Qintosec family

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The qintosec family tempers out the qintosec comma, 140737488355328/140126044921875 = [47 -15 -10.

Qintosec

Subgroup: 2.3.5

Comma: 140737488355328/140126044921875

Mapping: [5 1 22], 0 2 -3]]

Mapping generators: ~524288/455625, ~16384/10125

POTE generator: ~16/15 = 111.105

Vals10, 55, 65, 140, 205, 270, 1955c, 2225c, 2495bc, 2765bc, 3035bc, 3305bcc, 3575bcc

Badness: 0.139191

Septimal qintosec

The qintosec temperament can be described as 10&65d temperament, tempering out the marvel comma, 225/224 in the 7-limit.


Subgroup: 2.3.5.7

Comma list: 225/224, 2560000/2470629

Mapping: [5 1 22 21], 0 2 -3 -2]]

Wedgie⟨⟨10 -15 -10 -47 -44 19]]

POTE generator: ~15/14 = 111.553

Vals10, 55d, 65d, 75, 140d, 215dd

Badness: 0.156764

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 3840/3773

Mapping: [5 1 22 21 0], 0 2 -3 -2 5]]

POTE generator: ~15/14 = 111.311

Vals: 10, 55d, 65d, 140de, 205dde

Badness: 0.077907

Qinto

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 332750/321489

Mapping: [5 1 22 21 -7], 0 2 -3 -2 7]]

POTE generator: ~15/14 = 112.448

Vals: 10, 75, 160cde

Badness: 0.127732

Sengasec

The sengasec temperament (10&55) tempers out the cloudy comma, 16807/16384 and the sengic comma, 686/675 in the 7-limit.


Subgroup: 2.3.5.7

Comma list: 686/675, 16807/16384

Mapping: [5 1 22 14], 0 2 -3 0]]

Wedgie⟨⟨10 -15 0 -47 -28 42]]

POTE generator: ~16/15 = 111.113

Vals10, 55, 65, 140dd, 205ddd, 270ddd

Badness: 0.156259

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 385/384, 686/675

Mapping: [5 1 22 14 0], 0 2 -3 0 5]]

POTE generator: ~16/15 = 110.659

Vals: 10, 55, 65

Badness: 0.081607

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 243/242, 686/675

Mapping: [5 1 22 14 0 22], 0 2 -3 0 5 -1]]

POTE generator: ~16/15 = 110.910

Vals: 10, 55, 65

Badness: 0.056390

Decoid

See also: Breedsmic temperaments #Decoid

Subgroup: 2.3.5.7

Comma list: 2401/2400, 67108864/66976875

Mapping: [10 0 47 36], 0 2 -3 -1]]

Mapping generators: ~15/14, ~8192/4725

Wedgie⟨⟨20 -30 -10 -94 -72 61]]

POTE generator: ~16/15 = 111.099

Vals10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc

Badness: 0.033902

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 5632/5625, 9801/9800

Mapping: [10 0 47 36 98], 0 2 -3 -1 -8]]

POTE generator: ~16/15 = 111.070

Vals: 10e, 130, 270, 670, 940, 1210, 2150c

Badness: 0.018735

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715, 4096/4095

Mapping: [10 0 47 36 98 37], 0 2 -3 -1 -8 0]]

POTE generator: ~16/15 = 111.083

Vals: 10e, 130, 270, 940, 1210f, 1480cf

Badness: 0.013475