Very high accuracy temperaments: Difference between revisions
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= Rank-2 temperaments = | = Rank-2 temperaments = | ||
== Kwazy == | == Kwazy == | ||
Kwazy ({{nowrap| 118 & 612 }}) tempers out the [[kwazy comma]], {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[marvel temperaments #Gwazy|gwazy]], | Kwazy ({{nowrap| 118 & 612 }}) tempers out the [[kwazy comma]], {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[marvel temperaments #Gwazy|gwazy]], [[hemimage temperaments #Bisupermajor|bisupermajor]], and [[ragismic microtemperaments #Crazy|crazy]]. | ||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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{{Mapping|legend=1| 2 1 6 | 0 8 -5 }} | {{Mapping|legend=1| 2 1 6 | 0 8 -5 }} | ||
: mapping generators: ~94921875/67108864, ~1125/1024 | : mapping generators: ~94921875/67108864, ~1125/1024 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~94921875/67108864 = 600.000000{{c}}, ~1125/1024 = 162.743279{{c}} | * [[WE]]: ~94921875/67108864 = 600.003398{{c}}, ~1125/1024 = 162.743548{{c}} | ||
* [[POTE]]: ~94921875/67108864 = 600.000000{{c}}, ~1125/1024 = 162.742626{{c}} | : [[error map]]: {{val| +0.0068 -0.0032 -0.0111 }} | ||
* [[CWE]]: ~94921875/67108864 = 600.000000{{c}}, ~1125/1024 = 162.742801{{c}} | |||
: error map: {{val| 0.0000 -0.0126 -0.0277 }} | |||
<!-- * [[CTE]]: ~94921875/67108864 = 600.000000{{c}}, ~1125/1024 = 162.743279{{c}} | |||
* [[POTE]]: ~94921875/67108864 = 600.000000{{c}}, ~1125/1024 = 162.742626{{c}} --> | |||
{{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }} | {{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }} | ||
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[[Comma list]]: {{monzo| 91 -12 -31 }} | [[Comma list]]: {{monzo| 91 -12 -31 }} | ||
{{Mapping|legend=1| 1 | {{Mapping|legend=1| 1 -26 13 | 0 31 -12 }} | ||
: mapping generators: ~2, ~{{monzo| 39 -5 -13 }} | |||
: mapping generators: ~2, ~{{monzo| - | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| - | * [[WE]]: ~2 = 1199.994636{{c}}, ~{{monzo| 39 -5 -13 }} = 1067.800558{{c}} | ||
* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| - | : [[error map]]: {{val| -0.0054 +0.0018 +0.0099 }} | ||
* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 39 -5 -13 }} = 1067.805278{{c}} | |||
: error map: {{val| 0.0000 +0.0086 +0.0230 }} | |||
<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 39 -5 -13 }} = 1067.805146{{c}} | |||
* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 39 -5 -13 }} = 1067.805332{{c}} --> | |||
{{Optimal ET sequence|legend=1| 9, …, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }} | {{Optimal ET sequence|legend=1| 9, …, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }} | ||
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[[Comma list]]: {{monzo| -70 72 -19 }} | [[Comma list]]: {{monzo| -70 72 -19 }} | ||
{{Mapping|legend=1| 1 | {{Mapping|legend=1| 1 -8 -34 | 0 19 72 }} | ||
: mapping generators: ~2, ~{{monzo| -18 19 -5 }} | |||
: mapping generators: ~2, ~{{monzo| 19 - | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 19 - | * [[WE]]: ~2 = 1200.002817{{c}}, ~{{monzo| -18 19 -5 }} = 605.366856{{c}} | ||
* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| 19 - | : [[error map]]: {{val| +0.0028 -0.0073 +0.0041 }} | ||
* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo| -18 19 -5 }} = 605.365482{{c}} | |||
: error map: {{val| 0.0000 -0.0108 +0.0010 }} | |||
<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| -18 19 -5 }} = 605.365544{{c}} | |||
* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo| -18 19 -5 }} = 605.365435{{c}} --> | |||
{{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }} | {{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }} | ||
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[[Comma list]]: {{monzo| 37 25 -33 }} | [[Comma list]]: {{monzo| 37 25 -33 }} | ||
{{Mapping|legend=1| 1 | {{Mapping|legend=1| 1 -16 -11 | 0 33 25 }} | ||
: mapping generators: ~2, ~625/432 | |||
: mapping generators: ~2, ~ | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000000{{c}}, ~ | * [[WE]]: ~2 = 1199.997806{{c}}, ~625/432 = 639.452005{{c}} | ||
* [[POTE]]: ~2 = 1200.000000{{c}}, ~ | : [[error map]]: {{val| -0.0022 -0.0037 +0.0106 }} | ||
* [[CWE]]: ~2 = 1200.000000{{c}}, ~625/432 = 639.453117{{c}} | |||
: error map: {{val| 0.0000 -0.0022 +0.0142 }} | |||
<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~625/432 = 639.453048{{c}} | |||
* [[POTE]]: ~2 = 1200.000000{{c}}, ~625/432 = 639.453174{{c}} --> | |||
{{Optimal ET sequence|legend=1| 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }} | {{Optimal ET sequence|legend=1| 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }} | ||
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{{Mapping|legend=1| 1 0 -27 | 0 2 37 }} | {{Mapping|legend=1| 1 0 -27 | 0 2 37 }} | ||
: mapping generators: ~2, ~{{monzo| 27 -18 1 }} | : mapping generators: ~2, ~{{monzo| 27 -18 1 }} | ||
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{{Mapping|legend=1| 1 15 16 | 0 -51 -52 }} | {{Mapping|legend=1| 1 15 16 | 0 -51 -52 }} | ||
: mapping generators: ~2, ~6/5 | : mapping generators: ~2, ~6/5 | ||
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{{Mapping|legend=1| 1 13 -36 | 0 -14 47 }} | {{Mapping|legend=1| 1 13 -36 | 0 -14 47 }} | ||
: mapping generators: ~2, 7381125/4194304 | : mapping generators: ~2, 7381125/4194304 | ||
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{{Mapping|legend=1| 1 11 19 | 0 -35 -62 }} | {{Mapping|legend=1| 1 11 19 | 0 -35 -62 }} | ||
: mapping generators: ~2, ~{{monzo| -6 23 -13 }} | : mapping generators: ~2, ~{{monzo| -6 23 -13 }} | ||
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{{Mapping|legend=1| 1 45 -18 | 0 -47 22 }} | {{Mapping|legend=1| 1 45 -18 | 0 -47 22 }} | ||
: mapping generators: ~2, ~{{monzo| -45 7 15 }} | : mapping generators: ~2, ~{{monzo| -45 7 15 }} | ||
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{{Mapping|legend=1| 1 0 -554 | 0 1 351 }} | {{Mapping|legend=1| 1 0 -554 | 0 1 351 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
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{{Mapping|legend=1| 1 0 500 | 0 1 -314 }} | {{Mapping|legend=1| 1 0 500 | 0 1 -314 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
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{{Mapping|legend=1| 1 28 73 | 0 -37 -99 }} | {{Mapping|legend=1| 1 28 73 | 0 -37 -99 }} | ||
: mapping generators: ~2, ~6561/4000 | : mapping generators: ~2, ~6561/4000 | ||
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{{Mapping|legend=1| 1 43 15 | 0 -49 -15 }} | {{Mapping|legend=1| 1 43 15 | 0 -49 -15 }} | ||
: Mapping generators: ~2, ~{{monzo| -23 -4 13 }} | : Mapping generators: ~2, ~{{monzo| -23 -4 13 }} | ||
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{{Mapping|legend=1| 12 0 161 | 0 1 -7 }} | {{Mapping|legend=1| 12 0 161 | 0 1 -7 }} | ||
: mapping generators: ~{{monzo| -67 35 5 }}, ~3 | : mapping generators: ~{{monzo| -67 35 5 }}, ~3 | ||
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{{Mapping|legend=2| 1 12 5 | 0 -19 -4 }} | {{Mapping|legend=2| 1 12 5 | 0 -19 -4 }} | ||
: mapping generators: ~2, ~24576/16807 | : mapping generators: ~2, ~24576/16807 | ||
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{{Mapping|legend=2| 1 0 109 | 0 1 -67 }} | {{Mapping|legend=2| 1 0 109 | 0 1 -67 }} | ||
: mapping generators: ~2, ~3 | |||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||