from McLaren

From: mclaren
Subject: Paul Turner's ideas on xenharmonic
theory & Geralrd G. Balzano's group theoretic
micrtonal ideas
---
The talented Australian composer Paul Turner
recently wrote me a letter in which he described
some provocative ideas about microtonality.
Paul's ideas were based on group theory. Because
different equal temperaments exhibit different
cyclic rotational properties, Paul pointed out that
a number of different tunings which appear outwardly
dissimilar share underlying structural properties.
This idea is particularly interesting because Paul
appears to have arrived at it independently.
Gerald G. Balzano also came up with similar ideas
about 15 years ago. His best-known paper is
his Computer Music Journal article "The Group
Theoretic Structure of 12-fold and Microtonal
Tunings."
Balzano's CMJ paper is interesting insofar as it
distills a number of properties which Balzano
sees as definitive of the major mode in Western
music. He then goes on to show that tunings
of the form (N)*(N+1) satisfy this criterion.
Thus for N = 3 Balzano's theory gives a
12-TET scale; for N = 4 Balzano's theory gives
a 20-TET scale; and for N = 5 Balzano derives
a 30-TET scale.
He was able to show that all three scales
exhibit similar melodic properties.
This is an interesting idea because it
proceeds solely from a consideration of
the melodic properties of the scales in
question. To my knowledge, the only only
microtonal theorists who have put forth
theories of microtona scales based solely
on the melodic properties of the tunings
in question are R. Vermeulen, Max Meyer
and Boomsliter & Creel.
The advantage of such a theory is that it
reveals similarities between tunings which
would otherwise appear to have nothing in
common. The disadvantage of such a theory
is that--because it's solely concerned with
the melodic properties of scales--the harmonic
properties of the scales thus generated tend
to be unpredictable.
In the case of the 20-TET and 30-TET scales,
neither one has fifths particularly close to
the value of the third member of the harmonic
series. This is neither "good" nor "bad," of
course, but it is certainly *different* from
12-TET...which has a perfect fifth which
falls within 1/600 of an octave of the third
member of the harmonic series.
Thus, while the 20- and 30-TET systems
will likely sound similar melodically to
12, they will sound harmonically very
different.
Paul Turner also recently sent me a number
of piano pieces in 5, 7, 8 and 9 tones per
octave.
Why is it that the most interesting music
being done today always seems to arrive
in the mail on someone's cassette?
Maybe someone can explain this to me.
Whenever I buy a CD of the "latest" so-called
"serious" contemporary music done in New
York or Boston or some other high-powered
place, the music usually sounds okay--it's
generally performed with verve and gusto,
and the acoustics are very nice.
But the *really* interesting new music seems
to come out of nowhere, from people I've
scarcely heard of, on cassettes.
There must be a good reason for this. Perhaps
gobs of hard cash can't substitute for musical
talent...?
Nahhhhhh! This America. Gobs of hard cash
can substitute for *anything.*
As Bill Wesley remarked when I asked why
the French and Germans and Japanese had
bullet trains when we in the U.S.A. didn't:
"This is America. We've got bullets, we
don't need trains."
--mclaren



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