source file: m1516.txt
Date: Thu, 27 Aug 1998 15:18:53 EDT

Subject: Re: XH 17: n-tet's and harmony

From: DFinnamore@aol.com

Thanks to Margo Schulter for the paper in TD 1513!  I found it thought
provoking and informative, especially the parts about regarding the consonance
of an interval as a point on a spectrum rather than a binary choice.

That's helped me make more sense of a set of 7-(prime)limit, 12-tone/2:1
tunings, the heptatonic subsets of which I've been exploring for use with what
might be thought of as neo-/Xeno-Medieval/Gothic/Rennaissance compositions
(for lack of more concise term :-).  Those tunings are built of five
alternating 21:20s and 15:14s, with two 256:243s sandwiched in here and there
to fill out the octave.  Note that 9:8 can be divided into 21:20 and 15:14.

Here's my 2-cents-worth on a few minor points from the paper:

>Thus while both 13th-century and 18th-century Western European music
>are harmonically oriented, they are "harmonic" in very different ways,
>differing in their historical tunings, stable and unstable interval
>categories, and directed cadences. Curiously, certain scales such as
>53-tet can provide an excellent fit with _either_ harmonic system.

That may not be as surprising as it seems.  I think that the more finely you
divide the octave, the more likely it is that you will have "an excellent fit"
with a set of relatively smaller (in terms of tones per octave) systems when
one system's  prime limit encompasses the other's, as in the case of Western
18th century 5-limit and 13th century Pythagorean.

>most complex prime number

Is it accepted practice to refer to primes as "complex"?  Aren't primes, by
definition, the simplest whole numbers?  Perhaps "highest prime number" would
be a better way to state it?

>the septimal minor
>seventh (7:4) also becomes literally and figuratively a "prime factor"
>in defining the scale,

Figuratively?  How do you mean?

Thanks again, Margo, for an inspiring work!

David J. Finnamore
Just tune it!

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End of TUNING Digest 1516
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