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More 72-et hexatonics

🔗genewardsmith <genewardsmith@juno.com>

1/6/2002 4:23:56 PM

These I found starting from 2401/2400~1, which is a very small 7-limit comma. Perhaps not surprisingly, the result is actually RI in the 7-limit; but the 11-limit results are quite good.

[0, 9, 23, 35, 49, 58]
[9, 14, 12, 14, 9, 14]
edges 4 9 14 connectivity 0 2 4

[0, 14, 23, 35, 49, 58]
[14, 9, 12, 14, 9, 14]
edges 3 9 14 connectivity 0 2 4

[0, 14, 23, 35, 44, 58]
[14, 9, 12, 9, 14, 14]
edges 3 8 13 connectivity 0 2 4

[0, 14, 23, 35, 49, 63]
[14, 9, 12, 14, 14, 9]
edges 3 8 13 connectivity 0 1 3

[0, 14, 28, 37, 46, 58]
[14, 14, 9, 9, 12, 14]
edges 2 6 11 connectivity 0 0 3

[0, 9, 23, 35, 49, 63]
[9, 14, 12, 14, 14, 9]
edges 2 6 11 connectivity 0 1 2

Six things taken two at a time is 15, so the two scales with 14 edges are missing only a single consonant interval to be maximally connected, and even this counts as consonant if we are willing to go to 15/11. The first scale listed in the 7-limit can be tuned as

1--35/32--5/4--7/5--8/5--7/4

It is based on three steps which avoid the use of 3, so these are in the 2^a 5^b 7^c system, with scale steps

(35/32)^2 (8/7)^3 (28/25) = 2

Because of the high degee of connectedness in the 11-limit, all kinds of modal transposition and other games could be played with this scale, somewhat along the lines of a hexany.