14/03/2015Flute Finger Hole Locations Flute Finger Hole Locations Determining approximate finger hole locations for a simple 6 hole flute is somewhat complicated. Much of what follows is due to the analysis of A. H. Benade (see "Fundamentals of Musical Acoustics," A. H. Benade, Oxford Univ Press, or "The Physics of Musical Instruments," N. H. Fletcher and T. D. Rossing, SpringerVerlag.) The wavelength of the sound produced is determined by the flute tube and tone holes. For a pipe of length L, open at both ends, and ignoring end effects, the wavelength of the sound is twice the length of the tube. The frequency produced is given by dividing the speed of sound (345 m/s) by the wavelength. The method described here is to estimate an effective length for a real (cylindrical) tube taking into account end effects, the size of the tone holes, etc. If the fundamental (all tone holes closed) corresponds to an effective length Leo, then the desired effective lengths for a six (or fewer) hole flute to produce notes of the (Western major) scale are given by: Length Note Units of L Number Note eo 0 Do 1 1 Re 8/9 2 Mi 4/5 3 Fa 3/4 4 So 2/3 5 6 La Ti 3/5 8/15 The actual physical length of the flute will be shorter than Leo and the distance to the tone holes (from the blow end) will be shorter than the values calculated in the table. As described by Benade, the end effects (at both the blow hole and at the first open hole) act (approximately) as an additional length which must be subtracted from the calculated effective lengths to get the physical lengths desired. As long as you don't deviate too much from typical flute proportions, these approximate calculations should get you pretty close. If you are serious about getting your flute in tune, plan on making at least two flutes. First, make your flute with no tone holes and adjust the length to match the desired lowest note. The blow hole is typically 1/2 to 2/3 the tube's inner diameter, and the stopper will be about an equal distance from the center of the blow hole. Then get out your ruler and measure the following: t = wall thickness of the tube Lo = length of the tube from the center of the blow hole to the open end. http://www.phy.mtu.edu/~suits/fingers.html 1/3 phy. From each Lei. http://www. s = 1/2 of the spacing between first and second open holes from the blow end [i.6a) to get your first approximate hole positions. Smaller tone holes will give a mellower sound and larger holes give a brighter (and louder) sound. and only their positions are to be adjusted.5b)/D ) where D = Lo L1 else (for all other holes) Lc = s [ ( 1 + 2(1.html 2/3 . and d = distance from center of blow hole to stopper (see below) Then. If this results in tone hole positions which are uncomfortable (or unusable) then adjust one or more of the tone hole sizes and recompute. which is not known. Call these Lei where "i" corresponds to the first column in the table. s = ( Li1 Li )/2 ] endif For each of these calculations.37 Lb Now use your value of Leo and the table above to get desired effective lengths for each of the hole positions. Your holes do not need to be all the same size.mtu. Lb can be determined approximately by: b = radius of blow hole Heff = (t+1. you will need to repeat them several times. measured from the center of the blow hole to the center of the tone hole. Leo = (Lb + Lo + 0.5b)/( (b/a)2 + (t+1. (e. The actual position for each hole will depend on the tone hole size and the position of any other open tone holes. for the first tone hole.14/03/2015 Flute Finger Hole Locations a = inside radius of tube (2a = inside diameter). an initial value of D is used which was computed from the previous approximate positions.25 to 0.edu/~suits/fingers.33 Note: using a single Lb for all notes is a reasonable approximation IF d is close to 0. For example. Below I will assume that all the tone holes are fixed in size. Now compute the first corrections: Linew = Lei Lb Lc where if i = 1 (for Re) then Lc = (t+1. subtract (Lb + 0.e. Li. Hence. etc). you have some leeway to choose one or the other of these. Le1 = 8/9 Leo.6 a = approximate end correction at the open end and Lb is the length correction at the blow end.5b + t) (a/b)2 /s )1/2 1 ] where b = tone hole radius (2b = diameter) of first open hole from the blow end.g.7b) Lb = Heff (1 e) (a/b)2 where e = fraction of blow hole covered by the player's lip e is typically 0. so it is possible to make some choices which affect the ergonomics of your flute.6 a) where 0. Me a little flatter.g. but if necessary.g. Use Li = Lei Lb Lc Lt where Lt = t (b/a)2 /4 times the number of closed holes between the first open hole and the blow end.phy. Continue until the answer doesn't change much. If you see systematic problems (e. If a note is a bit flat. Now check the tuning of your flute. Do this one hole at a time. If you just want to calculate. and by the time you get to Ti it is very flat) then your value of Lb can be adjusted to fix all the holes at once. you might be able to bring your flute into tune without having to make a second one.edu To Suits Page To MTU Physics Home Copyright Info http://www. Now drill your holes. by comparing to another instrument which is in tune and listening to the beats). Note: if you have particular thick walls on your flute (like some wood flutes) you will need to add another correction.html 3/3 . A frequency counter is best for this. a recorder) the correction at the mouth can be approximated by Lb = 2. For a fipple flute (e. then see the flutomat javascript by Pete Kosel Questions to: [email protected] a2 / (area of fipple opening)1/2 though this is only a rough approximation. etc. If you drill your holes a little small to begin with. move the hole 3% closer to the blow hole.mtu. For the other holes. Re is a little flat. or need to check your calculations. compute the new value of D and recompute the correction.14/03/2015 Flute Finger Hole Locations Once the correction is found. If you correct all the holes. you can enlarge the first open hole (from the blow end) a bit to sharpen it.edu/~suits/fingers. That is. if your note is 3% flat. then go back and redo the calculations for all the holes. you can get into numerical trouble in some cases.g. You will also need to shorten your tube a bit as the presence of the closed holes will flatten the fundamental as well. recompute s using the corrected position to obtain a better correction. and estimate adjustments to make your second flute. you can do it "by ear" (e.