Circulating miracles

Here are Miracle[20], Miracle[21] and Miracle[22], this time 11-limit
reduced assuming 72 et. Miracle[22] seems well worth exploring for
anyone interested in 11-limit harmony.

I had before been restricting myself to where the Graham complexity
was less than the scale size; since 11/10 is a consonance of the
11-limit, this means it could never appear, whereas ratios of
consonances such as
15/14 = (5/4)/(7/6) could so long as we did not insist on getting
twice the Graham complextity less than the scale size. However, it
occurred to me this was unduly restrictive, given that 11/10 is well
outside of the range of 7-limit Graham complexity.

Miracle

72 et commas [225/224, 243/242, 385/384, 4000/3993]

Miracle commas [225/224, 243/242, 385/384]

Wedgie [6, -7, -2, 15, -25, -20, 3, 15, 59, 49]

Circulating miracles

Miracle[20]

Chroma 25/24

Scale

[1, 15/14, 12/11, 8/7, 7/6, 11/9, 5/4, 21/16, 4/3, 7/5, 10/7, 3/2,
32/21, 8/5, 18/11, 12/7, 7/4, 11/6, 15/8, 49/25]

[12/11, 7/6, 5/4, 4/3, 10/7, 32/21, 18/11, 7/4, 15/8, 1, 15/14, 8/7,
11/9, 21/16, 7/5, 3/2, 8/5, 12/7, 11/6, 49/25]

Chords in chains of secors

[1, 6/5, 3/2, 27/16] [1, 6/5, 3/2, 12/7]
[1, 6/5, 3/2, 27/16] [1, 6/5, 3/2, 12/7]
[1, 6/5, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 6/5, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 6/5, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 6/5, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 6/5, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 5/4, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 5/4, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 5/4, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 5/4, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 5/4, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 5/4, 3/2, 16/9]
[1, 5/4, 3/2, 7/4] [1, 5/4, 3/2, 16/9]
[1, 5/4, 14/9, 7/4] [1, 5/4, 14/9, 16/9]
[1, 5/4, 14/9, 7/4] [1, 5/4, 14/9, 16/9]
[1, 5/4, 14/9, 7/4] [1, 5/4, 14/9, 16/9]
[1, 5/4, 14/9, 7/4] [1, 5/4, 14/9, 16/9]
[1, 5/4, 14/9, 7/4] [1, 5/4, 14/9, 16/9]
[1, 5/4, 14/9, 7/4] [1, 5/4, 14/9, 16/9]

[1, 9/7, 3/2, 9/5] [1, 9/8, 3/2, 8/5] [1, 9/8, 3/2, 27/16]
[1, 9/7, 3/2, 15/8] [1, 9/8, 3/2, 8/5] [1, 9/8, 3/2, 27/16]
[1, 9/7, 3/2, 15/8] [1, 9/8, 3/2, 8/5] [1, 9/8, 3/2, 7/4]
[1, 9/7, 3/2, 15/8] [1, 9/8, 3/2, 8/5] [1, 9/8, 3/2, 7/4]
[1, 9/7, 3/2, 15/8] [1, 9/8, 3/2, 8/5] [1, 9/8, 3/2, 7/4]
[1, 9/7, 3/2, 15/8] [1, 9/8, 3/2, 8/5] [1, 9/8, 3/2, 7/4]
[1, 4/3, 3/2, 15/8] [1, 9/8, 3/2, 8/5] [1, 9/8, 3/2, 7/4]
[1, 4/3, 3/2, 15/8] [1, 9/8, 3/2, 8/5] [1, 9/8, 3/2, 7/4]
[1, 4/3, 3/2, 15/8] [1, 7/6, 3/2, 8/5] [1, 7/6, 3/2, 7/4]
[1, 4/3, 3/2, 15/8] [1, 7/6, 3/2, 8/5] [1, 7/6, 3/2, 7/4]
[1, 4/3, 3/2, 15/8] [1, 7/6, 3/2, 8/5] [1, 7/6, 3/2, 7/4]
[1, 4/3, 3/2, 15/8] [1, 7/6, 3/2, 8/5] [1, 7/6, 3/2, 7/4]
[1, 4/3, 3/2, 15/8] [1, 7/6, 3/2, 8/5] [1, 7/6, 3/2, 7/4]
[1, 4/3, 3/2, 15/8] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 4/3, 14/9, 15/8] [1, 7/6, 14/9, 5/3] [1, 7/6, 14/9, 7/4]
[1, 4/3, 14/9, 15/8] [1, 7/6, 14/9, 5/3] [1, 7/6, 14/9, 7/4]
[1, 4/3, 14/9, 15/8] [1, 7/6, 14/9, 5/3] [1, 7/6, 14/9, 7/4]
[1, 4/3, 14/9, 15/8] [1, 7/6, 14/9, 5/3] [1, 7/6, 14/9, 7/4]
[1, 4/3, 14/9, 15/8] [1, 7/6, 14/9, 5/3] [1, 7/6, 14/9, 7/4]
[1, 4/3, 14/9, 15/8] [1, 7/6, 14/9, 5/3] [1, 7/6, 14/9, 7/4]

[1, 11/9, 11/7, 11/6] [1, 11/9, 3/2, 12/7] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 3/2, 12/7] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 3/2, 12/7] [1, 9/7, 11/7, 12/7]
[1, 11/9, 18/11, 11/6] [1, 11/9, 3/2, 12/7] [1, 9/7, 18/11, 12/7]
[1, 11/9, 18/11, 11/6] [1, 11/9, 3/2, 12/7] [1, 9/7, 18/11, 12/7]
[1, 11/9, 18/11, 11/6] [1, 11/9, 3/2, 12/7] [1, 9/7, 18/11, 12/7]
[1, 11/9, 18/11, 11/6] [1, 11/9, 3/2, 12/7] [1, 4/3, 18/11, 12/7]
[1, 11/9, 18/11, 11/6] [1, 11/9, 3/2, 12/7] [1, 4/3, 18/11, 12/7]
[1, 11/9, 18/11, 11/6] [1, 11/9, 3/2, 12/7] [1, 4/3, 18/11, 12/7]
[1, 11/9, 18/11, 11/6] [1, 11/9, 3/2, 12/7] [1, 4/3, 18/11, 12/7]
[1, 11/9, 18/11, 11/6] [1, 11/9, 3/2, 12/7] [1, 4/3, 18/11, 12/7]
[1, 11/9, 18/11, 21/11] [1, 11/9, 3/2, 12/7] [1, 4/3, 18/11, 12/7]
[1, 11/9, 18/11, 21/11] [1, 11/9, 3/2, 16/9] [1, 4/3, 18/11, 16/9]
[1, 11/9, 18/11, 21/11] [1, 11/9, 3/2, 16/9] [1, 4/3, 18/11, 16/9]
[1, 11/9, 18/11, 21/11] [1, 11/9, 14/9, 16/9] [1, 4/3, 18/11, 16/9]
[1, 11/9, 18/11, 21/11] [1, 11/9, 14/9, 16/9] [1, 4/3, 18/11, 16/9]
[1, 11/9, 18/11, 21/11] [1, 11/9, 14/9, 16/9] [1, 4/3, 18/11, 16/9]
[1, 14/11, 18/11, 21/11] [1, 14/11, 14/9, 16/9] [1, 4/3, 18/11, 16/9]
[1, 14/11, 18/11, 21/11] [1, 14/11, 14/9, 16/9] [1, 4/3, 18/11, 16/9]
[1, 14/11, 18/11, 21/11] [1, 14/11, 14/9, 16/9] [1, 4/3, 18/11, 16/9]

Miracle[21] (Blackjack)

Chromas 33/32, 36/35

Scale

[1, 45/44, 15/14, 12/11, 8/7, 7/6, 11/9, 5/4, 21/16, 4/3, 7/5, 10/7,
3/2, 32/21, 8/5, 18/11, 12/7, 7/4, 11/6, 15/8, 49/25]

[45/44, 12/11, 7/6, 5/4, 4/3, 10/7, 32/21, 18/11, 7/4, 15/8, 1, 15/14,
8/7, 11/9, 21/16, 7/5, 3/2, 8/5, 12/7, 11/6, 49/25]

Chords in chains of secors

[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 9/5] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 9/7, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 16/11, 7/4] [1, 7/6, 16/11, 5/3]
[1, 5/4, 16/11, 7/4] [1, 7/6, 16/11, 5/3]
[1, 5/4, 16/11, 7/4] [1, 7/6, 16/11, 5/3]
[1, 5/4, 16/11, 7/4] [1, 7/6, 16/11, 5/3]
[1, 5/4, 16/11, 7/4] [1, 7/6, 16/11, 5/3]
[1, 5/4, 16/11, 7/4] [1, 7/6, 16/11, 5/3]

[1, 11/9, 11/7, 11/6] [1, 11/9, 8/5, 11/6] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 8/5, 11/6] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 8/5, 11/6] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 8/5, 11/6] [1, 9/7, 11/7, 12/7]
[1, 11/9, 32/21, 11/6] [1, 11/9, 8/5, 11/6] [1, 9/7, 32/21, 12/7]
[1, 11/9, 32/21, 11/6] [1, 11/9, 8/5, 11/6] [1, 9/7, 32/21, 12/7]
[1, 11/9, 32/21, 11/6] [1, 11/9, 8/5, 11/6] [1, 9/7, 32/21, 12/7]
[1, 11/9, 32/21, 11/6] [1, 11/9, 8/5, 11/6] [1, 5/4, 32/21, 12/7]
[1, 11/9, 32/21, 11/6] [1, 11/9, 8/5, 11/6] [1, 5/4, 32/21, 12/7]
[1, 11/9, 32/21, 11/6] [1, 11/9, 8/5, 11/6] [1, 5/4, 32/21, 12/7]
[1, 11/9, 32/21, 11/6] [1, 11/9, 8/5, 11/6] [1, 5/4, 32/21, 12/7]
[1, 11/9, 32/21, 11/6] [1, 11/9, 8/5, 11/6] [1, 5/4, 32/21, 12/7]
[1, 11/9, 32/21, 16/9] [1, 11/9, 8/5, 16/9] [1, 5/4, 32/21, 12/7]
[1, 11/9, 32/21, 16/9] [1, 11/9, 8/5, 16/9] [1, 5/4, 32/21, 5/3]
[1, 11/9, 32/21, 16/9] [1, 11/9, 14/9, 16/9] [1, 5/4, 32/21, 5/3]
[1, 11/9, 32/21, 16/9] [1, 11/9, 14/9, 16/9] [1, 5/4, 32/21, 5/3]
[1, 11/9, 32/21, 16/9] [1, 11/9, 14/9, 16/9] [1, 5/4, 32/21, 5/3]
[1, 11/9, 32/21, 16/9] [1, 11/9, 14/9, 16/9] [1, 5/4, 32/21, 5/3]
[1, 25/21, 32/21, 16/9] [1, 25/21, 14/9, 16/9] [1, 5/4, 32/21, 5/3]
[1, 25/21, 32/21, 16/9] [1, 25/21, 14/9, 16/9] [1, 5/4, 32/21, 5/3]
[1, 25/21, 32/21, 16/9] [1, 25/21, 14/9, 16/9] [1, 5/4, 32/21, 5/3]

Miracle[22]

Chroma 11/10

Scale

[1, 45/44, 21/20, 15/14, 12/11, 8/7, 7/6, 11/9, 5/4, 21/16, 4/3, 7/5,
10/7, 3/2, 32/21, 8/5, 18/11, 12/7, 7/4, 11/6, 15/8, 49/25]

[45/44, 12/11, 7/6, 5/4, 4/3, 10/7, 32/21, 18/11, 7/4, 15/8, 1, 15/14,
8/7, 11/9, 21/16, 7/5, 3/2, 8/5, 12/7, 11/6, 49/25, 21/20]

Chords in chains of secors

[1, 11/8, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 27/14] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 11/8, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 14/9]
[1, 5/4, 3/2, 7/4] [1, 12/11, 3/2, 14/9]
[1, 5/4, 15/11, 7/4] [1, 12/11, 15/11, 14/9]
[1, 5/4, 15/11, 7/4] [1, 12/11, 15/11, 14/9]
[1, 5/4, 15/11, 7/4] [1, 12/11, 15/11, 14/9]
[1, 5/4, 15/11, 7/4] [1, 12/11, 15/11, 14/9]
[1, 5/4, 15/11, 7/4] [1, 12/11, 15/11, 14/9]
[1, 5/4, 15/11, 7/4] [1, 12/11, 15/11, 14/9]

[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 27/14]
[1, 9/7, 3/2, 9/5] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 7/4]
[1, 9/7, 3/2, 18/11] [1, 9/7, 3/2, 11/6] [1, 9/7, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 11/6] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 3/2, 18/11] [1, 7/6, 3/2, 5/3] [1, 7/6, 3/2, 7/4]
[1, 7/6, 15/11, 18/11] [1, 7/6, 15/11, 5/3] [1, 7/6, 15/11, 7/4]
[1, 7/6, 15/11, 18/11] [1, 7/6, 15/11, 5/3] [1, 7/6, 15/11, 7/4]
[1, 7/6, 15/11, 18/11] [1, 7/6, 15/11, 5/3] [1, 7/6, 15/11, 7/4]
[1, 7/6, 15/11, 18/11] [1, 7/6, 15/11, 5/3] [1, 7/6, 15/11, 7/4]
[1, 7/6, 15/11, 18/11] [1, 7/6, 15/11, 5/3] [1, 7/6, 15/11, 7/4]
[1, 7/6, 15/11, 18/11] [1, 7/6, 15/11, 5/3] [1, 7/6, 15/11, 7/4]

[1, 11/9, 11/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 9/7, 11/7, 12/7]
[1, 11/9, 11/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 9/7, 11/7, 12/7]
[1, 11/9, 10/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 9/7, 10/7, 12/7]
[1, 11/9, 10/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 9/7, 10/7, 12/7]
[1, 11/9, 10/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 9/7, 10/7, 12/7]
[1, 11/9, 10/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 7/6, 10/7, 12/7]
[1, 11/9, 10/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 7/6, 10/7, 12/7]
[1, 11/9, 10/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 7/6, 10/7, 12/7]
[1, 11/9, 10/7, 11/6] [1, 11/9, 12/7, 49/25] [1, 7/6, 10/7, 12/7]
[1, 11/9, 10/7, 11/6] [1, 11/9, 12/7, 16/9] [1, 7/6, 10/7, 12/7]
[1, 11/9, 10/7, 5/3] [1, 11/9, 12/7, 16/9] [1, 7/6, 10/7, 12/7]
[1, 11/9, 10/7, 5/3] [1, 11/9, 14/9, 16/9] [1, 7/6, 10/7, 14/9]
[1, 11/9, 10/7, 5/3] [1, 11/9, 14/9, 16/9] [1, 7/6, 10/7, 14/9]
[1, 11/9, 10/7, 5/3] [1, 11/9, 14/9, 16/9] [1, 7/6, 10/7, 14/9]
[1, 11/9, 10/7, 5/3] [1, 11/9, 14/9, 16/9] [1, 7/6, 10/7, 14/9]
[1, 11/9, 10/7, 5/3] [1, 11/9, 14/9, 16/9] [1, 7/6, 10/7, 14/9]
[1, 10/9, 10/7, 5/3] [1, 10/9, 14/9, 16/9] [1, 7/6, 10/7, 14/9]
[1, 10/9, 10/7, 5/3] [1, 10/9, 14/9, 16/9] [1, 7/6, 10/7, 14/9]
[1, 10/9, 10/7, 5/3] [1, 10/9, 14/9, 16/9] [1, 7/6, 10/7, 14/9]