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The 41 rank three consonantly-generated subgroups of the 11-limit group

🔗genewardsmith <genewardsmith@juno.com>

1/18/2002 1:19:59 AM

By "consonantly generated" I mean each of the generators is an
11-limit consonance, and by "rank 3" that there are three independent generators. It turns out that there are 41 of them, each of which could, in theory, be treated as something to locate linear temperaments in. Some, however, are clearly more significant than others.

[3,5,7]

[3,5,11]

[3,7,11]

[5,7,9]

[5,7,11]

[5,9,11]

[7,9,11]

[5,7,11/9]

[3,7/5,11]

[7/5,9,11]

[5/3,7,11]

[3,7,11/5]

[7,9,11/5]

[5,7/3,11]

[9/5,7,11]

[5,9/7,11]

[5,7,11/3]

[5,9,11/7]

[3,5,11/7]

[5,7/3,11/9]

[5,9/7,11/3]

[5/3,9/7,11]

[5/3,7,11/9]

[5,9/7,11/7]

[7/3,9/5,11]

[9/5,7,11/5]

[5,7/3,11/3]

[7/5,9/5,11]

[5/3,7/3,11]

[9,7/5,11/5]

[5/3,7,11/3]

[3,7/5,11/5]

[9/5,7,11/3]

[5/3,7/3,11/3]

[7/5,9/5,11/5]

[5/3,7/3,11/9]

[7/3,9/5,11/3]

[5/3,9/7,11/3]

[7/5,9/5,11/3]

[5/3,9/7,11/7]

[9/5,7/3,11/5]