Ed Zubrow writes:

>This is very interesting.  I thought I understood that in a piano the
>overtones are caused by the fact that other strings vibrate in addition
>to the ones struck.  What causes the overtones in wind instruments?

I think we're confusing overtones and sympathetic resonances here.
Fourier demonstrated that a complex repetitive vibration can be treated
as if it were a weighted sum of simple (pure sinusoidal) vibrations whose
frequencies are integral multiples of some fundamental (there's a further
qualification about phase angle, but we can ignore that for the purposes of
this discussion).  These integral multiples of the fundamental frequency
are called harmonics, overtones, or partials.  They are inherent in any
complex oscillation, be it of a string, air column, reed, membrane,
sounding board, whatever.

In virtually all instruments, there is a primary resonator (the thing that
vibrates to produce the instrument's sound) and many secondary resonators.
These secondary resonators contribute incidentally to the instrument's
sound quality.  They are generally not deliberately or directly excited
by the player, but unavoidably by their physical proximity to the primary
resonator.  Energy "leaking" from the primary resonator causes them to
vibrate "in sympathy", and they have their own harmonic characteristics,
which can significantly color the overall sound of the instrument; e.g,
the cavity and surfaces of a violin.  The bow only excites the strings;
the vibrating strings excite the top surface through the bridge, and the
top surface in turn excites the sides and air cavity, etc..

len.