The Question Now, the red key(and the trill keys) are about half the diameter of

Question

The Question

Now, the red key(and the trill keys) are about half the diameter of the other keys. I suspect that this is quite significant here, but I can't explain it myself.

My main question is, why does disturbing the air column as shown in the section "the weird stuff" not change the pitch? One has added an escape route for air, the column should then vibrate as if the remaining keys were open--that is C#.

I suspect that the underlying principle is the same, so I have a few other related questions (optional):

Why does the red key not change the pitch on D/E flat, but makes it go into the second fundamental/harmonic for E and above?
Why does the red key change the pitch to notes which are not harmonics, instead close to C#(one of them isn't even part of the chromatic scale--it is between two notes) for B flat and A?
The red key is pretty similar to the trill keys with respect to size and general location. Yet, using a trill key on D changes the pitch, whereas using the red key doesn't. Why is this so?

Explanation / Answer

I've been doing experiments related to this back in 1994, so it's going to take a bit of recall.

The idea of a flute is that you create standing waves, which have a frequency that depends on the (variable) geometry. The reason they're standing waves is because you fix specific boundary conditions. In particular, p=0 at an open end.

Now, consider that you have a standing wave in a flute, with an wavelength that is a fraction of your flute length. That means that you have several nodes in the middle. If you would open a key at a node, there would be no effect. If you'd open one near a node, the pitch would change slightly.

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