Quintosec family

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: ~16384/10125 = 831.105 (~16/15 = 111.105)

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: ~80/49 = 831.553 (~15/14 = 111.553)

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: ~80/49 = 831.311 (~15/14 = 111.311)

Optimal GPV sequence: Template:Val list

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: ~44/27 = 832.448 (~15/14 = 112.448)

Optimal GPV sequence: Template:Val list

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: ~45/28 = 831.113 (~16/15 = 111.113)

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: ~45/28 = 830.659 (~16/15 = 110.659)

Optimal GPV sequence: Template:Val list

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: ~45/28 = 830.910 (~16/15 = 110.910)

Optimal GPV sequence: Template:Val list

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: ~8192/4725 = 951.099 (~16/15 = 111.099)

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: ~400/231 = 951.070 (~16/15 = 111.070)

Optimal GPV sequence: Template:Val list

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: ~26/15 = 951.083 (~16/15 = 111.083)

Optimal GPV sequence: Template:Val list

Badness: 0.013475