identical . in a book entitled Dodecachordon. and shows their connection with the For some not very evident reason. i. * The names by which the modes are now known were first given to them by Glareanus. though in a much more restricted sense. but. or Church modes . above it. The order of tones and semi' ' G major is the same scale as C major. It will be impossible within the limits of this volume to deal in detail with so large and intricate a subject as that of the old Ecclesiastical. which were in use before sharps or flats were introduced. but transposed a fifth higher. the semitones must evidently fall between other degrees of the scale. The term is still employed in modem music. as a certain amount of knowledge of them will be of great use to the student in helping him to understand much of the music of the older composers. But there is a most important difference between the ancient modes and modern keys. as we should tonic. misunderstanding. Each as Authentic. such transposition was impossible. etc. the ecclesiastical Dorian being the Greek Phrygian. published in 1547. 664. The word " Mode" is the equivalent of what is now called key. we shall here give a short account of them. probably from a ancient Greek modes. In fact. which was inadmissible because its fifth is a diminished fifth. THE ECCLESIASTICAL MODES. Ltdian. e. with the addition of the 669. 668. These modes contain the same notes as the corresponding authentic modes. Ex. or dependent mode. Phrygian." 670.g. would change one authentic might be supposed mode into another. MlXOLTDIAM. was substituted for it. we show the position of Dorian.313 Harmony. that the Hypo-Mixolydian . It — the Greek preposition first meaning "under. Each of these modes had a note called a Dominant. which note now comes in the middle of the scale." Each of the six modes of which we have been speaking had an inferior. or prevailing note. as the nearest note to B. It was so called from its being next in melodic importance to the Final. instead of as the first and last notes. its final . In the scales we have just given the dominant is marked of with "D. Aeolian. In this mode therefore C. not because its harmonic relation to that note. 688. known as a Plagal mode. In the authentic modes the dominant was always the fifth note above the final. connected with it. because it could not take a common chord above it. This word was used in quite a different sense from that in which it is now understood. [Appendix A mode begins and ends upon the semitones by slurs. except only in the Phrygian mode. in which B was inadmissible as a dominant. The connection of the plagal modes with their respective authentic modes is shown by their having the same names. but begin on the fourth note below the final. at that the beginning on a different degree of the scale (a fourth lower). prefix Hypo-. 313 would become the Dorian. though each plagal mode except the Hypo-Phrygian begins upon the dominant of the authentic mode. in the case of two modes containing the same notes (one being authentic and the As the other plagal. Hypo-Lydian.) by noticing which note was the final. It must not be supposed that all melodies written in modes were necessarily at the pitch here given. G is still the final.] The Ecclesiastical Modes. We now give Ex. or the Hypo-Aeolian the Phrygian mode. and. In the Dorian mode D is the final . Hypo-Ionian. C is chord above it. But this was not the case. that note is now no longer the dominant. I Hyfo-Fhrygian. is unavailable as a dominant. taken as the dominant. They could be transposed to any pitch that was most conthese venient." Hyfo-Dorian. 672. though its initial note is D.Appendix A. The dominant of any plagal mode is always a third below the dominant of the corresponding authentic mode. Obviously the Mixolydian and Aeolian modes would be too high. except in the HypoMixolydian. Hypo-Aeolian. and the nature of a mode would be ascertained by observing the positions of the semitones. 589. the third below D. in the Hypo-Mixolydian. {a) the six plagal modes. as in the Phrygian mode. last chord was always a chord on the final. because it has no common Here therefore. indicating the finals by " F " and the dominants by " D. Hypo-Mixolydian. just as it is as a final. 671. Besides this. there was no difficulty . and the Hypo-Dorian and Hypo-Ionian too low for ordinary use. in which B. it was allowed in some of the modes to sharpen the note below the final. * [Appendix a in this. 588. 673. Mixolydian. teristic notes of the Dorian mode (Ex. we have a transposed Mixolydian mode . pointing article * Those who wish to study the subject are recommended to consult the " Musica Ficla" in Grove's Dictionary 0/ Mmic and Musicians. could be effected in two ways to the modern change of key. but into these we cannot now enter. a change of mode. 676. and its major sixth. 588 (a) ) are its minor third. but as the development of the art advanced even as early as the^ middle of the sixteenth century the necessity for a leading note in the penultimate In this case. the mode becomes a transposed Aeolian.. as will be explained presently. and Ionian. either the final itself would be changed. and the intervals above altered — change of mode. If we change F to F jf. so as to have a major instead of a minor chord on the dominant. But while in modern music we modulate freely between any two keys. corresponding —an analogous procedure to the modern modulation between the tonic major and minor. and Aeolian. a. as we shall see directly. the modulations of the old modes were more restricted. 675. fore. while in a plagal mode the melody would lie between the fourth below the final and the fifth above it. no alteration whatever was permitted . We spoke just now (§ 674.) have major chords on their finals. as we now change the tonic in modulating.314 Harmony. Vol.) of the possible alteration In the oldest music of the non-characteristic notes of a mode. we shall see directly that the characis produced.) have minor chords. it will be noticed that three (the Lydian. therechord of a final cadence began to be felt. 674. that is a modulation. B. or the same final could be retained. in the other modes the final is approached by a tone from below. while the other three (the It will Dorian. Of the six authentic modes shown in Ex. if we substitute B j? for B t}.* — — 677. For instance. We now give a short account of each mode. But the non-characteristic notes of a mode could in certain cases be chromatically altered. also be seen that only the Lydian and Ionian have a leading note . There were a few other cases in which alteration was also permissible . If a characteristic note of a mode be inflected. Phrygian. In an authentic mode the melody would lie approximately between the final and its octave. Each mode had certain characteristic notes which distinguished it from every other mode. Modulation — it that is. . and each mode had what may be termed its own favourite modulations. F. Its characteristic notes were the minor third and major sixth of the scale . C." -i-n~l J""' 1 . ** J. or the Tierce de Picardie In the whole of Bach's Chorals. The following choral the Dorian mode. IV. is a fine example of a melody in Cruger. while the Lydian. if all its also major thirds. is chord being major. numbering was employed. 315 out its special features. We begin with I.) have also minor sixths. not one of the characteristic notes. it was changed in the cadence.] The Ecclesiastical Modes. and Ionian modes. very nearly four -hundred. their occurrence in the same melody are sufficient to establish the mode. to C||. It was also the general practice not to conclude with a minor chord on the final either the third was omitted altogether. have The primary chords of this mode. as the plagal are derived from these. The principal modulations of the Dorian mode were to the Aeolian. only the subdominant But. Mixolydian. The Dorian Mode. Mixolydian. as the seventh note of the scale. One of the most important and most frequently used of the old modes. Jesu. 678. and Ionian modes. which have major sixths. Ez. It will only be needful to speak of the authentic modes. because the other modes which have minor thirds (the Phrygian and Aeolian. and v. notes are unaltered will be i.Appendix A. not more than about half a dozen end on a minor chord. thus becoming a leading note. meine Freude. 590. The third line modulates to the Aeolian mode . the Lydian mode has no chord on the fourth of its 682. The second line has clearly a modulation to the 591 (3). the final of the . It should also be noticed that it is not uncommon for a melody which ends in the Phrygian mode to begin in the Aeolian or Dorian . with D. with the cadence seen at Ex. Ionian mode is Ionian. This is the first of the three Like the Phrygian. while (^) was used in the plagal (Hypo. 68 r. Ex. The Phrygian modes could modulate into any of the and Aeolian being among the most frequently used. it will be remembered that C. 680. the semitone between D and E was always E b. We give as our example of the Phrygian mode an others. instead of on the final. 592. A. — . and the form of the final cadence distinctly proves the mode to be Phrygian. or in the Phrygian. as the last two the Phrygian bass notes.3i6 Harmony. [Appendix A. the cadence of the Dorian mode was unavailable. but just as the Phrygian has no chord on the fifth. The last chord. The chords on the final and the dominant are both major . Old Latin : "A solis ortus cardine. which is an augmented fourth above the. when the melody ended upon its initial note. in this case the real mode is not defined until later. rather than mode. except in some of the most ancient harmonies. though the first cadence can be harmonized equally well in the Dorian mode. special feature of the Phrygian mode is its final cadence. Bt). the Dorian. In the older music the note tt did not exist . The usual cadences A D were therefore Ex.Phrygian.) mode.'' *=ts The first line of this hymn is certainly the Dorian. Ionian. 691. is always major. the fourth of the scale. ancient hymn. it has one characteristic note. major modes. III. the dominant of the Phrygian mode. The Lydian Mode. of which {a) and (J>) were employed in the authentic mode. and as there was no common chord on the fifth of the scale.final. ] The E'SCLEsiastical Modes.Appendix A. more common than the Lydian mode just spoken of. in the original. 683. A. divided by interludes. melody with the sr^es of the modes given be seen that belongs to the plagal. which distinguishes it from the We Ionian. and but few old melodies are to be found which are Beethoven has employed written in the genuine Lydian mode. au^^M -J-hrt in I ^^ r-Mr this it r v \ rr\^ it By comparing Exs. in the Lydian mode. ) as a fine example of this mode. 589. But. and v. 132. it was early supplanted by the latter. Quartett in :i: A minor." that is the "soft kind. 132. it is less frequently met with than any of the other modes. and if it be sharpened the mode becomes a The usual cadence was therefore the transposed Ionian. or Hypo. 593. the slow entitled movement of which he "Song God by a We Ex. Op. somewhat like our "melodic minor" scale. which it It has two characresembles in being one of the major modes." theme of the hymn. Marx points out that as early as 1274 the old theorist Marchettus of Padua gives a rule that in the Lydian mode the B was natural in ascending and flat in descending the scale. 317 Probably for this reason. modulations could be made to any of the I other modes except the Phrygian. make a final cadence for the seventh is — . ) to one of the characteristic notes of the scale. ^'•- J J J I lj^ ^ v \ Beethoven. 588. The Mixolydian Mode. minor. B." name given to the modes when transposed a perfect fifth below their proper pitch. A of thanks to give the convalescent. old musicians the "genus molle. teristic notes. it for a special purpose in his Quartett in tic V— . the major third.Lydian mode. it is seen in the following example. he will find that in his harmonization Beethoven has most studiously avoided the introduction of the note B V. will This mode is much 684. (the lines of which are. Dr. The final cadence in this mode was our modern authencadence. IV. IV. and the minor seventh. "plagal" cadence IV I. which is the last line of Bach' s harmonization of the old Ambrosian cannot in this mode sharpen . owing to its near relationship to the Ionian mode. which distinguishes it from the Dorian. If the student will examine the quartett. — the seventh (as in the Dorian. — — scale. Op. and it has a great tendency to modulate into the Ionian mode by the substitution of B I? for This change gives the Ionian mode in what was called by Bij. Its three primary chords will be I. r Ex. the most frequently employed modulations being to the Ionian (the fifth below. inasmuch as the characteristic notes. 694. we select the old choral "Gelobet Ex. As an example of seist du.) a transposed Ionian mode.) and the Dorian (the fifth above). 'cj- :-\:2S J g J i-. 595. The Mixolydian modes could modulate into any of the others except the Phrygian . are the same in both. G — 685. Mixolydian was so closely connected with the latter mode that.r>j3_ — It will be seen that^ this cadence is identical with the modem The half-cadence in the key of C major the Ionian mode. due to the ever growing feeling of the importance of the leading note in a cadence. even in the older harmonizations." ^^ . it is not uncommon to find the final cadence of a Mixolydian melody in our modern key of This was probably (withFj{.ji8 Harmony." [Appendix A hymn "Veni. Creator. F and B. It should be noticed that the latter mode is especially connected with the Mixolydian. Jesu Christ. this mode. and too high in the upper. one of the characteristic notes. unless their compass was very limited. The only which distinguishes it from the Mixolydian mode.) mode. . most melodies. iv. acteristic specimen. and not a minor second above the final. has many points of resemblance to the modern minor key yet it is by no means identical with it. from A to A—too Owing to the pitch of the authentic Aeolian "St. corresponds exactly to our modern major key. In the second line there The third a modulation to C. not to our modern key of E minor. It will suffice to point out one important difference. VI. modulation is to the minor key a fifth above e.Appendix A. it was (as in the Dorian mode.] Ths Ecclesiastical Modes. and v. minor key in Chapter VII.) that in old music the note D || did not exist. in the Aeolian mode it was absolutely forbidden. not one of the 689. But.) being all minor. In speaking of the Phrygian mode. the dominant of the mode. But with the Aeolian mode this would be impossible. low in the lower octave. Another point of difference is. The Ionian Mode.Aeolian. line gives the entire descending scale of the mode.) is known . 319 The Aeolian major. but to E Phrygian. This mode.g. that in the modern minor key the augmented second between the minor sixth and the major seventh of the scale is often employed with excellent effect . most frequently used in old music. Its characteristic note is the major seventh. it will be seen. ) sharpened The Aeolian could moduin the dominant chord of a cadence. I Vf^S" ^ $^ The melody is < f U_|:a£:=p=^g=:£ ( ^ — 1 1 E is clearly Hypo-Aeolian. from A minor to E minor. In any modern minor key a common 688. Whenever therefore a modulation was made in the Aeolian mode to the mode a fifth higher. this would always be. 596. is the most mournful in its character of all modes. As a charwere written in the plagal (Hypo. other scale which has a major seventh (the Lydian. we give the familiar hymn-tune known as 687. its three primary triads (i. it was modern minor scale was formed from the Dorian and the Aeolian scales. In treating of the said that the . as in the Mixolydian. the Ionian and Phrygian being among those most frequently chosen. the seventh note of the scale not being. The Aeolian mode. with F and D naturals. Bride's"— Ex. late into any other mode. it was said (§ 680. mode. ' As an example of an Ionian melody we ' ' choose the old choral Ex. the primary all chords of the loivian iinal mode are major is (I. modem her. Vom Himmel hoch da komm' ich =t=l ^ full ("1 ^ T-nrr-'^ The At {b") and at first (^I p full _m — is 1 This melody in the "genus molle " (§ 682). A further difficulty is found in the fact that the modes are fre- quently mixed in the same piece. were to the Aeolian.320 Harmony. It will be seen that these modulations are quite modem in character. transposed into the key of its dominant. by augmented fourth. line is of the choral ends with a there (^) is a close on the dominant of the Aeolian mode close a on the final of the Ionian mode in its original key. This was effected very simply by introducing B|7 in the scales instead of B Ij. . and at (^) a the dominant key. in approaches more nearly than any of the others to our ideas of tonality. of notes or proto the gressions foreign mode itself Even the old in theorists were not always agreed as to the mode which a particular . B97. C. but to the introduc- whether in the melody or the harmony. A little thought will show the student is that this alteration in the position of the semitones exactly the same as that produced by transposing the scale a fifth lower. This mode. to modulation from tion. The modulations most to the Ionian quently used — at all events in the middle of the eighteenth century. the plagal modes were generally transposed to the same pitch as their corresponding authentic modes. the Ionian could modulate into any other mode except the Phrygian. and mode itself fact. cadence at (a). As in our major key. By this we are not referring one mode to another. V). We should now describe there was a plagal cadence in full close in them by saying that at {F) the relative minor. IV. and the cadence was also the same as now employed —V-I. A source of trouble to the student in investigaarises ting these old modes from the fact that. from the begin- ning of the sixteenth century. fre- Like the Mixolydian mode. its [Appendix A. fruitful 690. ." which he gives as one of his illustrations. * Some idea of the complexity of the subject may be formed by reading work A Concise Explanation of the the following quotation from that excellent Church Modes. will conclude by referring those who wish for fuller information on the subject to the articles by the late Mr. 32 of music was written. W. which appears to be that of the Lydian mode.] ThE ECCLESIASTICAL MODES. the chief points in which they differed from our and modem is major chiefly and minor keys. B. 6th from A).. S. historical. hardly an^ two are in exact piece agreement. by Charles Child Spencer. says of a certain passage. Marx's " Composition.Appendix A. is really that of the authentic dominant (2. to furnish the student with a general idea of the nature of the old modes. 691. but it is really in the Phrygian mode on A. The author in speaking of the harmony of the old hymn " Lucis Creator optime. We have been unable to do more here than to give a it is brief outline of the subject. and. and the harmony at the close of this line. " The passage appears to be in the Hypo-Dorian mode on D. Their interest at the present day when a special archaic effect is desired.. and Hypo-Phrygian on E.* Of the numerous authorities which the author has consulted. We they are hardly ever employed in modern compositions. to Chapter XIII of the first volume of A." . sufficient. hoped." and to C. excepting C. Spencer's Concise Explanation of the Church Modes. Rockstro in Grove's Dictionary of Music and Musicians. but in any other aliquot parts. it is nevertheless true that a certain amount of knowledge of the phenomena of rests solely the production of musical sounds is of great assistance to the student in helping him to understand the relationship of the We shall different notes in a key. . or sixteenths. the half will give the G two octaves above. SERIES.328 Harmony.. the quarter The division of any string into halves. as it has been already seen that the half of a string always .e. for the Taking. APPENDIX THE HARMONIC 692. the eighth will give the C in the string third space of the treble staff. each half will sound the octave above. as before. stated is not in the nature of theory. vibrates not only throughout its whole length. Though modern harmony it B. would be by no means correct to say that on natural laws. Thus. will give & ' ." or '^fundamental tone. e. etc. the etc. and so on. ilarly. • and. if the whole string sound the note viz. the note produced by the vibration of the whole length of the string. and to the note produced by the vibration of the whole string. Sim- string. it produces the twelfth of the fundamental tone. the octave above.'. so far as it may be What is now to be necessary for the student to apply them. in halves. i. If the whole sound a G. quarters^ eighths. and of one key to another. quarters. etc. and is perfectly familiar to students of natural philosophy. the whole string sounded this last C. perfect fifth in the second octave. fourths. . but of physical fact. may be : —A the different aliquot parts will always bear the same relation to one another. But any string will vibrate not only in halves." that is. fifths. G 694. and the musical tones produced by the vibration of 693. if fe" J - . the half of this (and therefore the quarter of the longer string first '- taken). The general law regulating the production of Harmonics sonorous body. it will be found that one-third of the " Obviously one sixth is half of one third. If a string vibrate in thirds. but in aliquot parts of that length. [Appendu b.g. therefore here give an account of these laws. such as the string of a thus stated piano or violin. : " fe* . thirds. @ string gives ^S^ fundamental tone. gives the various upper octaves of the "generator. oscillation. though a less strictly accurate one. The law of vibration corresponds to the bob of the pendulum. and the string be held by the other end. it will move at a rate which will depend on the length of string. clear that the sixth part of the string will give 695. What we call low notes are produced by much slower vibrations than high notes.Appendix B] TuE HaRMONIC it SerIES. If a given above can be shown by a very simple experiment. for every vibration of the whole string there will be in the same time two vibrations of each half. Here ^ J and the twelfth it must be said that the pitch of a note depends upon the rapidity of its vibration. and ' harmonics purposes . ball be fastened to one end of a string. be seen that all the even numbers of the series are octaves of some lower number. etc. that we have spoken of above.are all formed by vibra- parts of the whole string. that exactly as the length of the string </^creases. they are sometimes called "upper partial tones" or "overtones. three of each third. the difference between a pendulum and a musical string being that the former is free at one end. we get what is called the "harmonic ' ' ' — ' We shall now give the first part of this series from C. but as the word generally understood. that is to say. And this relation of length to vibration is invariable. An important law of nature as bearing on this point is that entirely rapidity of vibration varies inversely as the length of the string. are many sounds which are unavailable for harmonic partials is convenient. the more the ball will swing much faster rapid the vibration. four of each fourth. As the sounds we are explaining. the four(See Diagram on p. Thus in the long string C. When these notes are tabulated in the order in which they are produced. tions. Vibratioii is a periodic with a pendulum. etc. and the middle of the string. everyone knows that the shorter the string. It ' ' will . we shall retain it in speaking of these partial tones." A more common name for them. while the string is fixed at both. is Harmonics. and therefore have more rapid and a higher pitch than the generator. as — . series. because those first produced in the series that is by ' ' ' — ' the vibration of the larger aliquot parts of the string belong Among the higher ' ' upper to the harmonies of the generator.) teenth of the seventh. is 323 gives the octave above the whole. the rapidity of vibration z«creases. Now if the string be held in the middle. and so on. where the deviation from a position of rest is greatest. because (as has been shown above) the half of a string always sounds the octave of a whole string thus the tenth harmonic will be the octave of the fifth. 324. 696. and the ball allowed to swing like a pendulum. ^Appendix B.Major third.) Interval from the generator (or its upper octaves). Minor ninth. Generator (Fundamental tone. 2i < . .334 Harmony. Minor third. . Minor seventh. Perfect fifth. say. of a perfect fourth between the third and .Appendix B. and 1 5:= 3 X 5. These are therefore called "sec9 = 3X3 698. but from the seventh note of the series. The fractions below the notes show the aliquot part of the whole string which produces any given sound. 325 697. Hence we : get the following ratios for the principal musical intervals INTERVAL. being somewhat too flat. 11th. they are obtained by multiplying smaller numbers together. as well as the 13th. inclusive. the 14th). The 7th. ondary harmonics.] The Harmonic Series. Perfect fifth Perfect fourth Major third " Minor third Major sixth Minor sixth Major tone Minor tone Major diatonic semitone Minor diatonic semitone . and the nth decidedly too The 9th and 15th are not "prime numbers. etc. Octave .. first produced are all consonant to the fundamental tone .e." A very important use of this series is that it enables us to calculate the ratios of vibration of different musical intervals Thus between numbers i and 2 of the series is with accuracy. fourth. all the uneven numbers) are dissonant. NOTES. 13th. an interval of an octave therefore in every octave there are two vibrations of the upper note to one of the lower in the same time. and the "vibration ratios" underneath give the proportion of vibrations in the same time of the fractional It will be seen that the harmonics parts of the whole string. and 14th notes of the series are enclosed in brackets because these harmonics are not exactly in tune in the key of the generator. the 7th (and of course its octave." that is to sharp. Similarly we get the interval of a perfect fifth between the second and third notes. all the new notes produced {i. In this diagram the notes produced by the vibration of the aliquot parts of a string are given. The in the minor common chord therefore is an artificial product . and Harmonic Tissues does not rest solely upon unalterable natural laws. 701. Of the notes given in the harmonic series shown in our diagram. then. the more nearly they are related. This chord may therefore be regarded as a product of nature. the first six form the major common chord on C. 358.* " the system of Scales. and this harmonic is never audible compound tone spoken of in the last paragraph. in other ways. In each of these there is only one note of the diatonic scale differing from * Sensations of Tone. [Appendix B. one containing some upper partials together with and that the different quality of various its fundamental tone instruments depends on the presence in varying strength of these — — upper partials. but is at least partly also the result of aesthetical principles.336 HaRMONT. each giving the note proper to itself. or are so faint that the ear cannot distinguish them without artificial aid. he will hear iirst the fundamental tone. The rule is this Tlie simpler the harmonic ratios of the tonics of two major keys. 700. the major third above this. as shown above. but no prime numbers above 20 are available for harmonic purposes. as soon as it begins to vibrate. to found our whole system of yet of much service to us In the first place. even What takes place is that the string. Modes. An example will make this clear. and listen carefully. It has been shown that upper partial tones can be obtained by causing a string to vibrate in aliquot parts. and related. But the same can hardly be said of the minor common chord . p. the octave. Though we are unable harmony on the harmonic series. which gives a minor third above the generator is No. 1 9 of the series . most nearly related major keys to C are F and G. together with the If the student will fundamental tone when a string is struck. more faintly. and the same may be said of both major and minor keys taken as a whole. under favourable circumstances. ' ' ' ' ' 702. As a matter of fact many of these tones are so produced. it is : We know that the 703. But the higher harmonics are either not produced at all. It has been shown by the researches of Helmholtz that a good musical tone is a compound tone that is. to the fundamental tone. double octave. . As Helmholtz has well put it. which have already changed. twelfth. it gives us a good working rule for reckoning the comparative nearness or remoteness of relationship of any two major keys. divides of itself into its aliquot parts. for the first upper partial. strike one of the bass notes of a piano. and. and will still further change with the progressive development of humanity. it was said (§ 272. This is the reason why the 5 and 5 next most nearly related keys to C. viz : D and B flat. identical in pitch are heard together. It might have been supposed a priori that the next nearest related keys would therefore have been those in which only two notes were different. : : : : . from C to D is 8 9. 327 the key of C. while that of the perfect fifth is 2 3. But this is not the case . the ratio of the semitone being The views here given on scientific grounds 15: 16 or 16 117. after F and G. 705. These beats produce a certain harshness in the tone. and of the major and minor thirds 4 6 respectively. Sedley Taylor's Sound and Music.) that two major keys are related when their tonics are consonant. When two musical sounds nearly. It will now be understood why two keys. he will see that the ratio of a major tone. The nature of the difference between consonance and dissonance has been investigated by Helmholtz. are E 1^ and A ^. 704. and that if the consonance be perfect the relationship is nearer than if it be imperfect. The student will find the questions fully discussed in Dr. If the student will refer to the table of ratios given in § 698. No two major keys are related in which the ratios of the tonics contain any number higher than 6. who has shown that it is closely connected with the compound nature of musical tones spoken of in § 700. these two keys are not even in the second degree of relationship to C. It has been impossble here to deal with this subject in detail. which varies according to the strength and number of the dissonant sounds. W. what are known as "beats. but not quite. both of which can be warmly recommended. When treating in Chap. Pole's Philosophy of Music and M.] The Harmonic Series.Appendix B. the tonics of which are only a semitone apart are considered so remote ." or throbbings are produced. In consonances they are so few or so weak as not to disturb to any appreciable extent the purity of the tone . This effect is perfectly familiar to anyone who has heard an organ being tuned. though each contains only three notes common to itself and to C. but in dissonances they are much more prominent. IX of keyrelationship. are borne out by the practice of the great masters. . 213. Analysis of Harmony Anticipations. chromatic triads. 420.M. 468. how figuring. 216. 479. 312. Augmented thirteenth.560. dominant eleventh. chord of the. enth. . 328 exercise worked. Aeolian Scale or mode. . 90. 315. enharmonic modulation. 214. tonic thirteenth. 531.569. derivatives of. 554. 400. 253. diminished. . 686 scale or mode in connection with the . 423 dominant thirteenth deriva. 42. auxiliary notes. 562. 280. 138. 545. 591 . Ambiguous chords in modulation. secondary discords. 578. 322. 445. 549. not the pages. dominant thirteenth inversions. 553. inverted. root position. ornamental resolutions. 558:559. triads. false re- . 577. 568. 325 defined. 44. diatonic position. modern minor scale. chromatic chords of the ninth. indicated in the Added sixth. chromatic elevenths. sixth (see Chromatic chord of the augmented sixth ) sixth changed to minor triad on mediant of seventh. supertonic eleventh. 239. modes. dominant eleventh. 90. domi. The numbers refer to the paragraphs. : in four-part writing. 61 1 minor key. 436. 326.5o3. major. major and minor. 330. changing 330. 245 dominant seventh. tonic. analysis. 570.488. 308. 117. interval defined. minor key. eleventh. 330 appoggiatura. 331 example by Weber.33o. 368 dominant ninth. triad. 60 interval in sequences. chord of.565. 558.496. 383 . chromatic. 89. 31 1. 41. . tonic sev- notes. 415. 590. suspensions. . Accidentals. exceptional diatonic. 336. root 232. passing note. 326 examples by Bach. tween chords that are identical in appearance. 405. 23 interval in melody. 307 305 treatment of. dominant eleventh. dominant. minor. false notation.562. passing notes. 409. dominant eleventh inversions. pedal. major. 330 . Authentic cadence. Changing changing notes (see notes) distance above and below harmony note. 627 . more than one analysis sometimes possible. 558. dominant thirteenth. 403. 437. 567.3lo.derivatives of. 560. 315. 208. 346. written for minor 554. 667. 410. treatment 228. discords {see Secondary discords). supertonic seventh. dominant ninth. 394. 551. 164. augmented 214. 562. A. fifth . — 325- Appoggiatura. 166. Ambiguous suspensions. 406. 325. . . dominant ninth. 325. in harmony. 519. augmented 325 . supertonic thirteenth. . Anticipations Analysis. 559. 509> S'^) 511 519. 552. Arpeggios. 436. 325. chromatic tonic thirteenths. key.ANALYTICAL INDEX. 624 . supertonic ninth. 4 1 1 dominant thirteenth. triad. Auxiliary Notes : Accented. 529. derivatives of. 564. inversions of. 572. dominant seventh. 174. 39 common chord. 165. triads. 440. nant seventh. pedal.265. common : chord.A. Accented auxiliary notes. 436. 330 . modulation. 382. 411. 546. root position. chromatic chords of the seventh. 307. By Joseph Spawforth. added sixth. sixth. . keys. triads. 330. 467. how to distinguish be- 330. octave written for minor ninth. 207. 92. . major key. 281 . pedal. Alto Voice its 65 compass. root position. tonic ninth.R.499. passing chord. 560. 485. 566. transitional dominants.571. 326. second in minor scale. 295 . passing sevenths. 495. Handel. defined. 509. dominant seventh inversions. minor key. 308 . how to distinguish tonic and supertonic discords. 624 . Weber. tives of. dominant eleventh. of.550. 240. Broken chords and arpeggios. derivatives. inversions. when to use. 313. 374. . — — Cadential six-four. 378 . 266. 247 . 258. 306. figured (j« Figured Bass) thorough. 258. 370. 382. . rismg. how formed. 369. 118. 235. defined. 228. 379. 453 common. 36 how to find the root of. 243 . : analysis of deriva- 382. 372. fundamental. chord of. 384. 383 defined. 244. 15. 329. 163 voice in four-part writing. . derivative of. resolution of dissonances. 327. single. 233. 243. 36. on strong or weak accent. 381 leading seventh. 377. 118. 232. shakes. 379. 401 . half. 238. change best note to double. another key. 370. 239. 244. 236. dominant seventh in. analysis. fifth sometimes omitted. analysis of derivatives. seventh falling. 392. 260-262 . ornamental . hints on. 329 how taken and how left. 386 to 389. 417. omission of root. minor. root of a. 117. 312. . 232. 254 . 266 to to 374. melodies. 298-301 how to find. 161 . 380. 245. 240. fifth. minor key. stationary. 244-247 >ii> . 117. 313. avoid. 3^. 36. Root positions. 255. {d) second inversion. 405. diminished seventh. 242. Bass. falling. 382. . 232 how to find the root of. 376. ninth falling. dissonant notes. root omitted. 399. 327. 162. fig376. its compass. third. rising. dissonant. 117. or on a chord belonging to . rising a second to fall a third. 177. 370. 383 . 144. 313. how formed. the tonic chord. 410. major. consecutive fifths to avoid. leaping. 92. inverted. 370. 313. Best note to double notes). 384. 232. . root and generator. importance of. 370. derivaof third inversion. ornamental. position of final chord in a. of the Dominant Sevroot position. 117. 172. 250.Analytical Index. feminine ending. change of position. 175. 360. inversions very rare. 372. Chord enth : — Analysis. 390.4) exceptional. followed by tonic 232. 36. 232. 237. 41 1 enth : — chord absolutely defines the key. 368 . 252. 174.386. lation not caused by. {c) derivative of first inversion. 267. {e) derivative of second third tive Beats. 178. i^g) i^see Doubling of Borrowed chords. 261. generator of a note to. 178. 266. . example by Weber. position of the major ninth in the chord. Choice of chords in harmonization of Chord. major ninth in major key. 238. 394. Changing Notes: Analysis. consonant. 406. in one part. 368 tives. seventh. how to find the root. 263. .391Resolutions for. . 301 interrupted. authentic. . 117. eleventh rising. summary of. 381 derivatives. §36 . 306. {b) first inversions. 368. . turns. (. minor ninth in minor key. 400 . 235 of position. note omitted in four-part writing. cadential 177. 261 . — inversions. voice. 368. 314. 372 376. . 327. 704. 376 seventh. 456 to 459. 393. 376. (y) inverson. 314. ninth. chord of. 231. 436. six-four. of six-four. 25 1 seventh doubled. 373. 371. 312. modulation. 267 progression of third and seventh. Chord of the Dominant ElevAdded sixth. 265. consecutive fifths. close. figuring. — uring. 251. 265. 311. 375. 309. . — . 298. resolution. in more tlian one part. 330. defined. 383. hints on using. 375. inversion of a. 372. 374. plagal. 160. rule . fundamental discord. chromatic. 257-259 . 237-239 . Chord of the Dominant Ninth Analysis. 261. 305 unaccented. 251. 391. full. unessential discords. 17. 237. 368 . how formed. 327. 437- Cadence. 242. fundamental discord. 299. inversion. 241 hidden octaves. 268. 298. . Resolutions of- — (a) root position. 242 . middle. 240. effect of dominant and 234 tonic harmony. major key. leaping. derivatives of their importance. rules for. 329 323 figuring. 245. 264. 372. 253. 370. chord of. 234. 393 resolves either on its own root. 65 . 415. progression of third. 36. 232 in a full cadence. rules for. 256. origin of supertonic triad. of sixth. 315 . 236. in two parts. 484 keys from which they may be : — . V. passing notes. n. — The SUPERTONIC SEVENTH:— .330 Analytical Index. 396. analysis. 421. 420 minor thirteenth in minor key. and seventh. 593 — best note to double. 594 . 591 consecutive fifths. notes omitted in fourpart writing. 408. false 610. Chromatic Auxiliary Notes. minor ninth in minor notes omitted in fourpart writing. third and thir- best note to double. 494. 397. inversions. defined. German sixth Analysis. 617. figuring. 426. 402. FORM III— The . false notation. . defined. double genera- 584. 585. 485. 582. 484. 604 . 584. Analysis. 602. 593. 425 thirteenth. I. 601. . 602. 410-416. resolutions. principal . 430. Italian. 420. 499. figuring. 7. 434. derivatives. RARER FORMS:—Cou^Kn?. matic. derivatives. resolves inversions. 6. 498. 583 resolutions of the interval of 606. how formed. 596. . 399. 596. thirteenth ing. 614-618. how to distinguish between chords that are identical in appearance.610. 398. . 613. 399 584. 485. . 493. 497. 490-492 . inversions. 488 figuring. THE TONIC SEVENTH:—A. : I. 434-436 figuring. 496. 432. 425 stationary. chord. borrowed. FORM III—Root. position of the thirteenth in the chord. figuring. other root. false Chords. stationary. modulation. 35 . 42 . 496 . IV. inversions. 618. 583 . FORM teenth : 611. 506. 308. 396. 405. on either its own root. 609. suspension of complete. 430-43 J. 486-488.36. 425 varieties of the scale. examples. 602. 499 treatment of third . figuring. 495. principal resolutions. /F. 402 . tor. 440. 603 . false notation. leaping. inversions. resolutions. i MODULA 770iV. 394. its usual forms. 432. — third. 453 . 598. 424 resolves on its own generator or on tonic or submediant chord. 319. 397 progression of the eleventh. 422 how 42 1 formed. 483. Analysis. 418. /. $94. to avoid. falling. 503 . French and German sixth. examples. 42 1. 483. — 438 . consecutive fifths. Root position. figur- Resolutions: 489. 394 . when em- . 407. :— . relation. 442 progression of other notes of the chord. thirteenth Chromatic Chords of the Seventh Borrowed chords. 488 . 603 . FORM 593 . 597. $88. or some the augmented sixth. 605. origin of subdominant triad in major key. 610. 396. omission of third. figuring. 604-609. Italian sixth: — — Chord of the Dominant Thirteenth: Analysis. 607. — Analysis. 304. 396. false notation.—Root. 429. in minor key. 595. tone. 364. 587. 434-4. 441. 418. 430. position of thirteenth in the chord. 401. notes of a key. 602. position of the eleventh in the chord. resolution. chord. . DERIVATIVE.— The . ResoJutions : Root position. 404. 440. ninth. gradual resolution of. 438 .-— Enharmonic. tions possible. semi. . primary of major key. FOSM II. 399. ployed. inversions. 442 minor key. 605. 507//. defined. S90. figuring. 399. contains every note of the diatonic figuring. 599-601._Analysis. . 425 .— The French sixth: Analysis. 608. 601 figuring. seventh and Analysis. 423.443 major thirteenth in major key. 397. ysis.n3:i496. 429. fifth and Analysis. 419 in its complete form. 485 488 . . major ninth in major key. treatment of third and sev- 435-437- enth. resolutions. principal resolutions. 366. 412. third. 417. fifth. 394. 409. 402. 438. 598 . 589 on minor second and minor sixth of the scale. 6 . 603. resolutions. 440. Chromatic Chord of the AugAlways chromented Sixth : — key. — Root. 39 of minor key. FORM . derivation of. 486. origin of submediant triad major key. 420. — . 427. 425 "Sing. notation. 395. figuring. 474. 551. 7. 458. 556. 555. 512. 480 . 480. 529. (b") supertonic and tonic thirteenth. : 331 : —Root position. . 468 . melodic form. MODULATION: : Enhar- monic. 515-518. origin of. resolutions. 549. 479. Analysis. 467. 568. 470. 466-468 best note to double. //. Resolutions. 489. . VI. — ninth and thir- false nota- 562 false triads. Derivatives. 459 . 576. enharmonic between any two keys." 469 . 509. —Analysis. 476 . 568. Tonic: seventh. Neapolitan sixth. thirteenth. FORM and Chromatic Chords op the Ninth — Borrowed chords. table of. examples. 468 . 573 . . 474. —Analysis. OF A MAJOR KEY:—Analysis. Analysis. THE TONIC MAJOR AND MINOR NINTH: -AnaXysis. ninth Analysis. keys from which they may be borrowed. 478. 45 7-45 9. 537. FORM I. 572.ninth ana analysis. (b) — ( c) Major Chord on Supertonic : 481 . example. 511. ninth. sequence of diminchord of the Analysis. 572 510. examples. 542 to 544. 517. 506. 545. as a passing chord. 519. employment in minor keys. (e) . 5^9 > table 509. 457. 554. major and minor ninths. resolu • 503-505 . 577-579. defined. ninth and thirteenth 570. . two following. teenth: tion. 471 . 479 (a) Minor Chord on Tonic: — (d) Major Chord on Mediant Analysis. 469. correct notation of> 459 harmonic form. 477. 479. 468. 481. : — ished sevenths. rare in root position. 509.Analytical Index.558. resolutions. . best note to double. false notation. DOMINANT MINOS NINTH:— FORM to 575VIII. • Major Chord on Flattened (b) Supertonic : Analysis. deriva- 532-538 . With the generator : (a) dominant minor thirteenth false notation. 501. 560. 552. as "Tierce de Picarde.—Fifth^eventh. 481. 471-473. 566. thirteenth: resolution. 566. treatment of the third. derivatives. examples. keys from which chords may be borrowed. defined. false tetrad. false notation . — resolution. 470.559. 460. derivatives. 481. ninth. rule for its treatment. table of. . SUPERTONIC MAJOR AND MINOR NINTHS:—Anaiysis. — A. — seventh. — FORMIV. 569 fifth. vn. Chromatic Chords of the Thirteenth Analysis. 562 . resolution. 538. 567. 509 . 479. 570. eleventh and thirteenth: Analysis. of. how formed. referred to. 529. 563. 477. eleventh thirteenth: Analysis. Chromatic Scale Convenient — notation.— Third. 468. ninth and Analysis. Major Chord on Flattened Supertonic: Analysis. B. 519. modulation. 525-527///. 480.—Fifth. 510. 466.— Third. supertonic eleventh. derivatives. 468. Resolutions. Chromatic Triads 530-533. I OF A MINOR iir£K:_Analysis. 461.— Fifth. example.—-Third. 515. analysis. S36. 456.463. 460. : . 553. Analysis. — Minor Chord on Dominant — Analysis. 472. 531 tives. 508 . 453-455 . 546. //. 564> 5^5FORM II. 566. 467 borrowedchords. 459. as a passing chord. forms — mostly used. /K MODULATION diminished 464 466. Resolutions inversions. 502. best note to double. 561 resolutions. 469. 571. (a) Major Chord on — Chromatic Chords of the Elevdominant eleventh with enth : — : minor ninth. how to avert modulation. FORM III. 478 example. 539 . 479. 468. fifth. FORM v. 567- and — seventh. examples. 518. 528. of. : 569. Seventh. 500 thirteenth tion. 470. 462. 476. tonic eleventh.507. 550. 557- — — — (c) Major Chord on Supertonic • Analysis. — — Resolutions : —Example false notation. example. resolutions. 571. examples. 188. figuring. 39 . 481. . Compound 700. 213. Consonant chord defined. 162. 481 example. discords (see Secondary discords) . 479. . 102. Derivative and inversion. 99. chords of the sixth. augmented triad. 174. diminished triads. 97. Close. . Conjunct and disjunct motion. 9. Consecutive Fifths. 479. ysis. 89. First inversions. 163. Close and extended position. Church Modes \see Ecclesiastical modes. eleventh and thirteenth {see Chromatic chords of the supertonic seventh. fourths V PRIMARY AND SECONDARY TRIADS: ysis. best notes to double. distinction between. 182. triad. analysis. 227. 481 Major — Diatonic Triads of a Major —how /. 98. 89. 224. 178. of primary triads. sevenths. 93. 29. . PRIMARY AND SECONDARY Dimintable of. 187. 213. in approach- Degrees of the Scale. 140 IV. first sixth. 67-70 79- . 176-183 . semitone. 19. Secondinversions. ninth. 89. 172. 217-219. 1 1-13. names of. octaves and unisons. 169-171. 307 defined. 479 480. 174. eleventh and thirteenth (see diminished triad. 181. Chromatic chords of the tonic seTeleventh and thir- Major Chord on Flattened Mediant: Analysis. (g) a passing chord. 35 .-_Absolutely — define the key. 89. 7 . 213. eleventh and thirteenth (see Chords of the Dominant seventh. 481 ex- — . root.332 (d) Analytical Index. ninth. . figuring. inversions. rules for approaching and quitting. 92.) — PRIMARY 7WM/55. 29 . imperfect. teenth). one note example. iSConsonant interval defined. 166. (h) . "4Anal89 . PRIMARY AND SECONDARY TRIADS: Consonance imperfect. perfect. Chord on Flattened Sub-Mediant: Analysis. 38. 481. ished triad. how to find the 174. — cadential six-four. ninth. Leading Note : 481 example. 481. 117. exercise worked. defined. 19. seconds. use of. 189. 221. Key : formed. 481. 223. 78 . half cadence. 214. Key: —A Triads of a Minor 215. best note to double. 133 to interval. Leading Note 479. 481. Flattened (l) Minor Chord on Analysis. 58. 479. tone. 164. 178. best note to double. 216. how to find the root. 29. 64 ing a dissonance. 177. 252. scales) scales) major (see Major key and minor (see Minor key and . Minor Chord on Dominant as — 9 . 217. Derivatives of the Supertonic seventh. 97» 98. sometimes omitted. 184-187. scale defined. 174. defined. 8. how formed. ninth. 479. of secondary triads. defined. . compared with those of the major key. . 90. Anal174. Common chords defined. 113. 190 177. ample. (e) enth. interval. 6. sequences. Diatonic note of a triad sometimes omitted. 218. figuring.481. // SECONDARY TRIADS: ysis. ninths. eleventh and thirteenth). eleventh and thirteenth ) Derivatives of the Tonic seventh.175. diminished triad. 85. . ninth. analysis. 17s notes to double. 99///. 86. 88. Crossing of parts. Major Chord on Flattened Analysis. Anal166 best notes to double. 165. 71-73 with bass. TRIADS:— Jioot position. Dorian 210. how to find the sequence of best root. 15 . 102. Minor Chord on nant : (f) — Analysis. major chord on sub-dominant. Derivatives of the Dominant seventh. 175. interval. 112. 6. Analysis. auxiliary notes. 214. 36. 251. Contrary Motion. Compass of voices in four-part writing. 222. . ample. Subdomiex- Diatonic and chromatic elements of a key. ninth. best note to double. major (Dorian) sixth of the scale. — — perfect. 29. 27 . 42. 674.how formed. transitional defined. — . compass of voices in. Diminished Interval in Enharmonic change False notation) . suspension (see Sus- . 601. False tetrads. 97. defined. 163. 54-56- defined. chromatic scale. 166. 672. ^l. use of. Dorian mode. order Four. 670. line drawn through a figure. final. minor chord on supertonic. to 92. third sometimes omitted in final chord. Chords of the seventh. major and minor modes. . 295. 676. 220. fundamental Enharmonic Modulation by chord of augmented sixth (see Chord of augmented sixth V). 319. Lydian mode. 59in interval defined. 296. 665. line following a figure. Feminine endmg. Dorian sixth. its connection with the modern minor scale. 213. 562. defined. 669. Diminished fifth followed by perfect fifth. by chord of the minor thirteenth (see Chromatic chords of the thirteenth VIII. 51. Pedal). 684. second inversions. diminished. 99 . ninth. Eight-part writing. 685 . authentic thentic modes. 674. by chord of diminished seventh (see Chromatic chords of the ninth IV) . 504. Mixomode lydian mode. resolution of. . Four of tones and semitones different in three pensions). characteristic notes of. table of. notes. 667.683. 130 quence of sixths. 364. 115. how to find the key signature. 659-661. Diminished Triad. 163. 229. how to find the root of a chord from the figuring. pedal («« degree of the scale. table of.675. 688 alteration of noncharacteristic notes. for 7 '-73! primary triads. 224-227 . 24. 163. of notation (see melody. defined. — Accidentals. how formed. inversions of triads. 24. : —Auxiliary sixth. eleventh. 73. 143. 97. 74. Aeolian Ecclesiastical Modes mode. 228. rules for. 130. interval. . thirteenth (see ninth. 671. 118. Flat KEYS. fifth H. rules hidden. names of authentic modes. Disjunct motion defined. Discord major key. 170. 678. table of. 58. Picardie third. modulation. . 566. in minor key. 213. prefix. 665. 665. 16. pedal 636 minor thirteenths. 98. 51. 190. 175. leading note. 17. 679-681 669 plagal modes. 208. use of. 667 . dominant seventh. 269. consecutive. Double 365- octave. 233. seventh. augmented 605 to 609. names of plagal modes. and passing notes. 232. 573! tonic seventh. Final (see Ecclesiastical modes). signatures of. 65. Tierce de Picardie. root positions. 217. Dominants. 677. 566. minor seventh of the scale. 213 . rules for. 329 chords and their inversions (j« under each). 519. in diminished . 676. position of. 93. root chords. tonic (see Chromatic chords of the . False triads. 666. 28. 654 655. Dissonant chord. transeach . 673. 229. no figuring under a bass note. 98. audefined. authentic and plagal modes. Eleventh dominant [sec Chord of the dominant eleventh ) supertonic (see Chromatic chords of the eleventh). 174. minor ninths. Phrygian mode. 50. 16. 333 mode. difference between.524. 674. passing notes. 667. 637. Figured Bass: 164 . 460. False Notation 308 . 562. Dorian Mode. 24. keys. 19 . Five-part harmony. note.Analytical Index. table of. Extreme keys. 671.77. voices in. page 112. 682. 229 primary triads. defined.) Extended position of harmony. line under a note. 677. 16. dominants. 678. secseondary triads. figure under first bass note of an exauxiliary ercise. eleventh and thirteenth). Dominant. Hypo. 17. 668. 164. 168. 686.Part Harmony. Dissonance defined. unalterable. plagal defined. 171. 216. 164. Doubling of Notes triad. eleventh). Ionian mode. 235 Fifth augmented 23. 582 suspensions. 90. 53. Fifths. 689. 215. False relation. relative position of the parts. 698 secondary harmonics. three parts. 92. III. 24. 671. //. diatonic a. Hypo. seven parts.Dorian mode. compound.— I. 655. 703. Imperfect consonance. fundascale. 409. 29. ments of and chromatic ele35 . 9. how to end. 693. 197. 174. 252. 230. 151. 14S . consecutive. change its position. when indicated. Generator of a chord defined. Minor Key. 74-76. 29. 104- 93. 299. minor common chord. 332. dissonant. arpeggios. EXERCISE WORKED. Chromatic chords of the augmented sixth). how IV. 114. Harmonic minor chromatic scale. treatment of. (see Cadences). 302 . 693- ny. 671. of a chord. notes. of an interval. imperfect. 28. 228. 150. 201 clearness of tonality.334 Fourtlis. best position of. 41. part writing. 698. 693. five parts. 671. 119. 701. 25. for. 119. 645-650. 115. 114. 23. defined. figured bass {see Figured bass) . perfect. consonance and dissonance. consonant. leading note. 119. 331. 150. 161. exercises on. how produced. tone. 671. rules for {see Part writing rules II). Primary Triads in root position. Analytical Index. diminished triad. in two parts. 143. Indicating the roots of chords {see Analysis of harmony). rule to find inversion of. 178. ads and their inversions. 656. 201. ratios of. 671. major common chord. position. Inverted cadence. pitch and vibration. distinction between. 95 . 15. : — Fundamental 232 . 25. effect of using many secondary triads in succession. 1 10. 59-63. six parts. Hypio-Lydian mode. rules for. tition page 12. 658. with bass. 302 . 119-127. 21. vibration ratios. 151. . 329. stationary bass. key relationship. 627. 151. note to J 36. 146-150. hints on. 114. 704. 31 to . 657. 689. 30. best to Key: 35 — Analysis. discord. when a chord is repeated. in 638-644. to distinguish between chords which are identical in appearance. rules for. harmonics. 196. 77. 144. 346. to commence. Hypo-Ionian mode. diminished. 115. Generator and root. . find the root of a chord. rules for {see Part writing rules). rules for. rule Harmony Full cadence. choice of chords. Hypo-Phrygian mode. repeof a note in the melody. upper partial tones. major. 19. Half cadence. 100. 94. 436. 700. treatment of. 165 . 437 . 29. 693. how reckoned.sion. 193-199. close ercise and extended in. — Hidden How How to octaves. French sixth {see Chromatic chords of the augmented sixth). German sixth {see Chromatic chords of the augmented sixth). compass of voices 108 . minor. Inversion and derivative distinction between 251. how to commence an exercise. eight parts. 112. 26. 25. 206. exworked. Intervals. 24. 22. chords which define the key. 693. 694. . modulation when implied. 160. 78. enharmonic. weak. 17s. auxiliary Hypo-Aeolian mode. 152. defined. 21. short and open score. Hypo-Mixolydian mode. 704. compound tone. 7°l> overtones. Interrupted cadence. '697. diatonic material . how to end an exercise. mediant triad. Ionian mode. 28. 695 696 ratios of intervals. how treated. 26. 18. 29. 21. 74. 121. 697. 696. augmented. 200-203. mental tone. 4. 702. progres. 114. Primary and Secondary Triads. Harmonic Series: Beats defined. 300. Tri- 153-158. 659-661. root progressions. generator. large leaps in bass. necessity for. 145. inversion of. /// Primary and Secondary 21. Interval. 671. Italian sixth {see pedal. in melody. Analysis {see Analysis of harmony) . Harmonizing Melodies: and passing cadence — . Hidden fifths. 459. 22. table of. loi . 654. 113. 43.292. Minor Keys. 208. of a minor key. augmented sixth. —with Suspen- 50. Minor Scales: scale. 100. Leading seventh. 12. Lines under a note. 135. Note or musical sound defined. loi. 460. how to find key signatures of extreme keys. false relation. 286 to 289 to nearly-related minor keys. Mixolydian mode. Melodic chromatic scale. 539-546. 27s . enharmonic defined. chord chords 281 best note to double. Line drawn through a figure (see Figured Bass). 39. 39. conjunct. Middle cadences. by chord of the : — Ambiguous . 45- Modulating sequence. 683. 64 similar. 58 oblique. gradual 280. transition defined. Melodies. 290. intervals defined. 284. nearly-related minor keys. 53. analysis. 21 I . auxiliary {see Auxiliary notes). when it may fall. second degree of relationship. 21. chords common to two keys. 295. . table of. 2S4. 22. 42 triad on. signatures. by chord of the minor thirteenth. 272. unre- modes). 210. 207. 64. 64 disjunct. when indicated. . 384. 53. lated keys. treatment of. sharps. to nearly-related major keys. 275. 38. 40. 37. defined. characteristic notes of. its Minor common 22. no single chord can define a key. how to harmonize monizing melodies). cal ecclesiastical {see Ecclesiasti- table of. 58 contrary. 278. 280. passing {see Passing notes). chord of. leading note of. 685. 42 . table of. Secondary discords). defined. Nine to eight suspension sions). keys. Keys with fiats. 461 . 270.Analytical Index. pitch.46. 100. K. 37. of seventh on. characteristics of. 291. primary chords and notes of. changing {see Changing notes). table of. —Aeolian scale. chord of the [se-^ Chords of the ninth) . Neapolitan sixth. — with . difference between. 9. 37. 36. of. 37. 684. major and minor. 576-579. 283. 682. figuring. Modulation 50. 208 progression {see {see Part-writing rules I). 37. 206. when implied. of [see Diatonic triads of a major key). . 270. Ninth. primary notes of a minor key. 54~5S. 269. 384. nearly-related major keys.EY Relationship defined. 520-524. 278. 283-285. to snpertonic minor. triads chord of the diminished seventh. 21. 99. major and minor. interval defined. primary chords of a minor key. 211 . 296. . importance treatment of. 63. 47-49. 611-618 . 303. 100. 2lo. 43 . 631-634. tetrachords. Mediant. third degree of the scale. 2 10. transitional dominants. how effected. primary notes and chords of. modes. 2. harmonic form. 2. suspend'"d [see Suspensions). signatures. 211. Dorian 208 . from major keys. Musical sound defined. 206. 138. defined. tonic minor. Lydian mode. 51. 38 . 42. choice of modulations. Line following a figure. 542. 61 to Law Leading Note. j 335 characteristics of. 276. (see Major mode. leading note. in sequences. 39. Major common chord. 276. 47-50. Leap in a melody. chromatic [see Chromatic chords of the ninth) . of the sharpest note. 3. Major Keys. by . table of. with sharps in. 209. signatures. 100. when it must rise. Ninth. 276 . loi . Motion. 295. primary notes of a major. 294. 42. melodic form. Minor mode. from minor keys. table of minor keys. . 37 primary chords of a major. 298.279. note to page 112. sudden. 543. on a pedal. Har- Melody defined. chord. Notes. 273. Major Scales. 271 to 273. table of.43. 275. secondary {see minor scale. Nearly-Related major minor keys. 472. 90. of a major key. 36 . 42. 282. major and minor. 51. how formed flats. 206. . . 280. 42 relative major and minor keys. doubling of in arpeggios. 2. 302. Modes. from a . Pitch. Parallel keys [see Part defined. 78. 322. melodic {see Melodic progression). in more than one part. rules for. rule for. Progression. : anal- Oblique motion. 42. 63 by disjunct motion. 64 . 57. 310. hints on using. 59. 320 . 58. rules 193-199. 636 . harmonic (see Harmonic progression). 61. 175. &2. 346. 85. for. 310 passing seventh. 117. inverted. Diatonic Major. 85. 625. 85 . 42. Plagal cadence. 80. Root and generator. 92. defined. 310. hidden. 636. 324. and imperfect consonances. 8. and major intervals. names of the voices. 251. 329. defined. Parts. 628. by leap of a seventh. 71-73. 696. by leap of an val. 85. false relation not caused by. 21. how to find. summary of. 623. 627 . overlapping of. 327 . hidden fifths. 79. 19. 375Retardations {see Suspensions). 630. 83. in a middle part. figurysis. distinction be- Passing Notes. consecutive. Remote keys. 229. 631-634. 319. 352. false notation.336 Analytical Index.13. 330. 38. four-part harmony. Real sequence defined. accented. with flats. HARMONIC PROGRESSION :— Primary Consecutive fifths. degrees of named.ship of keys {see Key tionship). rules for. 624. chromatic. Overtones. 57. double. /. 316. 318. tween. 174. by augmented inter60. 319. ing. 42. their compass. of. 137. Prepared discords [see Secondary discords). treatment of harmony above a. how to indicate {see Analysis). 65. 64 overlapping of parts. 635. 695. chords of a key. 626 . SOj S'- . dominant. 64. 58. Passing Chords. Scale II. mentation of. 273. by leap after conjunct motion.64. 251. 1 1 1. Root progressions. //. in minor Root of a Chord defined. rules for. octave. 629. similar motion. Part-Writing Rules. by diminished interval. Overlapping of parts. Scales. 211. 138. 36. figuring. 85. 47-49. Resolution of dissonances. 237-239 sions. Open score and short score. Progression. 621. 63. 64. rules for. contrary motion. Octaves. consecutive octaves. rules for. 321. unaccented. 67-70. Octave defined. 351. 317. exercise worked. 316-318. 669. 620. with sharps. 104-109. for. 39. 67 to 70. 81. how approached. Relation. 146-149. 323. Preparation of suspensions {see Suspensions). 9. general rules MELODIC PROGRESSION:— Defined. 627. modulation on. crossing of parts. notes of a key. second to a unison. Plagal modes. 193 to 199. . two successive. tonic pedal. consecutive fourths with bass. passing chords. 74-76 how to approach a dissonance. 630 how Ornamental Resolutions of dominant seventh. 77. 318 . 622. 620 . defined. 2. Pedals Above and below. 635. analysis defined. orna- of suspeni Ornamentation of a pedal note. 74-76. 679-681. 62 . rela- unison. Note to page 83). 86. 38. hidden octaves. 629 : Notation false (see False notation). rules for. Progression of roots. Perfect Perfect 29. 698. 1 10. key. Pitch and vibration. sevenths and ninths. Preparation of secondary discords {see Secondary discords).62i. quitted by leap. 330. rules for. consecutive seconds. 146-149. organ point. to a unison. 57. . Relative major and minor keys. oblique motion. primary notes of. double. . 329. by conjunct motion. 322. Phrygian mode. formed. Ratios of intervals. defined. diatonic. 74. quitted. crossing of. Picardie third. how how formed. consecutive 79. 445. chord of the augmented {see Chromatic chord of the augmented sixth). augmented. 350. difference between. 461. 358. 133. in four-part writing. 520-524. Supertonic ninths. 693. 481. how to recognize. — discords). characteristic notes of. sixth degree of the scale. 134. Analysis. 336. 137- 135. Single changing notes. elevenths and thirteenths {see Chromatic chords of the seventh. chord of the added. secondary {see Secondary tardations. 92. 137. ornamental resolution. signatures of. Six-four chord. Seven to eight suspension {see Suspensions). 459. 12. eleventh and thirteenth. 218. 346. from a unison. 90. 64. rules for. 82. 344. 1 69-1 7 1. and fundamental String. — compass of. 53. 47-49. 348. cannot be prepared by a passingnote (Note to page 145) defined. treatment of. 449. SIX TO FIVE: — Ambiguous. sixth degree of the 449. 658. 48. 474 to 476. Supertonic discords. 447. 344. inversions. 356. 79. 351. chromatic figuring. 507. the pattern. second degree of the scale. 411. ninth. root position.356. 46. Seven-part harmony. minor. Scales. 444. diatonic {see Secondary discords) . Secondary harmonics. 697. formation of. 333. 6. 12. ///. of diminished sevenths. 479. or leading note. 209. 83. 346. chord of the. Seconds. consecutive. Sub-dominant. correct notation. no. 458. primary triads. preparation of. 162. real. 459. 448. 448. 81. to 171. how formed. 189. melodic form. 449 . 448. harmonic. Sixth. 657Six to five suspension {see Suspensions). 344. i. 357. Sixths. {see Subtonic. diatonic. 357. Ger- man. irregular. Scales. French. 136. — Seventh dominant {see Chord of the dominant seventh). sequence of. modulating. chromatic sevenths. Second inversions of triads. 449. 312. sequence of sevenths. 353. Secondary Discords : • Soprano Voice 65 . 12. 344. /. 23. — Augmented interval in 138. Submediant. fourth degree of the scale. 537. of diatonic sevenths. 21. analysis. old rule for. 22. inversions. 169 188. Second. vibration of explained. 353. resolution of. II. defined 132. 346. defined. defined. leading note doubled in a. Secondary sevenths and ninths Secondary discords). harmonic form. NINE TO EIGHT: — Figuring. 21. melodic. 596-601. 450. 208. Major. Supertonic. seventh degree of the scale. 352. 210. scale. 131. law of. 327. FOUR TO THREE: Figuring. Strong chords of the key are the discords. 80. resolution of. 217.Analytical Index. minor. . 447. Sequences. 354. 7. tonal. Sharpest note. 344. Neapolitan. "J. 459.' Suspensions: Ambiguous. Supertonic chromatic triad in major key. 314. 140. 460. 357. Similar Motion defined. 355. 206. *472. root position. upward suspensions. in minor key. Shakes. 602-609 > Italian. 7. to & unison. how treated. 593-595 . 348 . 135. 445 . 336-343. Sharp Keys. 355. . {see chromatic chords of the seventh) . secondary ninths. Secondary triads. Second to a unison. 344. table of. 334. Short score and open score. figuring. 22. secondary sevenths. 12. 447. Superdominant or submediant. false notation. //. 353. progression of a. 355. Second. root position. III. 347-35° 5 how to find the root. 350. of chromatic sevenths. 138. 206. 346. 355. 5. Diatonic Minor. Dorian. augmented in minor key. Chromatic. 172. 656. re- 334 . major. figuring. 334 . 137 . 353. rules for treatment of. Sevenths. 209. 337 Six-part harmony. preparation of. of sixths. 445. 344. chromatic. Semitone Sequence: a. are unessential discords. inversions. tone of disjunction.S42. Tetrad false. 696. VI. dominant thirteenth). Tone. . 362. false. changing notes. Discords. TWO TO THREE :—Y\^\-a^. Unisons. 144. minor. 229. enharmonic change of notation. compass. Tonal sequence. VIII. compass of voices. . 67. elevenths and thirteenths (see Chromatic chords of the seventh. 91. secondary. 360. 445. suspensions. 366. auxiliary notes. root position. 43.229. 276 primary triads major key.. major. Tenor voice in four-part writing. 229.32. chords in harmonizing. >"oot position. root progressions. approached by similarmotion. 88. SUSPENSION OF COMPLETE CHORDS: Defined.2i3. Triad defined. — Figuring. 39 primary triads minor key. 358. 65. Transition. of disjunction. diatonic triads of a major key. diatonic of a major key (see Diatonic triads of a major key. Two-part harmony. Tetrachord : — Unison. 92. 51 keys with nearly-related major sharps. choice of — Authentic enth and thirteenth). figuring. 46. 89 . 344. Vibration of a string explained. 363.) Thirteenths chromatic [see Chromatic chords of the thirteenth). Upper and lower generator in chords of the augmented sixth. 344. 671 keys. 21 1. 19. effect Tonic and dominant harmony. 468. major chord in minor<tey. discords. Tonality defined. 344. 365. 696. 82. Tables: modes. sevenths. pedal. 366. 361.338 JV. Transitional dominant. 698 major and minor keys. Triads: Chromatic of a major — key (see Chromatic triads) . 626.469 minor key. compound intervals. 42 relative ratios of intervals. 7 j . diminished seventh. Voices in four-part writing. 90. 645-650. passing notes. 562. 65. 275 . VII: Tonic SS8. 357. 584 Upper partial tones. discords. 92. Analytical Index. 83. augmented. 312. . primary. ninths. 1 1 major and minor scales. . its compass. V. 364. 90. 363. ninth. Unaccented Unessential 305 . ^g. e x- — Tonic. harmonic series {^page 324). 90 . Vibration ratios. 322. quitted by similar motion. key signatures. 364. 134. 360! root position. 562. 315. 344. 65 see auxiliary notes tions. inverted cadences. diminished. 48 keys. Treble or Soprano Voice in four- part writing. chromatic triads of a major key. diatonic triads of a minor key. 43. degrees of the scale. 693. first degree of the scale. Third. inversions. 89. 212. of 231. tonic and dominant. FOUR TO ^/KE. ornamental resolution. 700 defined. compound. . 214. 11. Turns. 364. Tierce de Picardie. 693 . 479. 295. Upward suspensions (see Suspensions. 32-34. upper partial. their compass. 13. diatonic of a minor key (see Diatonic triads of a minor key). SEVEN TO EIGHT: Figuring. or key note. DOUBLE SUSPENSION:— Defined. chro- matic of a minor key (see Chromatic triads). fundamental. 344. 344. . nearly-related minor plagal modes'. elev- amples. minor key. defined. Defined. consecutive. keys with flats. 46. 92. 46. 344. 42. . 358. how to recognize. Thirteenth dominant (see Chord of the its suspensions. Thorough bass [see Figured bass). 697. 270. 566. 146-150 secondary false triads. origin of the word. 46. 53. 299. Picardie. names of. intervals and their inversions {page 12). 667. figuring. anticipa- . passing notes. 92. 363. 46 . inversions. 286 152 317 194 300. 342. seid getrost" ^ 325 406 479 471. Schopfer" Matthaus Passion "Nimmvonuns.MUSICAL ILLUSTRATIONS. Gott. 430 429 427 283 2.'. J. Beethoven Adelaide Andante Concerto in F C minor Mass Mass in in C D . I. P. 301 560 261. 2. 552 122 Fugue in E minor. I. Herr" "O Ewigkeit. 314 118 265. wahr'r Mensch und Gott" "Ichbinein guterHirt" "Ich habe meine Zuversicht" '• 250 248 369 177 247 281 343 245 414 145 Inventio. lieber Gott" "Sehet. 284. " Ach Chromatic Fantasia "Dazu ist erschienen" "Es ist dir gesagt" Fourth partita Gott. Jesu Christ" "Gieb dich zufrieden" "Gott der Vater wohn'uns bei " Gott ist uns're Zuversicht" "Herr Gott. Le Dieu et la Bayadere 490 209. No. du Donnerwort" Organ Fugue in C minor Organ Fugue in F minor Organ Prelude in C minor Organ Prelude in E flat Organ Prelude in E minor Organ Toccata in F "Schau.. 431 192 346 282 313 252 581 Ende Fugue 2 Fugue 16 Fugue 22 Prelude 21 Prelude I Prelude II Prelude 20 " " 559 " " " " " " " " " " in Book Book Book Book Book Book I. wie nahe mir mein Wohltemperirte Clavier. 475 577 178. 277. Johannes Passion "Komm.. 566 Masaniello Fantasia in C minor . E. Example AuBER Bach. wir gehen hinauf " "Wachetauf! ruft uns die Stimme" " Wahrlich ich sage Each " "Was " War Gott thut" weiss. wie manches Herzeleid" lieben Christen. S. 436 363 186 275 306 382 326 279 141 (3). Bach. "Gelobet seist du. C. 399 2. Book I. dich loben alle wir" "Herr Jesu Christ. "Ach. I. 87 S. 387. No. No. 10. . 583 Hercules 213. Op. No. No. 17. Op. 280. 451 Joseph 386 '. 415. 579 201 112. 442 366 472 576 120 396. 9 Trio. 30.59> No. 24. 441. 43.273. Op. meine Freude" St.. 536 195. No. ID. 7 Susanna 207 206 136 J24 . Joshua Judas Maccabasus L' Allegro Messiah. 2 Studio. 251. i " Op. (Pathfitique) " Op. 53 " Op. 4 Cramer Cruger DvoiLCk Mazurka. No. W. live with me. 27. 31. 494 39* 208. No 3 Valse. 3 « Op.187. Op. 22 " Op. 132 Sonata. No.. 14. Op. 2 " . 565 498 564 483 197 390 449 299. No. 432. No. 304. Te Deum 354 175.200. No. 537 39a 409. No. 3 " Op. No.340 Beethoven Index to Musical Illustrations. 30. Example Prometheus Quartet. 151 Ludmila Gounod Spectre's Bride Stabat Mater Mireille Mors et Vita Graun Grieg. 2 " No.339 383. No 1 " Op. S7 Symphony. 260. No.228. 493. 345.191. 289 497 484 182 590 J71 393. Brahms Cherubini "Come. No. No.. 298. l8. 70. 2 " Op. 8 " No. 467 426 593 137 150. 14. 357 563 403.158. I « Op. 499 Bennett. 557 " Chopin inC. 3 " Op. 501 ». 6 " No. 519 Israel in Egypt. 33 "Jesu. 13. 142. 1 584 541 586 370.188. 450. 352. 553 285. 292 Samson Saul Solomon Suite de Pieces.143. Op. 202. 531}. No. 2 " Op. No I " Op. No. 5 '7 287. Op. 312 Handel Lyrische Stiickchen. 2.246. 4«9 Farnasso m^ Festa 585 159. 6 505 Athalia 253 Belshazzar J3a. 3 " Op 31. 368 364. 3 " Op." Part Song Deutsches Requiem Gesang der Parzen SchicksalsUed ff Credo ^ 8 Voci Mass in F. 294. E. 1 " Op. " " 1 341 Example No. No. 41. 20. Op. 6 391 Symphony. Haydn Mass. O^. 4 Quartet.Index to Musical Illustrations. 193. No. Fleurs Anim^es. No. Ruy 340. 546 39^. 2 No. 14 Requiem Rondo in Aminor Sonata in 453 153. 154 Bias. 59.. 5 Jagdlied. 316.410 176 ig6 211 384 113. No. No. Op." Op. Lauda Sion Lieder ohne Worte. No." Part Song. 6 Mendelssohn "Am Elijah Fantasia. First i Walpurgis Night Hirtenlied. 5 " Op.Mozart Petrus" Variations. No. 244 D flat " in F Symphony in E " in G minor Frout. No. 79. No. 527 56 331. No. E. 288. 3 Promenades d'un Solitaire. 496 318 Duet King Thamos Mass. 4 Ninety-eighth Psalm Octett Presto Agitato 397 408 121 180 456 380 Reformation Symphony. 332. 16." Op. Op. No. 264. 574 Sonata. 278. No. Op. 82 Dinorah Robert le Diable Concerto in C minor Die Zauberflote for Violin and Viola Fantasia in C minor 428 582 315. Liszt 86. J "Tues Meyerbeer .. 365. 30. No. 3 "Im Herbst. 568 466 57S 13S 86 578 254. 9. Paul IIS. 15 Quartet in D minor no S^i 535 " in E flat " in G. Op. 3 " No. Overture 149 St. 276. 3 Athalie " Auf dem See. 2 Sonata in A " in C sharp minor 183. No. 88." Op. i "While I listen to thy voice" (Song) Die Ideale The Creation The Seasons Dans les bois. 6 - 507 297 58 210 57. Op. 4S4 Mackenzie Colomba Jason The Bride Himmelsfahrtstage. 78. 534. 308 293 yjd 231 491 539 572 144 587 417. 474 230 558 184. HI (. Op. 165 5 Heller KULLAK La WES.b). Hundredth Psalm 229 5^2 290 255 525 411 ." No. No. H. '?Rokeby " 549 87 "Werde munter. 5 465 Wflldscenen. 21." Op. 570 "Ich groUe nicht. 580 Die Meistersinger 215. Op. Schubert "Am Meere" Die Zauberharfe Fierrabras Impromptu. No. J.500. 16.Op. Op. 90. 54^ Das Rheingold 455 Der Fliegende Hollander 389. 435. No. Op. 42. Op. 82. No. 463. 412. 125 358 The Daughter of Jairus 503 The Prodigal Son 542 The Sun Worshippers 398 Requiem 350. Op. No. 2 J44 " Op. Op.567 Parsifal 328 Tannhauser 392. Op. 141 " inEflat Rosamunde Sonata in A minor.529. 16. 416 " Op. 26. 31 464 Sonata. 20 214. 528. No. 164. 99 360. 167. izi.342 Index to Musical Illustrations. 2 433 Faschingsschwank aus Wien 359 Humoresque. 508 Tristan und Isolde 487. 6.. 547 Euryanthe 160 Invitation i laValse 232 " Se il mio ben. der herrlichste. SCHOP. 327. 48.486. 5 311 Neujahrslied.. 7 462 Kreisleriana. 518 Jessonda 485 Last Judgment 116." Op. Op. 4 305 Bunte Blatter. 506 492 356 400 452. Goring Verdi Wagner Weber 388 den Sonnenschein. Op. Op. 495.. Op. 361. No. Overture. 569 Romanze. 144 302 Novellette.437. 2 554 " Schone Wiege.509. 28. 402 Mass in C 473 Nonetto.. i 404 " Op. 526 303 307 385 478 274. No 4 Mass in B flat. SSI Schumann Spohr Stainer Sullivan Thomas. No. 21.. 323 Nordisches Lied." Duet 324 Sonata in A flat 249 Song of Miriam "An • . No. No. 395. No. 6 351 Calvary 381 Double Quartet. Op. Op. 545 Concerto in A minor. 122 " Op. 36. mein Gemiithe". 136 443 Fall of Babylon 461. 8 Op. 520." Op. No. 68 212 Paradise and the Peri 119." Op.. 54 401 " Er. Op. Example Prout. 42 " Op. 21. 538 413.476. 7 543 " No. 147 " Op. S30> 54°. E. oo London: AUGENER Ltd. Vol.. Mus. A PPLIED FORMS: A Sequel to ' 'Musical Form. with Analytical Index . Vol. II.. with Analytical Index and CANON. Technik der Instrumente.THEORETICAL WORKS BY PROF. Deutsch von O.20 AND SUBSEQUENT EDITIONS OF " HARMONY THEORY AND PRACTICE. Paper Paper 3 00 a. with Analytical Index .. bination.00 Being a Collection of Fugues put into Score aud Analyzed. .. ' Sixth Impression. . Coll.00 D k AS ORCHESTER. X7 FUGUE.oo 9183a. Bound TT ARMONY: . and Professor of Musio in the TTniversity of Dublin. 22 Newgate Street.. II. Hon.. with Analytical Index 9. Edition... 8vo..oo 9'84. /C OUNTERPOINT: STRICT AND FREE. 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