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Some classes of 72-et scales

🔗genewardsmith <genewardsmith@juno.com>

1/1/2002 8:59:47 PM

Here is the result of a search for other possibilities for 72-et scales, which start from the premise that in the 7-limit they work as 225/224 planar temperament scales. I've already done the 10-note example and one of the 12-note examples. The first list is a list of scale step sizes in 72-et steps; below that is the multiplicity of each step size. The number of steps is of course the sum of these multiplicities. Note that in the 22-note case, there are two "diferent" steps of size 3/72; in the corresponding planar temperament these actually are a little different in the rms optimized tuning.

4 notes

[7, 19, 23]
[1, 1, 2]

5 notes

[7, 12, 23]
[2, 1, 2]

8 notes

[5, 7, 16]
[1, 5, 2]

9 notes

[7, 12, 9]
[6, 1, 2]

10 notes

[7, 5, 9]
[7, 1, 2]

11 notes

[2, 5, 9]
[1, 5, 5]

12 notes

[6, 1, 11]
[8, 2, 2]

[7, 5, 2]
[9, 1, 2]

[6, 1, 11]
[2, 5, 5]

[7, 5, 6]
[5, 5, 2]

[6, 7, 5]
[8, 2, 2]

15 notes

[1, 7, 10]
[8, 2, 5]

[5, 2, 11]
[8, 5, 2]

[7, 4, 1]
[9, 1, 5]

[3, 7, 6]
[8, 6, 1]

16 notes

[2, 5, 7]
[6, 5, 5]

[6, 1, 9]
[8, 6, 2]

17 notes

[5, 2, 9]
[8, 7, 2]

[6, 1, 5]
[7, 5, 5]

19 notes

[5, 2, 7]
[8, 9, 2]

[3, 4, 5]
[9, 5, 5]

20 notes

[1, 7, 3]
[8, 7, 5]

21 notes

[3, 1, 6]
[8, 6, 7]

22 notes

[3, 3, 4]
[8, 8, 6]