Harmonics

> In nature, there are no physical
> objects that vibrate with a pure harmonic series of partials above the
> fundamental. The harmonic series is a construct of our mathematical
> minds, modeling a phenomenon first observed with our nonlinear hearing
> mechanism, and later with lab instruments.

I personally think that that, although essentially correct, is a bit of
an exaggeration.

First of all, a topic that made its rounds on the list recently: To say
that (for example) guitars, orchestral strings, almost all woodwind tones,
and most brass tones, have exactly harmonic partials, is only slight
oversimplification. The biggest departures from harmonic partials are
high- and mid-frequency noise components, from rosiny scrapes or breath
blowing through the tube.

If you force partials from those sorts of instruments to exact
harmonics, they take on a very clearly audible, but usually fairly subtle,
"robotic" crustiness. To say that most orchestral instruments have exactly
harmonic partials is definitely not pure 100% unadulterated truth, but the
amount those instruments deviate from pure harmonic partials is FAR too
small to have any significant effect upon tuning considerations.

But that's not really a point I want to get too much into, and perhaps
it wasn't really John's main issue either.

I think it's worth pointing out that whatever framework you build your
compositional or psychoacoustical model of musical psychology upon, how you
defy that framework is every bit as important as how you use it.

I personally believe that Neil is mostly correct in at least one sense:
Aside from some very important exceptions (e.g., very low pitch range),
simple whole-number ratios usually predict quite accurately what our ears
view as significant. They are the navigational bouys in the sea of tuning
possibilities.

BUuuuut... I don't believe that pitch relationship being significant to
our ears means that we must ideally use it, any more than we should sail
into collision course with navigation bouys! For example, intentionally
missing a 3:2 P5 by about 5 cents produces quarter-comma meantone, which to
my ears and those of many others, sounds really fantastic! And it sounds
great not (only) because it hits a 5:4 right on, but even more so because
of the specific way that it misses 3:2.

Obeying well-known ground rules sows the seeds of expectation in your
audience's minds, but defying those rules is what makes your audience
listen! Really brilliant music comes from cleverly and emotionally using
both expectation and defiance of expectation. Simple whole-number ratios,
being a pretty good model of what is fundamentally meaningful to our ears,
are one example of such a means of using and defying expectation. Regular
structures in a tuning system (like circles of fifths) are another, as are
consistency of meter and rhythm.

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> Paul Erlich's email system does not work right, and the MCI mail
> sysadmin is completely oblivious to the world. I have experimented a lot,
> and when I can get through to him, it is only with this specific address

It's much more likely that there is a badly configured internet node
somewhere (or more than one). I never had any problems sending mail to
Paul from this side of the water.
For the time being I shall act as e-mail intermediary.

Manuel Op de Coul coul@ezh.nl

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