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Re: Harmonic vs inharmonic sounds

At 6:17 AM -0400 3/12/07, David Schwartz wrote:
Since the spectral components of just about any sound are harmonic in the mathematical sense (i.e., they have a common denominator) ...

I would have said the opposite: Since a sound can never actually be mathematically harmonic...

The idea that all signals are made of a finite set of discrete spectral components is nonsensical in itself, but even for the set of signals that can be defined that way, there's no reason to expect those components to be in a rational frequency relationship, unless the only signals you are considering are periodic signals.

The relation between "signals" and "sounds" is also worth considering critically. No real sound lasts forever, and therefore no real sound is periodic or mathematically harmonic.

The set of signals that are exactly mathematically harmonic is the set of periodic signals. It's a boring set, totally uninformative with respect to auditory perception, and does not include signals that can be called "sounds" without further qualification. Just depends on how mathematically picky you need to be for what you're trying to do.