Iterated CPS

If S is a set of octave-equivalence classes, we can denote by CPS(S) the set of ratios of these classes, and we then can iterate this function, giving us CPS^2(S) = CPS(CPS(S)) and so forth. In octave reduced form, starting from the diminished 7th tetrad of the 31-et, the following would be an example (where "0" denotes the absence of an 11-limit consonance):

[0, 7, 15, 23]
edges 3 6 6 6 connectivity 1 3 3 3

[1, 7/6, 7/5, 5/3]
[7/6, 1, 6/5, 10/7]
[7/5, 6/5, 1, 6/5]
[5/3, 10/7, 6/5, 1]

[0, 7, 8, 15, 16, 23, 24]
edges 6 15 15 18 connectivity 1 3 3 5

[1, 7/6, 6/5, 7/5, 10/7, 5/3, 12/7]
[7/6, 1, 0, 6/5, 11/9, 10/7, 16/11]
[6/5, 0, 1, 7/6, 6/5, 7/5, 10/7]
[7/5, 6/5, 7/6, 1, 0, 6/5, 11/9]
[10/7, 11/9, 6/5, 0, 1, 7/6, 6/5]
[5/3, 10/7, 7/5, 6/5, 7/6, 1, 0]
[12/7, 16/11, 10/7, 11/9, 6/5, 0, 1]

[0, 1, 7, 8, 9, 14, 15, 16, 17, 22, 23, 24, 30]
edges 19 46 48 63 connectivity 2 6 6 9

[1, 0, 7/6, 6/5, 11/9, 11/8, 7/5, 10/7, 16/11, 18/11, 5/3, 12/7, 0]
[0, 1, 8/7, 7/6, 6/5, 4/3, 11/8, 7/5, 10/7, 8/5, 18/11, 5/3, 0]
[7/6, 8/7, 1, 0, 0, 7/6, 6/5, 11/9, 5/4, 7/5, 10/7, 16/11, 5/3]
[6/5, 7/6, 0, 1, 0, 8/7, 7/6, 6/5, 11/9, 11/8, 7/5, 10/7, 18/11]
[11/9, 6/5, 0, 0, 1, 9/8, 8/7, 7/6, 6/5, 4/3, 11/8, 7/5, 8/5]
[11/8, 4/3, 7/6, 8/7, 9/8, 1, 0, 0, 0, 6/5, 11/9, 5/4, 10/7]
[7/5, 11/8, 6/5, 7/6, 8/7, 0, 1, 0, 0, 7/6, 6/5, 11/9, 7/5]
[10/7, 7/5, 11/9, 6/5, 7/6, 0, 0, 1, 0, 8/7, 7/6, 6/5, 11/8]
[16/11, 10/7, 5/4, 11/9, 6/5, 0, 0, 0, 1, 9/8, 8/7, 7/6, 4/3]
[18/11, 8/5, 7/5, 11/8, 4/3, 6/5, 7/6, 8/7, 9/8, 1, 0, 0, 6/5]
[5/3, 18/11, 10/7, 7/5, 11/8, 11/9, 6/5, 7/6, 8/7, 0, 1, 0, 7/6]
[12/7, 5/3, 16/11, 10/7, 7/5, 5/4, 11/9, 6/5, 7/6, 0, 0, 1, 8/7]
[0, 0, 5/3, 18/11, 8/5, 10/7, 7/5, 11/8, 4/3, 6/5, 7/6, 8/7, 1]

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:

> If S is a set of octave-equivalence classes, we can denote by CPS
(S) the set of ratios of these classes,

CPS already has another meaning -- combination product set. What
you're looking at here might be called the "diamond".