cavities

Yesterday, Daniel Wolf asked:

Does anyone out there have information on cavity (as opposed to
tube) resonators? Are there any formulas for the dimensions of such
resonators or is trial and error the best we can do?

There are only a couple of different "shapes" for which
the equations have simple solutions. Kinsler and Fry's book looks
at the modes of rectagular cavities (a room is an example, albeit
one with larger dimensions than a typical musical instrument).
You could most likely also solve spherical cavities (and maybe
ellipsoidal?) in a similar manner, but you'd probaly need to do
some kind of iterative solution for more complex shapes.

There was also an article by Bart Hopkin a while ago in
Experimental Musical Instruments that discussed the placement of
tone holes in an ocarina. I don't have the article handy, but
there were several aspects including placement, width, and depth
of the tone holes that had significant impact on the pitch of the
resulting instrument. This was presented in a "rule of thumb" kind
of way.

Bill Sethares


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