Aberschismic family: Difference between revisions
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m Units & 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 = 1200.0000, ~3/2 = 702.7918, ~5/4 = 386.0144 | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.7918{{c}}, ~5/4 = 386.0144{{c}} | ||
[[Minimax tuning]]: c = 5120/5103 | [[Minimax tuning]]: c = 5120/5103 | ||
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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 = 1200.0000, ~3/2 = 702.6411, ~5/4 = 385.4452 | Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.6411{{c}}, ~5/4 = 385.4452{{c}} | ||
{{Optimal ET sequence|legend=0| 12, 29, 41, 53, 94, 99, 140, 152, 292h, 444dh }} | {{Optimal ET sequence|legend=0| 12, 29, 41, 53, 94, 99, 140, 152, 292h, 444dh }} | ||
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: Angle(3/2, 56/55) = 90.4578 degrees | : Angle(3/2, 56/55) = 90.4578 degrees | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 703.2829, ~5/4 = 386.5647 | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.2829{{c}}, ~5/4 = 386.5647{{c}} | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | * [[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 }}] | : [{{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|unchanged-interval (eigenmonzo) 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 = 1200.0000, ~3/2 = 703.4398, ~5/4 = 386.8933 | Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.4398{{c}}, ~5/4 = 386.8933{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 120: | Line 120: | ||
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 = 1200.0000, ~3/2 = 703.5544, ~5/4 = 387.9654 | Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.5544{{c}}, ~5/4 = 387.9654{{c}} | ||
{{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 99ef, 145 }} | {{Optimal ET sequence|legend=0| 29, 41, 46, 58, 87, 99ef, 145 }} | ||
| Line 144: | Line 144: | ||
{{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 = 1200.0000, ~3/2 = 702.5133, ~5/4 = 385.5563 | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.5133{{c}}, ~5/4 = 385.5563{{c}} | ||
[[Minimax tuning]] | [[Minimax tuning]] | ||
* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/3 0 2/21 -1/21 1/21 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 2 0 3/7 2/7 -2/7 }}, {{monzo| 2 0 3/7 -5/7 5/7 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 4/3 0 2/21 -1/21 1/21 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 2 0 3/7 2/7 -2/7 }}, {{monzo| 2 0 3/7 -5/7 5/7 }}] | ||
: [[ | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7 | ||
{{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 }} | ||
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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 = 1200.0000, ~3/2 = 702.4078, ~5/4 = 385.5405 | Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.4078{{c}}, ~5/4 = 385.5405{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 184: | Line 184: | ||
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 = 1200.0000, ~3/2 = 702.4062, ~5/4 = 385.5254 | Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.4062{{c}}, ~5/4 = 385.5254{{c}} | ||
{{Optimal ET sequence|legend=0| 41, 53, 58h, 94, 111, 152f, 415dffhh }}* | {{Optimal ET sequence|legend=0| 41, 53, 58h, 94, 111, 152f, 415dffhh }}* | ||
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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 = 1200.0000{{c}}, ~3/2 = 702.8909{{c}}, ~5/4 = 385.3273{{c}} | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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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 = 1200.0000, ~3/2 = 702.9018, ~5/4 = 385.4158 | Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.9018{{c}}, ~5/4 = 385.4158{{c}} | ||
Minimax tuning: | Minimax tuning: | ||
| Line 262: | Line 262: | ||
{{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 = 1200.0000, ~3/2 = 702.8941, ~5/4 = 388.5932 | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.8941{{c}}, ~5/4 = 388.5932{{c}} | ||
{{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 = 1200.0000, ~3/2 = 702.8670, ~5/4 = 388.6277 | Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.8670{{c}}, ~5/4 = 388.6277{{c}} | ||
{{Optimal ET sequence|legend=0| 46, 53, 58, 99, 104c, 111, 268cd }} | {{Optimal ET sequence|legend=0| 46, 53, 58, 99, 104c, 111, 268cd }} | ||
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{{Mapping|legend=1| 1 0 0 10 7 | 0 1 1 -5 -2 | 0 0 2 2 -1 }} | {{Mapping|legend=1| 1 0 0 10 7 | 0 1 1 -5 -2 | 0 0 2 2 -1 }} | ||
: mapping generators: ~2, ~3, ~128/99 | : mapping generators: ~2, ~3, ~128/99 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 702.8776, ~128/99 = 441.7516 | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.8776{{c}}, ~128/99 = 441.7516{{c}} | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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{{Mapping|legend=1| 1 0 0 10 -6 | 0 2 0 -12 9 | 0 0 1 1 1 }} | {{Mapping|legend=1| 1 0 0 10 -6 | 0 2 0 -12 9 | 0 0 1 1 1 }} | ||
: mapping generators: ~2, ~400/231, ~5 | : mapping generators: ~2, ~400/231, ~5 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~400/231 = 951.4956, ~5/4 = 386.7868 | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~400/231 = 951.4956{{c}}, ~5/4 = 386.7868{{c}} | ||
{{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 = 1200.0000, ~26/15 = 951.4871, ~5/4 = 386.6606 | Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~26/15 = 951.4871{{c}}, ~5/4 = 386.6606{{c}} | ||
{{Optimal ET sequence|legend=0| 29, 53, 58, 87, 111, 140, 198 }} | {{Optimal ET sequence|legend=0| 29, 53, 58, 87, 111, 140, 198 }} | ||
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== Kahoupokane == | == Kahoupokane == | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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{{Mapping|legend=1| 1 0 1 11 2 | 0 1 1 -5 1 | 0 0 -2 -2 -1 }} | {{Mapping|legend=1| 1 0 1 11 2 | 0 1 1 -5 1 | 0 0 -2 -2 -1 }} | ||
: mapping generators: ~2, ~3, ~11/10 | : mapping generators: ~2, ~3, ~11/10 | ||
[[Optimal tuning]] ([[CWE]]): 2, ~3 = 1903.042, ~11/10 = 157.992 | [[Optimal tuning]] ([[CWE]]): ~2 = 1200.000{{c}}, ~3 = 1903.042{{c}}, ~11/10 = 157.992{{c}} | ||
Badness (Sintel): 2.734 | Badness (Sintel): 2.734 | ||
=== 13-limit === | === 13-limit === | ||
[[Subgroup]]: 2.3.5.7.11.13 | [[Subgroup]]: 2.3.5.7.11.13 | ||
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{{Mapping|legend=1| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }} | {{Mapping|legend=1| 1 0 1 11 2 7 | 0 1 1 -5 1 -2 | 0 0 -2 -2 -1 -1 }} | ||
[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000{{c}}, ~3 = 1902.901{{c}}, ~11/10 = 158.166{{c}} | |||
[[Optimal tuning]] ([[CWE]]): 2, ~3 = 1902.901, ~11/10 = 158.166 | |||
Badness (Sintel): 1.269 | Badness (Sintel): 1.269 | ||
== | == References == | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||