[tuning-math] The 7-limit tetrads of Blackjack
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Thu, 11 Jul 2002 20:29:34 -0700
15/14, an approximate secor, translates to [0 0 2] in terms of the cubic
lattice representation. In the place of a chain of secors, we can regard
the chords of Blackjack as a chain of [0 0 1] generators, two of which
make up a 15/14 modulation up. The 7-limit commas of the 72-et are
225/224 [1 1 4]
1029/1024 [3 4 1]
4375/4374 [5 -6 -3]
and redundently but importantly,
2401/2400 [2 3 -3]
Our chain of [0 0 1] generators gives us this:
[0 1 -2] ~ [-2 -2 1] (2401/2400)
[-2 -2 0]
[-2 -2 -1] ~ [-1 -1 3] (225/224)
[-1 -1 2]
[-1 -1 1]
[-1 -1 0]
[-1 -1 -1]
[-1 -1 -2] ~ [0 0 2] (225/224)
[0 0 1]
[0 0 0]
[0 0 -1]
[0 0 -2]
[0 0 -3]
[1 1 0] ~ [0 0 -4] (225/224)
[1 1 -1]
[-1 -2 1] ~ [1 1 -2] (2401/2400)
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