Misty family: Difference between revisions
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=== Semimist === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 3136/3125, 5120/5103, 9801/9800 | |||
Mapping: [{{val| 6 0 52 112 173 }}, {{val| 0 1 -4 -10 -16 }}] | |||
Mapping generators: ~55/49, ~3 | |||
POTE generator: ~3/2 = 702.9764 | |||
Vals: {{Val list| 12, 174e, 186, 198, 408cde, 606bcde }} | |||
Badness: 0.0685 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 352/351, 847/845, 1716/1715, 3136/3125 | |||
Mapping: [{{val| 6 0 52 112 173 203 }}, {{val| 0 1 -4 -10 -16 -19 }}] | |||
POTE generator: ~3/2 = 703.0087 | |||
Vals: {{Val list| 12f, 174ef, 186, 198 }} | |||
Badness: 0.0441 | |||
=== Hemimist === | === Hemimist === | ||
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Mapping: [{{val| 3 0 26 56 8 }}, {{val| 0 2 -8 -20 1 }}] | Mapping: [{{val| 3 0 26 56 8 }}, {{val| 0 2 -8 -20 1 }}] | ||
POTE generator: ~ | Mapping generators: ~63/50, ~693/400 | ||
POTE generator: ~693/400 = 951.527 | |||
Vals: {{Val list| 24d, 87, 111, 198 }} | Vals: {{Val list| 24d, 87, 111, 198 }} | ||
| Line 122: | Line 152: | ||
Mapping: [{{val| 3 0 26 56 8 23 }}, {{val| 0 2 -8 -20 1 -5 }}] | Mapping: [{{val| 3 0 26 56 8 23 }}, {{val| 0 2 -8 -20 1 -5 }}] | ||
POTE generator: ~ | POTE generator: ~26/15 = 951.525 | ||
Vals: {{Val list| 24d, 87, 111, 198 }} | Vals: {{Val list| 24d, 87, 111, 198 }} | ||
Revision as of 13:42, 16 October 2021
The misty family tempers out the misty comma, 67108864/66430125 = [26 -12 -3⟩.
The second comma of the normal comma list defines which 7-limit family member we are looking at.
- Adding 3136/3125 (hemimean) leads to septimal misty.
- Adding 225/224 (marvel) leads to fog.
Misty
Subgroup: 2.3.5
Comma list: 67108864/66430125
Mapping: [⟨3 0 26], ⟨0 1 -4]]
POTE generator: ~3/2 = 703.111
Badness: 0.106540
Septimal misty
Subgroup: 2.3.5.7
Comma list: 3136/3125, 5120/5103
Mapping: [⟨3 0 26 56], ⟨0 1 -4 -10]]
Wedgie: ⟨⟨ 3 -12 -30 -26 -56 -36 ]]
POTE generator: ~3/2 = 703.021
Badness: 0.036802
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 4375/4356
Mapping: [⟨3 0 26 56 77], ⟨0 1 -4 -10 -14]]
POTE generator: ~3/2 = 703.210
Vals: Template:Val list
Badness: 0.035932
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 625/624
Mapping: [⟨3 0 26 56 77 92], ⟨0 1 -4 -10 -14 -17]]
POTE generator: ~3/2 = 703.303
Vals: Template:Val list
Badness: 0.027820
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 352/351, 364/363, 375/374, 595/594
Mapping: [⟨3 0 26 56 77 92 -2], ⟨0 1 -4 -10 -14 -17 3]]
POTE generator: ~3/2 = 703.233
Vals: Template:Val list
Badness: 0.023908
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 210/209, 352/351, 364/363, 375/374, 595/594
Mapping: [⟨3 0 26 56 77 92 -2 8], ⟨0 1 -4 -10 -14 -17 3 1]]
POTE generator: ~3/2 = 703.253
Vals: Template:Val list
Badness: 0.019878
Mystic
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 441/440, 896/891, 1001/1000
Mapping: [⟨3 0 26 56 77 -46], ⟨0 1 -4 -10 -14 12]]
POTE generator: ~3/2 = 703.311
Vals: Template:Val list
Badness: 0.036872
Semimist
Subgroup: 2.3.5.7.11
Comma list: 3136/3125, 5120/5103, 9801/9800
Mapping: [⟨6 0 52 112 173], ⟨0 1 -4 -10 -16]]
Mapping generators: ~55/49, ~3
POTE generator: ~3/2 = 702.9764
Vals: Template:Val list
Badness: 0.0685
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1716/1715, 3136/3125
Mapping: [⟨6 0 52 112 173 203], ⟨0 1 -4 -10 -16 -19]]
POTE generator: ~3/2 = 703.0087
Vals: Template:Val list
Badness: 0.0441
Hemimist
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 3136/3125, 5120/5103
Mapping: [⟨3 0 26 56 8], ⟨0 2 -8 -20 1]]
Mapping generators: ~63/50, ~693/400
POTE generator: ~693/400 = 951.527
Vals: Template:Val list
Badness: 0.047439
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845, 3025/3024
Mapping: [⟨3 0 26 56 8 23], ⟨0 2 -8 -20 1 -5]]
POTE generator: ~26/15 = 951.525
Vals: Template:Val list
Badness: 0.022923
Fog
The fog temperament (12&63) tempers out the marvel comma, 225/224.
Subgroup: 2.3.5.7
Comma list: 225/224, 156250/151263
Mapping: [⟨3 5 6 7], ⟨0 -1 4 6]]
Wedgie: ⟨⟨ 3 -12 -18 -26 -37 -8 ]]
POTE generator: ~3/2 = 704.118
Badness: 0.086866
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 2420/2401
Mapping: [⟨3 5 6 7 8], ⟨0 -1 4 6 10]]
POTE generator: ~3/2 = 704.411
Vals: Template:Val list
Badness: 0.051348