Re: [Phys-l] Harmonics vs Overtones

[John Denker <jsd@av8n.com>]

On 04/01/2009 09:12 AM, Dan Crowe wrote:

> I don't understand the distinction that you're making between a set
> and a series.  In mathematics, a series is a sum, but a set is not a
> sum, but that doesn't seem to be the distinction you're making.  Are
> you implying that the elements in a series are defined by a simple
> mathematical rule, but the elements of a set are not necessarily
> defined by a simple mathematical rule?  If yes, then how simple does
> the mathematical rule have to be?

Please don't ask me to explain what "series" means in this
context;  I was arguing that it was a misnomer.  If you are
arguing that it is a misnomer several times over, that's OK
with me.

The only reason I brought up "series" at all is that it seems 
to be common parlance in this context; see e.g.
  http://en.wikipedia.org/wiki/Harmonic_series_(music)

Even beyond the strict mathematical notion that series means
sum, all forms of the word "series" share a notion of _sequential_ 
arrangement, like beads on a string.  So when I hear the term
"harmonic series" I picture a well-ordered one-dimensional
arrangement.  But the physical facts do not agree with this
picture.  In general it is a multi-dimensional arrangement.
It is not well-ordered by kx (because of ky and polarization) 
and not well-ordered by ky (because of kx and polarization) and 
not well-ordered by frequency (because of degeneracy).

Bottom line:  AFAICT, no matter what you think "series" means, 
the term "harmonic series" doesn't fit.  It's a misnomer.