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7-limit hexatonic scales

🔗genewardsmith <genewardsmith@juno.com>

12/31/2001 11:58:51 PM

Here are the two most proper classes of superparticular scales

Blackwood = 2.825

[1, 16/15, 8/7, 4/3, 8/5, 28/15]
[16/15, 15/14, 7/6, 6/5, 7/6, 15/14] 3

[1, 16/15, 8/7, 4/3, 14/9, 28/15]
[16/15, 15/14, 7/6, 7/6, 6/5, 15/14] 2

[1, 16/15, 8/7, 4/3, 8/5, 12/7]
[16/15, 15/14, 7/6, 6/5, 15/14, 7/6] 2

[1, 16/15, 56/45, 4/3, 14/9, 5/3]
[16/15, 7/6, 15/14, 7/6, 15/14, 6/5] 2

[1, 16/15, 8/7, 4/3, 10/7, 5/3]
[16/15, 15/14, 7/6, 15/14, 7/6, 6/5] 1

[1, 16/15, 8/7, 4/3, 10/7, 12/7]
[16/15, 15/14, 7/6, 15/14, 6/5, 7/6] 1

[1, 16/15, 8/7, 4/3, 14/9, 5/3]
[16/15, 15/14, 7/6, 7/6, 15/14, 6/5] 1

[1, 16/15, 8/7, 48/35, 8/5, 12/7]
[16/15, 15/14, 6/5, 7/6, 15/14, 7/6] 1

[1, 16/15, 56/45, 4/3, 10/7, 5/3]
[16/15, 7/6, 15/14, 15/14, 7/6, 6/5] 1

[1, 16/15, 56/45, 4/3, 10/7, 12/7]
[16/15, 7/6, 15/14, 15/14, 6/5, 7/6] 1

[1, 16/15, 56/45, 4/3, 8/5, 12/7]
[16/15, 7/6, 15/14, 6/5, 15/14, 7/6] 1

Blackwood = 3.159

[1, 21/20, 6/5, 7/5, 3/2, 7/4]
[21/20, 8/7, 7/6, 15/14, 7/6, 8/7] 4

[1, 21/20, 6/5, 7/5, 3/2, 12/7]
[21/20, 8/7, 7/6, 15/14, 8/7, 7/6] 3

[1, 21/20, 9/8, 9/7, 3/2, 7/4]
[21/20, 15/14, 8/7, 7/6, 7/6, 8/7] 2

[1, 21/20, 9/8, 21/16, 3/2, 12/7]
[21/20, 15/14, 7/6, 8/7, 8/7, 7/6] 2