Sensipent family

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Sensipent

Subgroup: 2.3.5

Comma list: 78732/78125

Mapping: [1 6 8], 0 -7 -9]]

POTE generator: 162/125 = 443.058

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Sensi

Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. 46edo is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."

Subgroup: 2.3.5.7

Comma list: 126/125, 245/243

Mapping: [1 6 8 11], 0 -7 -9 -13]]

Mapping generators: ~2, ~14/9

Wedgie⟨⟨ 7 9 13 -2 1 5 ]]

POTE generator: ~9/7 = 443.383

Minimax tuning:

[[1 0 0 0, [1/13 0 0 7/13, [5/13 0 0 9/13, [0 0 0 1]
Eigenmonzos: 2, 7
[[1 0 0 0, [2/5 14/5 -7/5 0, [4/5 18/5 -9/5 0, [3/5 26/5 -13/5 0]
Eigenmonzos: 2, 9/5

Algebraic generator: The real root of x5 + x4 - 4x2 + x - 1, at 443.3783 cents.

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Badness: 0.0256

Sensor

Subgroup: 2.3.5.7.11

Comma list: 126/125, 245/243, 385/384

Mapping: [1 6 8 11 -6], 0 -7 -9 -13 15]]

POTE generator: ~9/7 = 443.294

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Badness: 0.0379

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 126/125, 169/168, 385/384

Mapping: [1 6 8 11 -6 10], 0 -7 -9 -13 15 -10]]

POTE generator: ~9/7 = 443.321

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Badness: 0.0256

Sensis

Subgroup: 2.3.5.7.11

Comma list: 56/55, 100/99, 245/243

Mapping: [1 6 8 11 6], 0 -7 -9 -13 -4]]

POTE generator: ~9/7 = 443.962

{{Val list|legend=1| 19, 27e, 73ee

Badness: 0.0287

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 78/77, 91/90, 100/99

Mapping: [1 6 8 11 6 10], 0 -7 -9 -13 -4 -10]]

POTE generator: ~9/7 = 443.945

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Badness: 0.0200

Sensus

Subgroup: 2.3.5.7.11

Comma list: 126/125, 176/175, 245/243

Mapping: [1 6 8 11 23], 0 -7 -9 -13 -31]]

POTE generator: ~9/7 = 443.626

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Badness: 0.0295

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 126/125, 169/168, 352/351

Mapping: [1 6 8 11 23 10], 0 -7 -9 -13 -31 -10]]

POTE generator: ~9/7 = 443.559

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Badness: 0.0208

Sensa

Subgroup: 2.3.5.7.11

Comma list: 55/54, 77/75, 99/98

Mapping: [1 6 8 11 11], 0 -7 -9 -13 -12]]

POTE generator: ~9/7 = 443.518

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Badness: 0.0368

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 66/65, 77/75, 143/140

Mapping: [1 6 8 11 11 10], 0 -7 -9 -13 -12 -11]]

POTE generator: ~9/7 = 443.506

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Badness: 0.0233

Hemisensi

Subgroup: 2.3.5.7.11

Comma list: 126/125, 243/242, 245/242

Mapping: [1 13 17 24 32], 0 -14 -18 -26 -35]]

POTE generator: ~25/22 = 221.605

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Badness: 0.0487

Sensei

Subgroup: 2.3.5.7

Comma list: 225/224, 78732/78125

Mapping: [1 6 8 23], 0 -7 -9 -32]]

Wedgie⟨⟨ 7 9 32 -2 31 49 ]]

POTE generator: ~125/81 = 757.245

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Badness: 0.0592

Bison

Subgroup: 2.3.5.7

Comma list: 6144/6125, 78732/78125

Mapping: [2 5 7 3], 0 -7 -9 10]]

Wedgie⟨⟨ 14 18 -20 -4 -71 -97 ]]

POTE generator: ~35/32 = 156.925

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Badness: 0.0704

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 6144/6125, 8019/8000

Mapping: [2 5 7 3 3], 0 -7 -9 10 15]]

POTE generator: ~35/32 = 156.883

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Badness: 0.0371

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 364/363, 441/440, 10985/10976

Mapping: [2 5 7 3 3 4], 0 -7 -9 10 15 13]]

POTE generator: ~35/32 = 156.904

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Badness: 0.0235

Heinz

Subgroup: 2.3.5.7

Comma list: 1029/1024, 78732/78125

Mapping: [1 13 17 -1], 0 -21 -27 7]]

POTE generator: ~48/35 = 546.815

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Badness: 0.1154

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 78732/78125

Mapping: [1 13 17 -1 4], 0 -21 -27 7 -1]]

POTE generator: ~11/8 = 547.631

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Badness: 0.0424

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 385/384, 441/440, 847/845

Mapping: [1 13 17 -1 4 -5], 0 -21 -27 7 -1 16]]

POTE generator: ~11/8 = 547.629

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Badness: 0.0258

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 351/350, 385/384, 441/440, 847/845

Mapping: [1 13 17 -1 4 -5 3], 0 -21 -27 7 -1 16 2]]

POTE generator: ~11/8 = 547.635

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Badness: 0.0185

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968

Mapping: [1 13 17 -1 4 -5 3 -5], 0 -21 -27 7 -1 16 2 17]]

POTE generator: ~11/8 = 547.614

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Badness: 0.0190