# Mathematical formulae and wind instrument help.?

Is there a mathematical formula for the arrangement of hole on a flute or better a recorder.

In addition has anyone every tried to make a saxophone mouthpiece ?

I am interested in trying to make a DIY version of a Xaphoon http://www.youtube.com/watch?v=j3Wnx2VYZq8

In addition has anyone every tried to make a saxophone mouthpiece ?

I am interested in trying to make a DIY version of a Xaphoon http://www.youtube.com/watch?v=j3Wnx2VYZq8

active| newest | oldestf) of a note produced isf=^{v}/_{2L}where v = speed of sound in air (340m/s), and L is the length of the tube. For you, that is the distance between the mouthpiece and the first un-covered hole.Rearranging to solve for L, you're looking at L =

^{v}/_{2f}For instance...Google reveals that "middle C" is 523.28Hz

L =

^{340}/_{(2x523.28)}= 0.324873872mWith rounding, the length of a tube that gives a middle C = 0.325m = 32.5cm = 12.8 inches.

If the first hole uncovered by your finger is 32.5cm from the top, you will get a middle C.

http://en.wikipedia.org/wiki/Acoustic_resonance#Open

I quoted maths above assuming that the tube resonated as a closed tube.

However, the maths for a closed tube traditionally places the sound generator at the open end. These Xaphoons have the sound source at the closed end.

Damn. I've over-thought myself.

Is the measurement made from the tube end or from the sound source? in my case there may be some slight difference

The U-Tube video I linked to shows the original "inventor" making them by hand from bamboo BUT he is a musician and sax player and I am not but I would like to try to make one from PVC pipe.

My reason for wanting the maths is I have a profile of a Xaphoon and They say it is 12.5 inches long, I have made an "accurate" scale drawing f the picture and want to check the measurements I get from it.

Even flutes and recorders, in fact all musical wind instruments AFAIK, produce the sound at the closed end.

Thanks for all your efforts guys - any more input is welcome before I start dismantling the house plumbing!

1) Air flow though the open holes is obviously significant, so we can't consider it a tube...

2) I have no idea of how to calculate a standing wave inside such a thing, but I can't believe it continues to be the same formula.

PS I think that a tube closed at one end is a thing where the wave meets a solid wall at the end.

and a dude says 'the math is difficult, but I wrote software to calculate it"...

http://www.logarithmic.net/pfh/design

I have not tested this software nor can I presume it's remotely safe.