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Date: Thu, 17 Jul 1997 
From: Mark Hodgson
Subject: Re: Using Pandiatonic harmony for Modes.

I hope you don't mind me responding to your posting personally, which I
read with interest. I just happened upon this rec.music.classical while
checking out verification of Glenn Miller's mysterious death, which is
now a matter of controversy again.

In any event, I have been toying with the mathematics of the 12-tone
system, the relationships that exist with natural harmonics, and other
tone systems. In fact the "equidistant tone" and "harmonic tone" concept
lead to different sets of tones altogether. By the harmonic series of
tones, I mean the tonic, the first octave, then, progressively, the 3x,
4x, 5x, 6x...N times the fundamental frequency tones, and it is perhaps
coincidental that, for example, the 3x harmonic for the fundamental note
C (to pick one) is very close to G, but actually slightly different. It
is so close, however, that it is used as a basis for tuning stringed
instruments: in the case of the guitar the string just above the 5th
fret of the low E string can be touched and released to produce a
harmonic which is two octaves above low E, and the string just above the
7th fret of the A string produces the 3x harmonic for A as a
fundamental, which is close enough for tuning purposes to get those two
strings "in tune". This can be carried on to tune the whole guitar, with
a variation required for the G-B pair of strings.  The odd-numbered
harmonics generate unique pitches from C, and, of course there are an
infinite number of them. Quite fascinating actually. So one could build
a scale that is based on the pitches generated from harmonics of one
fundamental note. In terms of the geometric progression of frequencies
of the twelve tone system, it is quite unique in that the tones on a
geometric scale, are not equidistant, yet they are "natural".

But this is just one idea. Another idea is to define, instead of twelve,
10, or 15, or any number really, of evenly spaced tones between the
octave to define a scale. If for instance, as the number is increased
greater than 12, the set of set of chords combinations increases
rapidly, with a trade off in that, if it gets too high, the demands on
the average person's ear to distinguish them increases.

I played around with this a bit using a spreadsheet to calculate the
pitch bends required to simulate these "new" notes, and coding in the
pitch bends to a sequencer program I own. Unfortunately, the means of
doing this with the sequencer I have at the moment is very cumbersome,
so I haven't attempted any compositions beyond running up and down these
"new" scales to see how they sound. What I did discover, however, is
that the first impression was that something was "out of tune", but
after replaying them a few times, my ear adjusted to them and they
sounded just "different" rather than "out of tune". Definitely a
possibility for avante garde composition I believe! If only I could find
a sequencer that had the flexibility to just do it without all the extra
coding required to introduce the pitch bends or an instrument with
adjustable frets! The violin lends itself to this, of course, but it
would take some time to perfect the fingering and ear to reproduce the
pitches, and I think my ear would need some help to conjure up the
melody and harmonies under a new pitch system.

I am curious about the subject of your posting - I've never actually
heard of the term "Pandiatonic" before, and am only guessing that my
experimentation would fall into the same, or a similar, category. If you
like, you could respond to me and we could have a chat about this
interesting subject. No pressure.