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More lattice based 11-limit scales

🔗Gene Ward Smith <gwsmith@svpal.org>

3/27/2005 7:12:59 PM

These are centered on |* 2/5 1/5 1/5 1/5>, and wrap themselves around
the 11-limit otonal hexad. It isn't hole-based, in case anyone cares.

Shell 1 radius sqrt(3/5)
[3]

Shell 2 radius sqrt(8/5)
[1, 5, 7, 9, 11]

Scale 6 notes (hexad)
[1, 9/8, 5/4, 11/8, 3/2, 7/4]

Shell 3 radius sqrt(13/5)
[5/3, 7/3, 11/3, 15, 21, 33]

Scale 12 notes
[1, 33/32, 9/8, 7/6, 5/4, 21/16, 11/8, 3/2, 5/3, 7/4, 11/6, 15/8]

Shell 4 radius sqrt(23/5)
[1/3, 15/11, 21/11, 15/7, 21/5, 33/7, 33/5, 35/3, 55/3, 77/3, 27]

Scale 23 notes
[1, 33/32, 21/20, 15/14, 9/8, 55/48, 7/6, 33/28, 5/4, 21/16, 4/3,
15/11, 11/8, 35/24, 3/2, 77/48, 33/20, 5/3, 27/16, 7/4, 11/6, 15/8, 21/11]

Shell 5 radius sqrt(28/5)
[5/11, 5/9, 7/11, 5/7, 7/9, 9/11, 11/9, 9/7, 7/5, 11/7, 9/5, 11/5,
35/11, 35/9, 45/11, 63/11, 55/9, 45/7, 55/7, 77/9, 63/5, 99/7, 77/5,
99/5, 35, 45, 55, 63, 77, 99]

Scale 53 notes
[1, 45/44, 33/32, 21/20, 77/72, 15/14, 35/32, 11/10, 10/9, 9/8, 55/48,
7/6, 33/28, 77/64, 11/9, 99/80, 5/4, 14/11, 9/7, 21/16, 4/3, 15/11,
11/8, 7/5, 45/32, 10/7, 63/44, 35/24, 3/2, 55/36, 99/64, 14/9, 11/7,
63/40, 35/22, 77/48, 45/28, 18/11, 33/20, 5/3, 27/16, 55/32, 7/4,
99/56, 9/5, 20/11, 11/6, 15/8, 21/11, 77/40, 35/18, 55/28, 63/32]