Deryk Barker on overtones:

>All instruments produce overtone structures; the difference between them
>is largely what makes them sound characteristic.  Although other strings
>can resonate on a piano, even if all other stringds are damped, you still
>get an overtone series.
>
>A tone with overtones, basically a sine wave, is actually very dull.
>AFAIK the instrument which comes closest is the flute...no comment.

I think that Deryk means "a tone WITHOUT overtones" 2 lines up. That
indeed is a pure sine wave.

Any string or wind column in principle is capable of supporting a series
of standing waves (or modes) which are ultimately responsible for the
overtones.  An open string can produce all the frequencies consistent with
the boundary condition that there are nodes (zero amplitude) at the fixed
ends.  Generally the fundamental is easier to excite than the overtones.
If you get an open string vibrating, then lightly touch the string at its
midpoint, you get a change in sound because the standing waves which don't
have nodes at that point are damped out by the interfering finger.

In my experience an organ pipe is the nearest thing to a producer
of a single pure tone.  A standard physics demonstration uses what is
essentially an organ pipe, a microphone and an oscilloscope to demonstrate
this.

Bernard Chasan