source file: m1578.txt
Date: Wed, 11 Nov 1998 04:49:57 -0800

Subject: Septimal schisma as xenharmonic bridge?

From: monz@juno.com

In TD # 1559, 20 Oct 1998, Margo Schulter wrote:

> An open question: might an extended Pythagorean
> tuning with its contrasts of basic 3-based,
> quasi-5-based, and quasi-7-based intervals in
> some way have a kinship to the three genera
> (diatonic, chromatic, enharmonic) or to Guido
> d'Arezzo's three hexachords (soft, natural, and
> hard)? 

I wish I had read this while the discussion on it
was hot, because I've been thinking along exactly
these lines.

In my book, I demonstrate how it would have been
possible for the ancient Greeks to formulate both
the chromatic and enharmonic genera in their tuning
of the famous "lyre with 12-strings" for which
Timotheus was ridiculed, by retuning the strings
continuously by 3:2 "5th"s and 4:3 "4th"s until
the proper intervals were reached.

I'm not well-read on the following idea, but it's
been documented that the Babylonians (c. 2000 BC)
tuned by ear by means of consecutive 3:2 "5th"s
and 4:3 "4th"s, and I think it's quite possible
that all four of the great ancient centers of
civilization -- China, Egypt, the Indus valley,
and Mesopotamia -- could have either independently
"discovered" extended 3-Limit tuning or adopted
it thru trade from whichever developed it first.
This in turn would have been incorporated into
Greek practice, as the Greeks imported much of
the scientific knowledge of all but China.

Knowing first-hand how far a curious mind will
go with what he thinks is a great new idea, I
think that when any brilliant ancient theorist
first discovered the principle of generating new
notes from a succession of 3:2s, it would be
highly unlikely that he would stop after the 12th
just because it sounded so close to the starting
pitch.  Indeed, the fact that it _was_ so close
and yet not the same certainly would have impelled
him on to see what other kinds of relationships
there were.  He probably wouldn't have stopped
until he just plain got tired of doing all that
calculating.

If he had the same kind of inquisitiveness that
Darreg, Partch, and Schoenberg had, and many of
us have, he would have written pieces that
utilized all those unusual notes, to see just
what that would sound like.  So maybe there
was some ancient Greek walking around with a
toga that said "quasi-7-Limit Rules!".

- Joe Monzo
  monz@juno.com
  http://www.ixpres.com/interval/monzo/homepage.html

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