Is this really true?
I know if you excite a string (or any mechanical resonance) to vibrate
on an overtone, that the overtone is not exactly a harmonic of the
fundamental mode, just like a quartz crystal.
But in this case the string is vibrating on the fundamental frequency
and I would think that nay harmonics generated harmonics would be
exact. If what you say is true, then you should be able to hear a beat
note with only ONE string. The beat note would be between the true
harmonics of the fundamental and the overtones. I don't think it works
that way. Anybody know for sure?
Anything metallic will have wandering overtones. A pitch fork,
metal snares, steel drum (in the extreme!), bells.
Even organ pipes made of too stiff material, (pure tin, silver)
have a cheap metallic sound.
You can see it for yourself by putting a microphone on on oscilloscope
and excite a pitch fork ( or is that tuning fork?).