Hemifamity family: Difference between revisions
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+link to pele; optimal tunings |
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: 3/2 length = 0.5670, 10/9 length = 1.8063 | : 3/2 length = 0.5670, 10/9 length = 1.8063 | ||
: Angle (3/2, 10/9) = 82.112 degrees | : Angle (3/2, 10/9) = 82.112 degrees | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.7918, ~5/4 = 386.0144 | |||
[[Minimax tuning]]: c = 5120/5103 | [[Minimax tuning]]: c = 5120/5103 | ||
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== Pele == | == Pele == | ||
{{Main| Pele }} | |||
{{See also| Pentacircle clan }} | {{See also| Pentacircle clan }} | ||
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{{Mapping|legend=1| 1 0 0 10 17 | 0 1 0 -6 -10 | 0 0 1 1 1 }} | {{Mapping|legend=1| 1 0 0 10 17 | 0 1 0 -6 -10 | 0 0 1 1 1 }} | ||
[[Mapping to lattice]]: [{{val| 0 1 4 -2 -6 }}, {{val| 0 0 -1 -1 -1 }}] | [[Mapping to lattice]]: [{{val| 0 1 4 -2 -6 }}, {{val| 0 0 -1 -1 -1 }}] | ||
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: 3/2 length = 0.3812, 56/55 length = 1.5893 | : 3/2 length = 0.3812, 56/55 length = 1.5893 | ||
: Angle(3/2, 56/55) = 90.4578 degrees | : Angle(3/2, 56/55) = 90.4578 degrees | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 703.2829, ~5/4 = 386.5647 | |||
[[Minimax tuning]]: | |||
* [[11-odd-limit]] | |||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 17/10 0 1/10 0 -1/10 }}, {{monzo| 17/5 -2 6/5 0 -1/5 }}, {{monzo| 16/5 -2 3/5 0 2/5 }}, {{monzo| 17/5 -2 1/5 0 4/5 }}] | |||
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.11/9 | |||
{{Optimal ET sequence|legend=1| 29, 41, 58, 87, 99e, 145, 186e }} | {{Optimal ET sequence|legend=1| 29, 41, 58, 87, 99e, 145, 186e }} | ||
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Mapping: {{mapping| 1 0 0 10 17 22 | 0 1 0 -6 -10 -13 | 0 0 1 1 1 1 }} | Mapping: {{mapping| 1 0 0 10 17 22 | 0 1 0 -6 -10 -13 | 0 0 1 1 1 1 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 703.4398, ~5/4 = 386.8933 | |||
Minimax tuning: | Minimax tuning: | ||
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{{Mapping|legend=1| 1 0 0 10 -18 | 0 1 0 -6 15 | 0 0 1 1 -1 }} | {{Mapping|legend=1| 1 0 0 10 -18 | 0 1 0 -6 15 | 0 0 1 1 -1 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.5133, ~5/4 = 385.5563 | |||
[[Minimax tuning]] | [[Minimax tuning]] | ||
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Mapping: {{mapping| 1 0 0 10 -18 -13 | 0 1 0 -6 15 12 | 0 0 1 1 -1 -1 }} | Mapping: {{mapping| 1 0 0 10 -18 -13 | 0 1 0 -6 15 12 | 0 0 1 1 -1 -1 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.4078, ~5/4 = 385.5405 | |||
Minimax tuning: | Minimax tuning: | ||
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: mapping generators: ~2, ~3, ~5 | : mapping generators: ~2, ~3, ~5 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.8909, ~5/4 = 385.3273 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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Mapping: {{mapping| 1 0 0 10 -3 2 | 0 1 0 -6 7 4 | 0 0 1 1 -2 -2 }} | Mapping: {{mapping| 1 0 0 10 -3 2 | 0 1 0 -6 7 4 | 0 0 1 1 -2 -2 }} | ||
Lattice basis: | Lattice basis: | ||
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Mapping to lattice: [{{val| 0 1 3 -3 1 -2 }}, {{val| 0 0 -1 -1 2 2 }}] | Mapping to lattice: [{{val| 0 1 3 -3 1 -2 }}, {{val| 0 0 -1 -1 2 2 }}] | ||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.9018, ~5/4 = 385.4158 | |||
Minimax tuning: | |||
* 13- and 15-odd-limit | |||
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 0 0 }}, {{monzo| 26/9 0 13/18 -7/18 -1/3 0 }}, {{monzo| 26/9 0 -5/18 11/18 -1/3 0 }}, {{monzo| 26/9 0 -5/18 -7/18 2/3 0 }}, {{monzo| 26/9 0 -7/9 1/9 2/3 0 }}] | |||
: eigenmonzo (unchanged-interval) basis: 2.7/5.11/5 | |||
{{Optimal ET sequence|legend=1| 34, 41, 46, 53, 87, 140, 321, 461e }} | {{Optimal ET sequence|legend=1| 34, 41, 46, 53, 87, 140, 321, 461e }} | ||
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{{Mapping|legend=1| 1 0 0 10 6 | 0 1 0 -6 -6 | 0 0 1 1 3 }} | {{Mapping|legend=1| 1 0 0 10 6 | 0 1 0 -6 -6 | 0 0 1 1 3 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.8941, ~5/4 = 388.5932 | |||
{{Optimal ET sequence|legend=1| 46, 53, 58, 99, 111, 268cd }} | {{Optimal ET sequence|legend=1| 46, 53, 58, 99, 111, 268cd }} | ||
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Mapping: {{mapping| 1 0 0 10 6 11 | 0 1 0 -6 -6 -9 | 0 0 1 1 3 3 }} | Mapping: {{mapping| 1 0 0 10 6 11 | 0 1 0 -6 -6 -9 | 0 0 1 1 3 3 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.8670, ~5/4 = 388.6277 | |||
{{Optimal ET sequence|legend=1| 46, 53, 58, 99, 104c, 111, 268cd }} | {{Optimal ET sequence|legend=1| 46, 53, 58, 99, 104c, 111, 268cd }} | ||
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: mapping generators: ~2, ~3, ~128/99 | : mapping generators: ~2, ~3, ~128/99 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.8776, ~128/99 = 441.7516 | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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: mapping generators: ~2, ~400/231, ~5 | : mapping generators: ~2, ~400/231, ~5 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~400/231 = 951.4956, ~5/4 = 386.7868 | |||
{{Optimal ET sequence|legend=1| 29, 53, 58, 87, 111, 140, 198 }} | {{Optimal ET sequence|legend=1| 29, 53, 58, 87, 111, 140, 198 }} | ||
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Mapping: {{mapping| 1 0 0 10 -6 -1 | 0 2 0 -12 9 3 | 0 0 1 1 1 1 }} | Mapping: {{mapping| 1 0 0 10 -6 -1 | 0 2 0 -12 9 3 | 0 0 1 1 1 1 }} | ||
Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 951.4871, ~5/4 = 386.6606 | |||
{{Optimal ET sequence|legend=1| 29, 53, 58, 87, 111, 140, 198 }} | {{Optimal ET sequence|legend=1| 29, 53, 58, 87, 111, 140, 198 }} | ||