Posted by Gerald J. on January 25, 2001 at 23:52:16:
In Reply to: Re: Re: 7 Valve Tuba posted by Rick Denney on January 25, 2001 at 10:05:09:
One slight complication. A vibrating string, whether piano or string instrument stretches each half cycle of vibration and that makes the oscillation not perfectly linear so the harmonics are at a higher pitch than the mathematical harmonic frequency. Pianos are tuned with stretch to allow for that. Last I knew, stretch was planned to be a bit greater in Europe than in the USA.
I haven't worked out the effect of air compression and ramification plus changes in diameter and direction in a wind instrument on harmonics. Clearly the differences between instruments by design and experiment have tendencies to make the harmonics also not the mathematical multiple of the fundamental. I suspect changes in diameter and direction are more significant effects. And where these changes occur with respect to acoustic nodes in the instrument make the effects more diverse.
Gerald J.