Schismic–Mercator equivalence continuum: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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Examples of temperaments with fractional values of ''n'': | Examples of temperaments with fractional values of ''n'': | ||
* [[Countritonic]] (''n'' = 4.5) | |||
* [[Quartonic]] (''n'' = 5.5) | * [[Quartonic]] (''n'' = 5.5) | ||
* [[Ditonic]] (''n'' = 6.5) | * [[Ditonic]] (''n'' = 6.5) | ||
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Comma list: {{monzo| -84 53 }} | Comma list: {{monzo| -84 53 }} | ||
Mapping: {{mapping| 53 84 123 | 0 0 1 }} | |||
{{Multival|legend=1| 0 53 84 }} | |||
Optimal tuning (CTE): ~531441/524288 = 1\53, ~5/4 = 386.264 | |||
{{Optimal ET sequence|legend=1| 53, 477, 530, 583, 636, 689, 742, 795, 848, 901, 1749, 2650 }} | {{Optimal ET sequence|legend=1| 53, 477, 530, 583, 636, 689, 742, 795, 848, 901, 1749, 2650 }} | ||
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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 | |||
Comma list: {{monzo| -69 45 -1 }} | Comma list: {{monzo| -69 45 -1 }} | ||
Mapping: {{mapping| 1 2 21 | 0 -1 -45 }} | |||
{{Multival|legend=1| 1 45 69 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~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: 0.09123 | ||
== Countritonic == | |||
{{See also| Ragismic microtemperaments #Countritonic }} | |||
Subgroup: 2.3.5 | |||
Comma list: {{monzo| 33 -34 9 }} | |||
Mapping: {{mapping| 1 6 19 | 0 -9 -34 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~14348907/10240000 = 588.636 | |||
{{Optimal ET sequence|legend=1| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }} | |||
Badness: 0.256 | |||
== 53 & 3684 == | == 53 & 3684 == | ||
Subgroup: 2.3.5 | |||
Comma list: {{monzo| -339 230 -11 }} | Comma list: {{monzo| -339 230 -11 }} | ||
Mapping: {{mapping| 1 2 11 | 0 -11 -230 }} | |||
{{Multival|legend=1| 11 230 339 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~10737418240/10460353203 = 45.2769 | |||
{{Optimal ET sequence|legend=1| 53, 3684, 11105 }} | {{Optimal ET sequence|legend=1| 53, 3684, 11105 }} | ||
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== 53 & 4190 == | == 53 & 4190 == | ||
Subgroup: 2.3.5 | |||
Comma list: {{monzo| 393 -267 13 }} | Comma list: {{monzo| 393 -267 13 }} | ||
Mapping: {{mapping| 1 6 93 | 0 -13 -267 }} | |||
{{Multival|legend=1| 13 267 393 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~{{monzo| -60 41 -2 }} = 407.5419 | |||
{{Optimal ET sequence|legend=1| 53, 4190, 4243, 4296 }} | {{Optimal ET sequence|legend=1| 53, 4190, 4243, 4296 }} | ||