source file: m1413.txt
Date: Mon, 11 May 1998 15:37:56 -0700 (PDT)

Subject: Paul's scale is the Triple Just

From: John Chalmers <non12@deltanet.com>

The scale Pauls Hahn and Erlich posted in TD 1412 is precisely the 
"Triple Just" scale that Bill Flavell has been promoting on the
rec.music.theory USENET newsgroup. Flavell derived his scale by 
combining just major scales on 1/1, 4/3 and 5/3.

This scale has only 12 major and minor triads in all. One might
also consider its inversion with 7 minor and 5 major triads.

Marion and I have examined a lot of 12-tone just scales and the most we
have found have only 7 major or minor triads (and 6 of the conjugate
type. The most efficient scales we found (independently) are these:

*   *              *    *    *

*   *   *          *    *    *    *

*   *   *   *		    *    *    *
    
    *   *   *                *    *

One can place the 1/1 on any  point in the 3 x 5 lattice.
(The threes' axis is horizontal, the fives' vertical).

The first of these is the same as Paul Hahn's scale, the second is the
inversion.

--John