source file: m1468.txt
Date: Tue, 7 Jul 1998 14:13:59 -0400

Subject: =?iso-8859-1?Q?A_=28roughly=29_24=D0per=D0octave_eight=D0fifth?=

From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

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Dave Hill-

You message was difficult to read due to some ASCII-like codes, but I
think I get the idea. Your scheme is similar, if not identical, to
Helmholtz's 24-tone schismatic temperament. Does anyone have that one
handy for comparison? Also similar is the 22-tone sruti system of India,
which can be described as a series of fifths, the 5th and 17th fifths
optionally altered by a schisma, to yield the eight-fifths-down major
thirds.

Let me ask you this, though -- did you find meantone harmonies
insufficiently pure? A 24-note meantone tuning would be able support a
larger repertoire than the schismatic temperament you describe. Also,
the tuning I mentioned in one of my first post to the list, two copies
of 12-tET separated by 15 cents, would yield purity comparable to that
of the pure-fifths version of your scheme, but, allowing for (fairly
imperceptible) 15-cent melodic shifts, would permit unlimited modulatory
freedom within the 5-limit. Personally, I'd get two of your 24-tone
pianos, put one in a 24-note meantone tuning and the other in 22-tET
(check out my tape swap tune for the kinds of sounds I'd get out of that
one).

-Paul Erlich

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