Syntonic–diatonic equivalence continuum: Difference between revisions
Move 5-limit uncle here |
Sorting (by ploidacot!); unify to 3 decimal places; note the badness metric being used |
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== Uncle == | == Uncle (5-limit) == | ||
: ''For extensions, see [[Trienstonic clan #Uncle]].'' | : ''For extensions, see [[Trienstonic clan #Uncle]].'' | ||
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* Dirichlet: 6.33 | * Dirichlet: 6.33 | ||
== | == Ultrapyth (5-limit) == | ||
: ''For extensions, see [[Archytas clan #Ultrapyth]].'' | : ''For extensions, see [[Archytas clan #Ultrapyth]].'' | ||
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[[Comma list]]: 5242880/4782969 | [[Comma list]]: 5242880/4782969 | ||
{{Mapping|legend=1| 1 0 -20 | 0 | {{Mapping|legend=1| 1 0 -20 | 0 1 14 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[POTE]]: ~2 = 1200. | * [[POTE]]: ~2 = 1200.000, ~3/2 = 713.829 | ||
{{Optimal ET sequence|legend=1| 5, 27c, 32, 37, 79bc, 116bbc }} | {{Optimal ET sequence|legend=1| 5, 27c, 32, 37, 79bc, 116bbc }} | ||
[[Badness]]: 0.795243 | [[Badness]] (Smith): 0.795243 | ||
== Trisatriyo (5 & 56) == | == Trisatriyo (5 & 56) == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[POTE]]: ~2 = 1200. | * [[POTE]]: ~2 = 1200.000, ~2560/2187 = 235.867 | ||
{{Optimal ET sequence|legend=1| 5, …, 51, 56, 117b, 173b }} | {{Optimal ET sequence|legend=1| 5, …, 51, 56, 117b, 173b }} | ||
[[Badness]]: 1.323443 | [[Badness]] (Smith): 1.323443 | ||
[http://x31eq.com/cgi-bin/rt.cgi?ets=5_56&limit=5 The temperament finder - 5-limit 5 & 56] | [http://x31eq.com/cgi-bin/rt.cgi?ets=5_56&limit=5 The temperament finder - 5-limit 5 & 56] | ||
== Hemiseven (5-limit) == | |||
: ''For extensions, see [[Gamelismic clan #Hemiseven]].'' | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| 32 -29 6 }} | |||
{{Mapping|legend=1| 1 4 14 | 0 -6 -29 }} | |||
: mapping generators: ~2, ~320/243 | |||
[[Optimal tuning]]s: | |||
* [[POTE]]: ~2 = 1200.000, ~320/243 = 483.247 | |||
{{Optimal ET sequence|legend=1| 5, 62c, 67c, 72, 149, 221, 370, 591b, 961bb }} | |||
[[Badness]] (Smith): 0.720465 | |||
== Counterpental == | == Counterpental == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[POTE]]: ~ | * [[POTE]]: ~729/640 = 240.000, ~3/2 = 704.572 | ||
{{Optimal ET sequence|legend=1| 5, …, 75, 80, 155, 390b, 545bbc }} | {{Optimal ET sequence|legend=1| 5, …, 75, 80, 155, 390b, 545bbc }} | ||
[[Badness]]: 1.500224 | [[Badness]] (Smith): 1.500224 | ||
== Septiquarter == | == Septiquarter (5-limit) == | ||
: ''For extensions, see [[Hemifamity temperaments #Septiquarter]].'' | : ''For extensions, see [[Hemifamity temperaments #Septiquarter]].'' | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[POTE]]: ~2 = 1200. | * [[POTE]]: ~2 = 1200.000, ~204800/177147 = 242.457 | ||
{{Optimal ET sequence|legend=1| 5, 89c, 94, 99, 193, 292, 391 }} | {{Optimal ET sequence|legend=1| 5, 89c, 94, 99, 193, 292, 391 }} | ||
[[Badness]]: 0.971284 | [[Badness]] (Smith): 0.971284 | ||
== Quinla-tritrigu (5 & 118) == | == Quinla-tritrigu (5 & 118) == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[POTE]]: ~2 = 1200. | * [[POTE]]: ~2 = 1200.000, ~320/243 = 477.961 | ||
{{Optimal ET sequence|legend=1| 5, 108c, 113, 118, 1057, 1175, 1293, 1411, 1529, 1647, 1765, 1883, 2001b, 3884b }} | {{Optimal ET sequence|legend=1| 5, 108c, 113, 118, 1057, 1175, 1293, 1411, 1529, 1647, 1765, 1883, 2001b, 3884b }} | ||
[[Badness]]: 0.617683 | [[Badness]] (Smith): 0.617683 | ||
== Tribilalegu (5 & 137) == | == Tribilalegu (5 & 137) == | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[POTE]]: ~2 = 1200. | * [[POTE]]: ~2 = 1200.000, ~320/243 = 481.742 | ||
{{Optimal ET sequence|legend=1| 5, 127c, 132, 137, 553, 690b, 827b, 964b }} | {{Optimal ET sequence|legend=1| 5, 127c, 132, 137, 553, 690b, 827b, 964b }} | ||
[[Badness]]: 3.620981 | [[Badness]] (Smith): 3.620981 | ||
[http://x31eq.com/cgi-bin/rt.cgi?ets=5_137&limit=5 The temperament finder - 5-limit 5 & 137] | [http://x31eq.com/cgi-bin/rt.cgi?ets=5_137&limit=5 The temperament finder - 5-limit 5 & 137] | ||
== 559 & 2513 == | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| -124 109 -21 }} | |||
{{Mapping|legend=1| 1 10 46 | 0 -21 -109 }} | |||
: mapping generators: ~2, ~3355443200000/2541865828329 | |||
[[Optimal tuning]]s: | |||
* [[POTE]]: ~2 = 1200.0000, ~3355443200000/2541865828329 = 480.8595 | |||
{{Optimal ET sequence|legend=1| 5, 267c, 272c, 277, 559, 1395, 1954, 2513, 40767, 43280, 45793, 48306, 50819, 53332, 55845, 58358, 60871, 63384, 65897, 68410, 70923, 73436, 75949, 78462 }} | |||
[[Badness]] (Smith): 0.134523 | |||
[http://x31eq.com/cgi-bin/rt.cgi?ets=2513_559&limit=5 The temperament finder - 5-limit 2513 & 559] | |||
[[Category:5edo]] | [[Category:5edo]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||