Hemifamity family: Difference between revisions
m Style |
m Spell 1\1 in decimal, note the badness metric being used, and misc. cleanup |
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: Angle (3/2, 10/9) = 82.112 degrees | : Angle (3/2, 10/9) = 82.112 degrees | ||
[[Optimal tuning]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 702.7918, ~5/4 = 386.0144 | ||
[[Minimax tuning]]: c = 5120/5103 | [[Minimax tuning]]: c = 5120/5103 | ||
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{{Optimal ET sequence|legend=1| 41, 53, 87, 94, 99, 239, 251, 292, 391, 881bd, 1272bcdd }} | {{Optimal ET sequence|legend=1| 41, 53, 87, 94, 99, 239, 251, 292, 391, 881bd, 1272bcdd }} | ||
[[Badness]]: 0.153 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.153 × 10<sup>-3</sup> | ||
[[Projection pair]]s: 7 5120/729 | [[Projection pair]]s: 7 5120/729 | ||
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Mapping: {{mapping| 1 0 0 10 -6 | 0 1 0 -6 5 | 0 0 1 1 1 }} | Mapping: {{mapping| 1 0 0 10 -6 | 0 1 0 -6 5 | 0 0 1 1 1 }} | ||
Optimal tuning (CTE): ~2 = | Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 702.6411, ~5/4 = 385.4452 | ||
{{Optimal ET sequence|legend=0| 12, 29, 41, 53, 94, 99, 140, 152, 292h, 444dh }} | |||
Badness: 0.212 × 10<sup>-3</sup> | Badness (Smith): 0.212 × 10<sup>-3</sup> | ||
== Pele == | == Pele == | ||
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: Angle(3/2, 56/55) = 90.4578 degrees | : Angle(3/2, 56/55) = 90.4578 degrees | ||
[[Optimal tuning]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 703.2829, ~5/4 = 386.5647 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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{{Optimal ET sequence|legend=1| 29, 41, 58, 87, 99e, 145, 186e }} | {{Optimal ET sequence|legend=1| 29, 41, 58, 87, 99e, 145, 186e }} | ||
[[Badness]]: 0.648 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.648 × 10<sup>-3</sup> | ||
[[Projection pair]]s: 7 5120/729 11 655360/59049 | [[Projection pair]]s: 7 5120/729 11 655360/59049 | ||
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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 = | Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 703.4398, ~5/4 = 386.8933 | ||
Minimax tuning: | Minimax tuning: | ||
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* 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.13/9 | * 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.13/9 | ||
{{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 145, 232 }} | |||
Badness: 0.703 × 10<sup>-3</sup> | Badness (Smith): 0.703 × 10<sup>-3</sup> | ||
=== 17-limit === | === 17-limit === | ||
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Mapping: {{mapping| 1 0 0 10 17 22 8 | 0 1 0 -6 -10 -13 -1 | 0 0 1 1 1 1 -1 }} | Mapping: {{mapping| 1 0 0 10 17 22 8 | 0 1 0 -6 -10 -13 -1 | 0 0 1 1 1 1 -1 }} | ||
Optimal tuning (CTE): ~2 = | Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 703.5544, ~5/4 = 387.9654 | ||
{{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 99ef, 145 }} | |||
Badness: 0.930 × 10<sup>-3</sup> | Badness (Smith): 0.930 × 10<sup>-3</sup> | ||
== Laka == | == Laka == | ||
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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 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 702.5133, ~5/4 = 385.5563 | ||
[[Minimax tuning]] | [[Minimax tuning]] | ||
| Line 142: | Line 142: | ||
{{Optimal ET sequence|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }} | {{Optimal ET sequence|legend=1| 41, 53, 58, 94, 99e, 152, 497de, 555dee, 707ddee, 859bddee }} | ||
[[Badness]]: 0.825 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.825 × 10<sup>-3</sup> | ||
[[Projection pair]]s: 5120/729 11 14348907/1310720 | [[Projection pair]]s: 5120/729 11 14348907/1310720 | ||
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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 = | Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 702.4078, ~5/4 = 385.5405 | ||
Minimax tuning: | Minimax tuning: | ||
| Line 160: | Line 160: | ||
: eigenmonzo (unchanged-interval) basis: 2.11.13/7 | : eigenmonzo (unchanged-interval) basis: 2.11.13/7 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 41, 53, 58, 94, 111, 152f, 415dff }}* | ||
<nowiki>*</nowiki> optimal patent val: [[205edo|205]] | <nowiki>*</nowiki> optimal patent val: [[205edo|205]] | ||
Badness: 0.822 × 10<sup>-3</sup> | Badness (Smith): 0.822 × 10<sup>-3</sup> | ||
=== 2.3.5.7.11.13.19 subgroup === | === 2.3.5.7.11.13.19 subgroup === | ||
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Mapping: {{mapping| 1 0 0 10 -18 -13 -6 | 0 1 0 -6 15 12 5 | 0 0 1 1 -1 -1 1 }} | Mapping: {{mapping| 1 0 0 10 -18 -13 -6 | 0 1 0 -6 15 12 5 | 0 0 1 1 -1 -1 1 }} | ||
Optimal tuning (CTE): ~2 = | Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 702.4062, ~5/4 = 385.5254 | ||
{{Optimal ET sequence|legend=0| 41, 53, 58h, 94, 111, 152f, 415dffhh }}* | |||
<nowiki>*</nowiki> optimal patent val: [[205edo|205]] | <nowiki>*</nowiki> optimal patent val: [[205edo|205]] | ||
Badness: 0.661 × 10<sup>-3</sup> | Badness (Smith): 0.661 × 10<sup>-3</sup> | ||
=== 17-limit === | === 17-limit === | ||
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: eigenmonzo (unchanged-interval) basis: 2.11.13/7 | : eigenmonzo (unchanged-interval) basis: 2.11.13/7 | ||
{{Optimal ET sequence|legend=0| 58, 94, 111, 152f, 205, 263df }} | |||
Badness: 1.19 × 10<sup>-3</sup> | Badness (Smith): 1.19 × 10<sup>-3</sup> | ||
== Akea == | == Akea == | ||
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{{Mapping|legend=1| 1 0 0 10 -3 | 0 1 0 -6 7 | 0 0 1 1 -2 }} | {{Mapping|legend=1| 1 0 0 10 -3 | 0 1 0 -6 7 | 0 0 1 1 -2 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 702.8909, ~5/4 = 385.3273 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
| Line 218: | Line 216: | ||
{{Optimal ET sequence|legend=1| 34, 41, 53, 87, 140, 181, 321 }} | {{Optimal ET sequence|legend=1| 34, 41, 53, 87, 140, 181, 321 }} | ||
[[Badness]]: 0.998 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.998 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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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 = | Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 702.9018, ~5/4 = 385.4158 | ||
Minimax tuning: | Minimax tuning: | ||
| Line 240: | Line 238: | ||
: eigenmonzo (unchanged-interval) basis: 2.7/5.11/5 | : eigenmonzo (unchanged-interval) basis: 2.7/5.11/5 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 34, 41, 46, 53, 87, 140, 321, 461e }} | ||
Badness: 0.822 × 10<sup>-3</sup> | Badness (Smith): 0.822 × 10<sup>-3</sup> | ||
Scales: [[akea46_13]] | Scales: [[akea46_13]] | ||
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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 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~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 }} | ||
[[Badness]]: 1.18 × 10<sup>-3</sup> | [[Badness]] (Smith): 1.18 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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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 = | Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 702.8670, ~5/4 = 388.6277 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 46, 53, 58, 99, 104c, 111, 268cd }} | ||
Badness: 0.908 × 10<sup>-3</sup> | Badness (Smith): 0.908 × 10<sup>-3</sup> | ||
== Kapo == | == Kapo == | ||
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: mapping generators: ~2, ~3, ~128/99 | : mapping generators: ~2, ~3, ~128/99 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 702.8776, ~128/99 = 441.7516 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
| Line 290: | Line 288: | ||
{{Optimal ET sequence|legend=1| 41, 87, 111, 152, 239, 391 }} | {{Optimal ET sequence|legend=1| 41, 87, 111, 152, 239, 391 }} | ||
[[Badness]]: 0.994 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.994 × 10<sup>-3</sup> | ||
== Namaka == | == Namaka == | ||
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: mapping generators: ~2, ~400/231, ~5 | : mapping generators: ~2, ~400/231, ~5 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~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 }} | ||
[[Badness]]: 1.74 × 10<sup>-3</sup> | [[Badness]] (Smith): 1.74 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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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 = | Optimal tuning (CTE): ~2 = 1200.0000, ~26/15 = 951.4871, ~5/4 = 386.6606 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 29, 53, 58, 87, 111, 140, 198 }} | ||
Badness: 0.781 × 10<sup>-3</sup> | Badness (Smith): 0.781 × 10<sup>-3</sup> | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||