Schismic–Mercator equivalence continuum: Difference between revisions
Move submajor here. -mercator (addressed in mercator family) |
m Some cleanup |
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Counterschismic is much like [[schismic]], but the harmonic 5 is located at +45 fifths instead of schismic's -8. They unite in [[53edo]], of course. | Counterschismic is much like [[schismic]], but the harmonic 5 is located at +45 fifths instead of schismic's -8. They unite in [[53edo]], of course. | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
Comma list: {{monzo| -69 45 -1 }} | [[Comma list]]: {{monzo| -69 45 -1 }} | ||
{{Mapping|legend=1| 1 2 21 | 0 -1 -45 }} | |||
{{Multival|legend=1| 1 45 69 }} | {{Multival|legend=1| 1 45 69 }} | ||
Optimal tuning (CTE): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9175 | ||
{{Optimal ET sequence|legend=1| 53, 412, 465, 518, 571, 624, 677, 730, 2973, 3703, 4433, 5163, 11056}} | {{Optimal ET sequence|legend=1| 53, 412, 465, 518, 571, 624, 677, 730, 2973, 3703, 4433, 5163, 11056}} | ||
Badness: 0.09123 | [[Badness]] (Smith): 0.09123 | ||
== Submajor == | == Submajor == | ||
| Line 159: | Line 159: | ||
{{Mapping|legend=1| 1 4 -1 | 0 -8 11 }} | {{Mapping|legend=1| 1 4 -1 | 0 -8 11 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000, ~10125/8192 = 362.321 | ||
{{Optimal ET sequence|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }} | {{Optimal ET sequence|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }} | ||
[[Badness]]: 0.130236 | [[Badness]] (Smith): 0.130236 | ||
== Countritonic == | == Countritonic == | ||
: ''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].'' | : ''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].'' | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
Comma list: {{monzo| 33 -34 9 }} | [[Comma list[[: {{monzo| 33 -34 9 }} | ||
{{Mapping|legend=1| 1 6 19 | 0 -9 -34 }} | |||
Optimal tuning (CTE): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~14348907/10240000 = 588.636 | ||
{{Optimal ET sequence|legend=1| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }} | {{Optimal ET sequence|legend=1| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }} | ||
Badness: 0.256 | [[Badness]] (Smith): 0.256 | ||
== 53 & 3684 == | == 53 & 3684 == | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
Comma list: {{monzo| -339 230 -11 }} | [[Comma list]]: {{monzo| -339 230 -11 }} | ||
{{Mapping|legend=1| 1 2 11 | 0 -11 -230 }} | |||
{{Multival|legend=1| 11 230 339 }} | {{Multival|legend=1| 11 230 339 }} | ||
Optimal tuning (CTE): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~10737418240/10460353203 = 45.2769 | ||
{{Optimal ET sequence|legend=1| 53, 3684, 11105 }} | {{Optimal ET sequence|legend=1| 53, 3684, 11105 }} | ||
Badness: 0.276036 | [[Badness]] (Smith): 0.276036 | ||
== 53 & 4190 == | == 53 & 4190 == | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
Comma list: {{monzo| 393 -267 13 }} | [[Comma list]]: {{monzo| 393 -267 13 }} | ||
{{Mapping|legend=1| 1 6 93 | 0 -13 -267 }} | |||
{{Multival|legend=1| 13 267 393 }} | {{Multival|legend=1| 13 267 393 }} | ||
Optimal tuning (CTE): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~{{monzo| -60 41 -2 }} = 407.5419 | ||
{{Optimal ET sequence|legend=1| 53, 4190, 4243, 4296 }} | {{Optimal ET sequence|legend=1| 53, 4190, 4243, 4296 }} | ||
Badness: 0.173433 | [[Badness]] (Smith): 0.173433 | ||
[[Category:53edo]] | [[Category:53edo]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||