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Schismic[24] and Tritonic[33]

🔗Gene Ward Smith <gwsmith@svpal.org>

3/21/2003 10:22:08 PM

The right way to do these seems to be always to look at the circle of
generators, which gets us out of any sticky business. Schismic[24] is
a hell of a 7-limit system, we see once again. I haven't considered
writing in it because it seemed to well-explored, but that may only be
in theory. In any case, when looking at 36/35 chroma systems it's nice
to have 3/2 as a generator, since that limits the damage of the wolf
fifth.

Tritonic[33] is not quite in the same league, but as you can see it
could be interesting also.

Schismic[24]

[1, -8, -14, -15, -25, -10]
[1, 50/49, 21/20, 15/14, 10/9, 9/8, 25/21, 6/5, 5/4, 63/50, 4/3,
27/20, 7/5, 10/7, 40/27, 3/2, 63/40, 8/5, 5/3, 27/16, 16/9, 9/5, 15/8,
40/21]
[40/27, 10/9, 5/3, 5/4, 15/8, 7/5, 21/20, 63/40, 25/21, 16/9, 4/3, 1,
3/2, 9/8, 27/16, 63/50, 40/21, 10/7, 15/14, 8/5, 6/5, 9/5, 27/20, 50/49]

3/2 generator circle

[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]

Tritonic[33]

[5, -11, -12, -29, -33, 3]
[1, 50/49, 21/20, 15/14, 160/147, 9/8, 8/7, 147/125, 25/21, 6/5,
49/40, 5/4, 80/63, 21/16, 4/3, 200/147, 7/5, 10/7, 147/100, 3/2,
32/21, 63/40, 8/5, 80/49, 5/3, 27/16, 250/147, 7/4, 16/9, 147/80,
15/8, 40/21, 49/25]
[6/5, 27/16, 147/125, 80/49, 8/7, 8/5, 9/8, 63/40, 160/147, 32/21,
15/14, 3/2, 21/20, 147/100, 50/49, 10/7, 1, 7/5, 49/25, 200/147,
40/21, 4/3, 15/8, 21/16, 147/80, 80/63, 16/9, 5/4, 7/4, 49/40,
250/147, 25/21, 5/3]

7/5 generator circle

[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 35/24, 7/4] [1, 7/6, 35/24, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]