> Phương pháp tính toán thông số vị trí lỗ bấm. Phần lớn phân tích sau là lấy từ A. H. Benade (xem "Fundamentals of Musical Acoustics," A. H. Benade, Oxford Univ Press, or "The Physics of Musical Instruments," N. H. Fletcher and T. D. Rossing, Springer-Verlag.)

Bước sóng của âm thanh chị ảnh hưởng của lòng ống, kích thước và lỗ bấm.
Đối với ống sáo có chiều dài L, thông 2 đầu, và bỏ qua các yếu tố ảnh hưởng, bước sóng của âm thanh là 2 lần chiều dài ống. Tần số được tính bằng vận tốc âm thanh (345 m/s) chia cho bước sóng

Phương pháp tính toán dưới đây, giúp chúng ta ước tính các thông số chính xác hơn sau khi
xét đến những yếu tố ảnh hưởng như lòng ống, kích thước lỗ, độ dày thành.

Gọi chiều dài từ đầu đến đuôi sáo là Leo,
Chiều dài từ đầu đến các lỗ tiếp theo sẽ nhiều hơn hoặc ít hơn thông số sau

Note
Number

Note
Length
Units of Leo
0 Do 1
1Re 8/9
2Mi 4/5
3Fa 3/4
4So 2/3
5La 3/5
6Ti 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.
a = inside radius of tube (2a = inside diameter), and
d = distance from center of blow hole to stopper (see below)
Then,
Leo = (Lb + Lo + 0.6 a)
where
0.6 a = approximate end correction at the open end and
Lb is the length correction at the blow end, which is not known.

Lb can be determined approximately by:

b = radius of blow hole
Heff = (t+1.7b)
Lb = Heff (1 - e) (a/b)2
where e = fraction of blow hole covered by the player's lip
e is typically 0.25 to 0.33
Note: using a single Lb for all notes is a reasonable approximation IF d is close to 0.37 Lb
Now use your value of Leo and the table above to get desired effective lengths for each of the hole positions, measured from the center of the blow hole to the center of the tone hole. Call these Lei where "i" corresponds to the first column in the table. (e.g. Le1 = 8/9 Leo, etc). From each Lei, subtract (Lb + 0.6a) to get your first approximate hole positions, Li.

The actual position for each hole will depend on the tone hole size and the position of any other open tone holes. Hence, you have some leeway to choose one or the other of these. Smaller tone holes will give a mellower sound and larger holes give a brighter (and louder) sound. Your holes do not need to be all the same size, so it is possible to make some choices which affect the ergonomics of your flute. Below I will assume that all the tone holes are fixed in size, and only their positions are to be adjusted. If this results in tone hole positions which are uncomfortable (or unusable) then adjust one or more of the tone hole sizes and recompute.

Now compute the first corrections:

Linew = Lei - Lb - Lc
where
if i = 1 (for Re) then
Lc = (t+1.5b)/( (b/a)2 + (t+1.5b)/D )
where D = Lo - L1
else (for all other holes)
Lc = s [ ( 1 + 2(1.5b + t) (a/b)2 /s )1/2 - 1 ]
where
b = tone hole radius (2b = diameter) of first open hole from the blow end,
s = 1/2 of the spacing between first and second open holes from the blow end
[i.e. s = ( Li-1 - Li )/2 ]
endif

For each of these calculations, you will need to repeat them several times. For example, for the first tone hole, an initial value of D is used which was computed from the previous approximate positions. Once the correction is found, compute the new value of D and recompute the correction. Continue until the answer doesn't change much. For the other holes, recompute s using the corrected position to obtain a better correction. Do this one hole at a time. If you correct all the holes, then go back and redo the calculations for all the holes, you can get into numerical trouble in some cases.

Now drill your holes. If a note is a bit flat, you can enlarge the first open hole (from the blow end) a bit to sharpen it. If you drill your holes a little small to begin with, you might be able to bring your flute into tune without having to make a second one.

Note: if you have particular thick walls on your flute (like some wood flutes) you will need to add another correction. 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.
You will also need to shorten your tube a bit as the presence of the closed holes will flatten the fundamental as well.

Now check the tuning of your flute, and estimate adjustments to make your second flute. That is, if your note is 3% flat, move the hole 3% closer to the blow hole, etc. A frequency counter is best for this, but if necessary, you can do it "by ear" (e.g. by comparing to another instrument which is in tune and listening to the beats). If you see systematic problems (e.g. Re is a little flat, Me a little flatter, 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.

For a fipple flute (e.g. a recorder) the correction at the mouth can be approximated by

Lb = 2.3 a2 / (area of fipple opening)1/2
though this is only a rough approximation.