Smate family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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== Smate == | == Smate == | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
[[Comma list]]: 2048/1875 | [[Comma list]]: 2048/1875 | ||
{{Mapping|legend=1| 1 3 2 | 0 -4 1 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 420.855 | ||
{{Optimal ET sequence|legend=1| 3, 11, 14, 17c, 20c, 37c }} | {{Optimal ET sequence|legend=1| 3, 11, 14, 17c, 20c, 37c }} | ||
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== Septimal smate == | == Septimal smate == | ||
{{ | {{See also| Mint temperaments #Smate }} | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 36/35, 2048/1875 | [[Comma list]]: 36/35, 2048/1875 | ||
{{Mapping|legend=1| 1 3 2 6 | 0 -4 1 -9 }} | |||
{{Multival|legend=1| 4 -1 9 -11 3 24 }} | {{Multival|legend=1| 4 -1 9 -11 3 24 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 422.275 | ||
{{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, | {{Optimal ET sequence|legend=1| 3d, 11d, 14, 17c, 37ccdd }} | ||
[[Badness]]: 0.077871 | [[Badness]]: 0.077871 | ||
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Comma list: 36/35, 56/55, 243/242 | Comma list: 36/35, 56/55, 243/242 | ||
Mapping: | Mapping: {{mapping| 1 3 2 6 7 | 0 -4 1 -9 -10 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 422.217 | ||
{{Optimal ET sequence|legend=1| 14, 17c, | {{Optimal ET sequence|legend=1| 3de, 14, 17c, 37ccddee }} | ||
Badness: 0.042518 | Badness: 0.042518 | ||
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Comma list: 26/25, 36/35, 56/55, 243/242 | Comma list: 26/25, 36/35, 56/55, 243/242 | ||
Mapping: | Mapping: {{mapping| 1 3 2 6 7 3 | 0 -4 1 -9 -10 2 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 423.020 | ||
{{Optimal ET sequence|legend=1| 14, 17c }} | {{Optimal ET sequence|legend=1| 3de, 14, 17c }} | ||
Badness: 0.036836 | Badness: 0.036836 | ||
== Hemismate == | == Hemismate == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 256/245, 392/375 | [[Comma list]]: 256/245, 392/375 | ||
{{Mapping|legend=1| 1 3 2 3 | 0 -8 2 -1 }} | |||
{{Multival|legend=1| 8 -2 1 -22 -21 8 }} | {{Multival|legend=1| 8 -2 1 -22 -21 8 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 210.452 | ||
{{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcd }} | {{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcd }} | ||
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Comma list: 56/55, 77/75, 256/245 | Comma list: 56/55, 77/75, 256/245 | ||
Mapping: | Mapping: {{mapping| 1 3 2 3 4 | 0 -8 2 -1 -3 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 210.481 | ||
{{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcde }} | {{Optimal ET sequence|legend=1| 6, 11, 17c, 40bcde }} | ||
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Comma list: 26/25, 56/55, 77/75, 256/245 | Comma list: 26/25, 56/55, 77/75, 256/245 | ||
Mapping: | Mapping: {{mapping| 1 3 2 3 4 3 | 0 -8 2 -1 -3 4 }} | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 210.974 | ||
{{Optimal ET sequence|legend=1| 6, 11, 17c }} | {{Optimal ET sequence|legend=1| 6, 11, 17c }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Smate]] | [[Category:Smate family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||