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Re: [Phys-l] Harmonics vs Overtones



On 04/01/2009 06:17 AM, Tim.Odonnell@CelinaSchools.org wrote:
Would people like to elucidate on the difference between harmonics
vs overtones?

This is a terminology question, right?

I prefer to talk about _modes_. It is necessary to mention harmonics
and overtones once or twice because the terms are common in the music
business ... but the rest of the time I talk about modes.

*) One major problem with "harmonics" is that many physical systems
(including pianos) are significantly anharmonic.

*) One problem with "overtones" is that it doesn't include the
fundamental. It is needlessly complicated to talk about "fundamental
plus overtones" and much simpler to talk about modes.

Also any discussion of modes is more general, since it is not
confined to "tones". It includes optics as well as acoustics.
It includes the spatial structure of a mode, not just its time
dependence.

*) A minor (if you'll pardon the expression) problem with "modes"
is that it collides with other uses of the word "mode" in the
music business: Ionian mode, Aeolian mode, et cetera. This is
not a problem in practice; the collision is easily resolved by
context.

If that answer wasn't what was wanted, please re-ask the question.

==============

On a related note (if you'll pardon the expression), it is better
to talk about a _set_ of modes rather than a "series" of modes.
In a one-dimensional tube the modes form a nice simple series,
but other systems are more complex. This includes strings (which
have two transverse polarizations) and drumheads, waveguides, atoms,
and three-dimensional resonant cavities, where it takes two or more
numbers to describe the structure of each mode.