Misty family: Difference between revisions
Expansion |
mNo edit summary |
||
| Line 46: | Line 46: | ||
POTE generator: ~3/2 = 703.210 | POTE generator: ~3/2 = 703.210 | ||
Optimal GPV sequence: {{Val list| 12, 87, 99e, 186e }} | |||
Badness: 0.035932 | Badness: 0.035932 | ||
| Line 59: | Line 59: | ||
POTE generator: ~3/2 = 703.303 | POTE generator: ~3/2 = 703.303 | ||
Optimal GPV sequence: {{Val list| 12f, 87, 99ef, 186ef, 273ef }} | |||
Badness: 0.027820 | Badness: 0.027820 | ||
| Line 72: | Line 72: | ||
POTE generator: ~3/2 = 703.233 | POTE generator: ~3/2 = 703.233 | ||
Optimal GPV sequence: {{Val list| 12f, 87, 99ef, 186efg }} | |||
Badness: 0.023908 | Badness: 0.023908 | ||
| Line 85: | Line 85: | ||
POTE generator: ~3/2 = 703.253 | POTE generator: ~3/2 = 703.253 | ||
Optimal GPV sequence: {{Val list| 12f, 87, 99ef, 186efgh }} | |||
Badness: 0.019878 | Badness: 0.019878 | ||
| Line 98: | Line 98: | ||
POTE generator: ~3/2 = 703.311 | POTE generator: ~3/2 = 703.311 | ||
Optimal GPV sequence: {{Val list| 12, 87, 186e, 273e }} | |||
Badness: 0.036872 | Badness: 0.036872 | ||
| Line 113: | Line 113: | ||
POTE generator: ~3/2 = 702.9764 | POTE generator: ~3/2 = 702.9764 | ||
Optimal GPV sequence: {{Val list| 12, 174e, 186, 198, 408cde, 606bcde }} | |||
Badness: 0. | Badness: 0.068509 | ||
==== 13-limit ==== | ==== 13-limit ==== | ||
| Line 126: | Line 126: | ||
POTE generator: ~3/2 = 703.0087 | POTE generator: ~3/2 = 703.0087 | ||
Optimal GPV sequence: {{Val list| 12f, 174ef, 186, 198 }} | |||
Badness: 0. | Badness: 0.044073 | ||
=== Hemimist === | === Hemimist === | ||
| Line 141: | Line 141: | ||
POTE generator: ~693/400 = 951.527 | POTE generator: ~693/400 = 951.527 | ||
Optimal GPV sequence: {{Val list| 24d, 87, 111, 198 }} | |||
Badness: 0.047439 | Badness: 0.047439 | ||
| Line 154: | Line 154: | ||
POTE generator: ~26/15 = 951.525 | POTE generator: ~26/15 = 951.525 | ||
Optimal GPV sequence: {{Val list| 24d, 87, 111, 198 }} | |||
Badness: 0.022923 | Badness: 0.022923 | ||
| Line 184: | Line 184: | ||
POTE generator: ~3/2 = 704.411 | POTE generator: ~3/2 = 704.411 | ||
Optimal GPV sequence: {{Val list| 12, 51, 63, 138de }} | |||
Badness: 0.051348 | Badness: 0.051348 | ||
Revision as of 06:29, 8 January 2022
The misty family tempers out the misty comma, 67108864/66430125 = [26 -12 -3⟩, equating the Pythagorean comma with a stack of three schismas, making it a member of the schismic-Pythagorean equivalence continuum. It features a third-octave period, which acts as the interval separating ~128/81 from ~5/4.
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.068509
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
Optimal GPV sequence: Template:Val list
Badness: 0.044073
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.051348