Septiennealimmal clan: Difference between revisions
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{{Val list|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }} | {{Val list|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }} | ||
== Enneaplonic == | |||
Enneaplonic (27 & 81) has a period of 1/27 octave and tempers out 126/125 and 540/539, as well as the [[Starling family #Aplonis|aplonis temperament]]. | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 126/125, 40353607/40310784 | |||
[[Mapping]]: [{{val|27 43 63 76}}, {{val|0 -1 -1 -1}}] | |||
[[POTE generator]]: ~3/2 = 701.244 | |||
{{Val list|legend=1| 27, 81, 108, 135c, 243c }} | |||
[[Badness]]: 0.173308 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 126/125, 540/539, 21609/21296 | |||
Mapping: [{{val|27 43 63 76 94}}, {{val|0 -1 -1 -1 -2}}] | |||
POTE generator: ~3/2 = 700.001 | |||
Optimal GPV sequence: {{Val list| 27e, 81, 108 }} | |||
Badness: 0.078060 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 126/125, 144/143, 196/195, 21609/21296 | |||
Mapping: [{{val|27 43 63 76 94 100}}, {{val|0 -1 -1 -1 -2 0}}] | |||
POTE generator: ~3/2 = 700.867 | |||
Optimal GPV sequence: {{Val list| 27e, 81, 108, 243ceef }} | |||
Badness: 0.057145 | |||
==== Enneaplonoid ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 126/125, 169/168, 540/539, 975/968 | |||
Mapping: [{{val|27 43 63 76 94 100}}, {{val|0 -1 -1 -1 -2 -1}}] | |||
POTE generator: ~3/2 = 699.179 | |||
Optimal GPV sequence: {{Val list| 27e, 54bdef, 81f, 108f }} | |||
Badness: 0.052732 | |||
== Undecentic == | == Undecentic == | ||
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POTE generator: ~11/8 = 552.024 | POTE generator: ~11/8 = 552.024 | ||
Optimal GPV sequence: {{Val list| 99ef, 198 }} | |||
Badness: 0.042547 | Badness: 0.042547 | ||
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POTE generator: ~11/8 = 551.322 | POTE generator: ~11/8 = 551.322 | ||
Optimal GPV sequence: {{Val list| 171, 342, 855ff, 1197fff }} | |||
Badness: 0.054029 | Badness: 0.054029 | ||
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POTE generator: ~11/8 = 551.365 | POTE generator: ~11/8 = 551.365 | ||
Optimal GPV sequence: {{Val list| 171, 342, 855ff, 1197fff }} | |||
Badness: 0.031323 | Badness: 0.031323 | ||
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POTE generator: ~11/8 = 551.625 | POTE generator: ~11/8 = 551.625 | ||
Optimal GPV sequence: {{Val list| 171, 342f, 513, 855f }} | |||
Badness: 0.046843 | Badness: 0.046843 | ||
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POTE generator: ~11/8 = 551.756 | POTE generator: ~11/8 = 551.756 | ||
Optimal GPV sequence: {{Val list| 171, 342f, 513, 855f }} | |||
Badness: 0.030622 | Badness: 0.030622 | ||
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POTE generator: ~11/8 = 551.4043 | POTE generator: ~11/8 = 551.4043 | ||
Optimal GPV sequence: {{Val list| 441, 882, 1323, 3528f, 4851ff, 6174dff }} | |||
Badness: 0.042975 | Badness: 0.042975 | ||
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POTE generator: ~11/8 = 551.3688 | POTE generator: ~11/8 = 551.3688 | ||
Optimal GPV sequence: {{Val list| 441, 882, 1323, 2205f, 3528f }} | |||
Badness: 0.029334 | Badness: 0.029334 | ||