Syntonic–kleismic equivalence continuum: Difference between revisions
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== Parakleismic == | == Parakleismic (5-limit) == | ||
{{Main| Parakleismic }} | |||
: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].'' | : ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].'' | ||
The 5-limit version of parakleismic tempers out the [[parakleisma]]. It corresponds to {{nowrap| ''n'' {{=}} 13/2 }}, and 13 generator steps give the interval class of [[3/1|3]]. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Comma list]]: 1224440064/1220703125 | [[Comma list]]: 1224440064/1220703125 | ||
{{Mapping|legend=1| 1 | {{Mapping|legend=1| 1 -8 -8 | 0 13 14 }} | ||
: mapping generators: ~2, ~ | : mapping generators: ~2, ~5/3 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.971{{c}}, ~ | * [[WE]]: ~2 = 1199.971{{c}}, ~5/3 = 884.7383{{c}} | ||
: [[error map]]: {{val| -0.029 -0.127 +0.253 }} | : [[error map]]: {{val| -0.029 -0.127 +0.253 }} | ||
* [[CWE]]: ~2 = 1200.000{{c}}, ~ | * [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 884.8576{{c}} | ||
: error map: {{val| 0.000 -0.106 +0.293 }} | : error map: {{val| 0.000 -0.106 +0.293 }} | ||
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== Counterhanson == | == Counterhanson == | ||
: ''For extensions, see [[Ragismic microtemperaments #Counterkleismic]].'' | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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[[Comma list]]: {{monzo| -20 -24 25 }} | [[Comma list]]: {{monzo| -20 -24 25 }} | ||
{{Mapping|legend=1| 1 -5 -4 | 0 25 | {{Mapping|legend=1| 1 -5 -4 | 0 25 24 }} | ||
: mapping generators: ~2, ~6/5 | |||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.0419{{c}}, ~6/5 = 316.0916{{c}} | |||
: [[error map]]: {{val| +0.042 +0.126 -0.282 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.0021{{c}} | |||
: error map: {{val| 0.000 +0.097 -0.344 }} | |||
{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }} | {{Optimal ET sequence|legend=1| 19, …, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }} | ||
[[Badness]] (Sintel): 7.45 | [[Badness]] (Sintel): 7.45 | ||
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{{Mapping|legend=1| 1 10 12 | 0 -20 -23 }} | {{Mapping|legend=1| 1 10 12 | 0 -20 -23 }} | ||
: mapping generators: ~2, ~78125/52488 | |||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.9478{{c}}, ~78125/52488 = 695.0566{{c}} | |||
: [[error map]]: {{val| -0.052 -0.301 +0.562 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~78125/52488 = 695.0846{{c}} | |||
: error map: {{val| 0.000 -0.264 +0.631 }} | |||
{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }} | {{Optimal ET sequence|legend=1| 19, …, 126, 145, 164, 183, 713, 896c, 1079c, 1262c, 1445c }} | ||
[[Badness]] (Sintel): 8.76 | [[Badness]] (Sintel): 8.76 | ||
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== Mowgli == | == Mowgli == | ||
: ''For extensions, see [[Hemimean clan #Mowglic]].'' | : ''For extensions, see [[Hemimean clan #Mowglic]].'' | ||
[[TE]], [[CTE]] and [[POTE]] coincide at 126.7237{{c}} with pure octaves since prime 2 is not involved in the comma to begin with. | |||
[[Subgroup]]: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
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{{Mapping|legend=1| 1 0 0 | 0 15 22 }} | {{Mapping|legend=1| 1 0 0 | 0 15 22 }} | ||
: mapping generators: ~2, ~27/25 | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2 = 1199.9478{{c}}, ~27/25 = 126.7236{{c}} | ||
: [[error map]]: {{val| -0.001 -1.100 +1.606 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~27/25 = 126.7237{{c}} | |||
: error map: {{val| 0.000 -1.100 +1.607 }} | |||
{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161, 303 }} | {{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161, 303 }} | ||
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{{Mapping|legend=1| 1 -1 6 | 0 7 -10 }} | {{Mapping|legend=1| 1 -1 6 | 0 7 -10 }} | ||
: mapping generators: ~2, ~675/512 | |||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1202.5641{{c}}, ~675/512 = 443.2124{{c}} | |||
: [[error map]]: {{val| +2.564 -2.033 -3.053 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~675/512 = 442.2692{{c}} | |||
: error map: {{val| 0.000 -6.071 -9.006 }} | |||
{{Optimal ET sequence|legend=1| 8c, 11, 19 }} | {{Optimal ET sequence|legend=1| 8c, 11, 19 }} | ||
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[[Comma list]]: {{monzo| -134 -185 184 }} | [[Comma list]]: {{monzo| -134 -185 184 }} | ||
{{Mapping|legend=1| 1 | {{Mapping|legend=1| 1 -134 -134 | 0 184 185 }} | ||
: mapping generators: ~2, ~5/3 | |||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.0094{{c}}, ~5/3 = 884.2568{{c}} | |||
: [[error map]]: {{val| +0.009 +0.033 -0.069 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 884.2499{{c}} | |||
: error map: {{val| 0.000 +0.026 -0.083 }} | |||
{{Optimal ET sequence|legend=1| 19, …, 1600, 3219, 4819 }} | {{Optimal ET sequence|legend=1| 19, …, 1600, 3219, 4819 }} | ||
[[Badness]] (Sintel): | [[Badness]] (Sintel): 751 | ||
[[Category:19edo]] | [[Category:19edo]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||