Quintosec family: Difference between revisions
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== Septimal qintosec == | == Septimal qintosec == | ||
The qintosec temperament can be described as 10&65d temperament, tempering out the [[marvel comma]], 225/224 in the 7-limit. | 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 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~15/14 = 111.311 | POTE generator: ~15/14 = 111.311 | ||
Optimal GPV sequence: {{Val list| 10, 55d, 65d, 140de, 205dde }} | |||
Badness: 0.077907 | Badness: 0.077907 | ||
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POTE generator: ~15/14 = 112.448 | POTE generator: ~15/14 = 112.448 | ||
Optimal GPV sequence: {{Val list| 10, 75, 160cde }} | |||
Badness: 0.127732 | Badness: 0.127732 | ||
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== Sengasec == | == Sengasec == | ||
The ''sengasec'' temperament (10&55) tempers out the [[cloudy comma]], 16807/16384 and the sengic comma, 686/675 in the 7-limit. | 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 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~16/15 = 110.659 | POTE generator: ~16/15 = 110.659 | ||
Optimal GPV sequence: {{Val list| 10, 55, 65 }} | |||
Badness: 0.081607 | Badness: 0.081607 | ||
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POTE generator: ~16/15 = 110.910 | POTE generator: ~16/15 = 110.910 | ||
Optimal GPV sequence: {{Val list| 10, 55, 65 }} | |||
Badness: 0.056390 | Badness: 0.056390 | ||
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POTE generator: ~16/15 = 111.070 | POTE generator: ~16/15 = 111.070 | ||
Optimal GPV sequence: {{Val list| 10e, 130, 270, 670, 940, 1210, 2150c }} | |||
Badness: 0.018735 | Badness: 0.018735 | ||
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POTE generator: ~16/15 = 111.083 | POTE generator: ~16/15 = 111.083 | ||
Optimal GPV sequence: {{Val list| 10e, 130, 270, 940, 1210f, 1480cf }} | |||
Badness: 0.013475 | Badness: 0.013475 | ||
Revision as of 00:51, 31 December 2021
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
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
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
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: ~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: ~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: ~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: ~16/15 = 110.910
Optimal GPV sequence: Template:Val list
Badness: 0.056390
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
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
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: ~16/15 = 111.083
Optimal GPV sequence: Template:Val list
Badness: 0.013475