source file: m1445.txt Date: Fri, 12 Jun 1998 15:33:54 -0400 Subject: RE: TUNING digest 1444 From: "Paul H. Erlich" >> >I'm having difficulty imagining an ET like this--can you give me an >> >example of such an ET, and then I'll try Fokker's method on it? > >> In all the cases you've mentioned so far, it is the case that the ETs >> have no better approximations to the just intervals than the ones >> represented by one step along the axes. >No, I meant can you give me an example of an ET which _does_ have a >better approximation. I would guess that 24tET would be a good example, since its best approximations of 3 and 5 coincide with those of 12tET, so the only way to generate it with Fokker's method would be to choose some rather large "comma" to vanish. For example, if the chromatic semitone vanishes, then (1 -2) is a unison vector, and then if the Pythagorean comma vanishes as well, (12 0) is a unison vector, and the determinant is (1*0)-(-2*12)=24. The 5 axis is then represented by 7deg24, while 8deg24 is of course a better approximation.