Maquila family

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The maquila family of rank-2 temperaments tempers out the maquila comma, 562949953421312/556182861328125 = [49 -6 -17.

Maquila

Subgroup: 2.3.5

Comma list: [49 -6 -17

Mapping[1 -6 5], 0 17 -6]]

Optimal tuning (POTE): ~2 = 1\1, ~512/375 = 535.437

Optimal ET sequence9, 38b, 47b, 56, 65, 186, 251, 316, 381, 697c

Badness: 0.472510

Septimal maquila

Subgroup: 2.3.5.7

Comma list: 225/224, 30233088/28824005

Mapping[1 -6 5 -7], 0 17 -6 22]]

Wedgie⟨⟨ 17 -6 22 -49 -13 68 ]]

Optimal tuning (POTE): ~2 = 1\1, ~48/35 = 535.322

Optimal ET sequence9, 56d, 65d

Badness: 0.232430

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 73728/73205

Mapping: [1 -6 5 -7 -1], 0 17 -6 22 10]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.321

Optimal ET sequence9, 56d, 65d

Badness: 0.072550

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 144/143, 176/175, 847/845

Mapping: [1 -6 5 -7 -1 -7], 0 17 -6 22 10 24]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.298

Optimal ET sequence9, 56df, 65d, 139df, 204ddff

Badness: 0.042198

Maquiloid

Subgroup: 2.3.5.7

Comma list: 686/675, 65625/65536

Mapping[1 -6 5 -3], 0 17 -6 13]]

Wedgie⟨⟨ 17 -6 13 -49 -27 47 ]]

Optimal tuning (POTE): ~2 = 1\1, ~175/128 = 535.482

Optimal ET sequence9, 38b, 47b, 56, 65, 121d, 186dd

Badness: 0.188977

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/242, 385/384, 686/675

Mapping: [1 -6 5 -3 -1], 0 17 -6 13 10]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.485

Optimal ET sequence9, 38be, 47b, 56, 65, 121d, 186dde

Badness: 0.066234

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 169/168, 245/242, 385/384

Mapping: [1 -6 5 -3 -1 -3], 0 17 -6 13 10 15]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.501

Optimal ET sequence9, 38be, 47b, 56, 65f, 121df, 186ddeff

Badness: 0.041850

Hemimaquila

Subgroup: 2.3.5.7

Comma list: 6144/6125, 184528125/184473632

Mapping[1 -6 5 -5], 0 34 -12 35]]

Wedgie⟨⟨ 34 -12 35 -98 -40 115 ]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 267.716

Optimal ET sequence9, 121, 130, 251, 381

Badness: 0.111465

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 5632/5625, 12005/11979

Mapping: [1 -6 5 -5 -1], 0 34 -12 35 20]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 267.717

Optimal ET sequence9, 121, 130, 251e, 381e

Badness: 0.047440

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 540/539, 676/675, 3584/3575

Mapping: [1 -6 5 -5 -1 -5], 0 34 -12 35 20 39]]

Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 267.719

Optimal ET sequence9, 121, 130, 251e, 381e

Badness: 0.024445