Re: Harmonic vs inharmonic sounds

["Richard F. Lyon" <DickLyon@xxxxxxx>]

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.

Dick