Misty family

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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

Main article: Misty

Subgroup: 2.3.5

Comma list: 67108864/66430125

Mapping: [3 0 26], 0 1 -4]]

POTE generator: ~3/2 = 703.111

Vals12, 51, 63, 75, 87, 99, 285, 384

Badness: 0.106540

Septimal misty

Main article: 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

Vals12, 87, 99

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: 12, 87, 99e, 186e

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: 12f, 87, 99ef, 186ef, 273ef

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: 12f, 87, 99ef, 186efg

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: 12f, 87, 99ef, 186efgh

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: 12, 87, 186e, 273e

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: 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: [6 0 52 112 173 203], 0 1 -4 -10 -16 -19]]

POTE generator: ~3/2 = 703.0087

Vals: 12f, 174ef, 186, 198

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: 24d, 87, 111, 198

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: 24d, 87, 111, 198

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

Vals12, 51, 63, 75

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: 12, 51, 63, 138de

Badness: 0.051348