TUNING digest 559

Regarding Mclaren's post:

> In fact one could just as easily "modulate" between different
> modes of vibration of a sphere: zonal harmonics, torsional
> vibrations, etc., each giving rise to a different non-just
> non-equal-tempered scale.
> This is a process conceptually akin to "modulation" in
> JI and equal temperament, but more complex: for the
> subinharmonic series formed on a given n-j n-e-t are,
> as we have seen, in general not as closely related to
> the vertical structures formed from inharmonic series
> as is the minor triad to the harmonic series of the major
> triad in traditional Western harmony.
> Regardless, this set of posts may have given a glimpse
> of the universe of new harmonies and melodies awaiting
> the composer adventurous enough to dare composing
> in non-just non-equal-tempered tunings.

Okay, I got the glimpse, and I'm completely excited.

But I'm missing a few pieces. Can someone help?

The 12 tone equal temperament scale is derived from the overtone
series of a vibrating string. Unfortunately for me, my only reference
on the derivation is Hindemith's Craft Of Musical Composition. If any
of you have read his work, you'll all groan with me. It's not helpful.
Apparently, this scale is generate by using 6 overtones, and then a few
approximations, which is where I get lost. I'd be very interested in hearing
someone concisely construct the scale in this forum.

I think this will help me attempt to construct other scales from other
vibrational modes, i.e., a cylinder, a rod, a sphere, etc. (a friend pointed
out that a cylinder would have two fundamentals...any comments on that?)

Thanks all. I loooove this list.

Marcus

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