# Modeling end-blown flute instrument using adaptive filter

I want to find the resonant frequency of specific end-blown flute called Persian ney, Using LMS in arrangement of system identification. Two signal is needed for algorithm:

1. system excitation (x)
2. desired signal (d).

The plant here is flute. The adaptive is coefficients describing flute behavior in time and frequency. Almost mostly x is white noise. The microphone outside the flute will capture the sound as d. All done. But mechanical-acoustic arrangement is like:

 -----------  Tubes, conducting acoustic:
|           | Including big tube, tube reducer and small tube (flute size)
|Noise(x)  / --------------\
|generator| |               -----*-------------- - - ----- --- ---
|speaker  | |               -----*------ -------------------------
|box       \ --------------/ Flute entrance
|           |                                   O
-----------                                    | Microphone(d)

* Marks flute entrance


Exciting approach seems to be wrong since to make flute work in playing time, we enclose all over flute entrance with lips, only small piece of it's circle remains open to let air move out and make friction with flute edge. If do not enclose, the instrument will not sound!

Small area marked with red is an open area(between teeth and tongue):

The question is how to model this type of flute excitation correctly? Since the white noise must enter the flute, but also it's entrance must be closed.

I'm not sure if maybe human lung also contribute to it's resonance.

• I believe your model is wrong on several counts, but only if I'm correct about the ney being a true flute. Flutes work by blowing air across a sharp edge; the acoustic properties of air blowing across that edge makes a negative resistance that can cause the assembly to produce a tone. I think that the edge in this case is the edge of one's tooth, and one basically whistles into a pipe to make a sound. Does that sound like a good description to you? Jun 5, 2023 at 14:15
• @TimWescott No I think tooth is just conducting air toward the edges. Though I'm noob in playing ney but I have one in my home. The edge is what really makes sound. Jun 5, 2023 at 14:38

I'm partially going on my own knowledge of electronic circuits, my own experience singing and playing (and playing with) wind instruments, and this page.

A better model for a flute is a resonator (mouth, throat, lungs, etc.), a negative acoustic impedance (the working edge, and the jet of air being blown against it), and then another resonator.

The magic (as with any wind instrument) happens at that "negative acoustic impedance". A positive acoustic impedance is any element that tends to make vibrations in the air turn into heat and dissipate away. A negative acoustic impedance is an element that tends to make vibrations in the air get stronger.

When you have a bunch of resonators (or just one, really) working against a negative acoustic impedance, then if all the elements work together correctly, you get an oscillation. This oscillation is what causes a wind instrument to make a steady tone.

So -- the random noise generator needs to come out, and you need to insert a negative acoustic impedance. To model this accurately you're going to have to learn a lot about acoustics -- but it'll be good for you.

What you should end up with is a model that generates a sine wave or nearly so, and that sounds like a flute when you generate a sound file and play it.

• You mean I need modal analysis? Have you simulated that on comsol or ansys? Can you explain how to measure please? Jun 8, 2023 at 20:25
• I'm not familiar with either of those. I would just use an ODE solver, with a model written in Python. Others may use Matlab/Simulink. Use what you're comfortable with. I don't think I said anything about measuring -- I was assuming you wanted something that sounds right. In that case the "measurement" is to listen to the result and see what you think. Jun 8, 2023 at 23:59
• @TimWescott, Thanks for sharing your knowledge. +1.
– Royi
Jul 6, 2023 at 6:29