Catalog of rank-4 temperaments: Difference between revisions
→Pentacircle (896/891): +gentle as an alias of tridecimal pentacircle |
→Swetismic (540/539): we can't leave out the best extension (+729/728) |
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: mapping generators: ~2, ~3, ~5, ~7 | : mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.6167, ~5/4 = 386.0717, ~7/4 = 969.5334 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.6950, ~5/4 = 386.1796, ~7/4 = 969.6366 | |||
{{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }} | {{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }} | ||
[[Badness]]: 0.0105 × 10<sup>-6</sup> | |||
=== Commas 540/539, 729/728 === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 540/539, 729/728 | |||
{{Mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 0 3 6 | 0 0 1 0 1 0 | 0 0 0 1 -2 -1 }} | |||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.6687, ~5/4 = 386.0441, ~7/4 = 969.5668 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.7230, ~5/4 = 386.1818, ~7/4 = 969.6607 | |||
{{Optimal ET sequence|legend=1| 12e, 14cf, 17c, 19, 22f, 31f, 39df, 41, 53, 58, 72, 111, 130, 183, 224, 354, 578, 985d, 1267ddef }} | |||
[[Badness]]: 1.73 × 10<sup>-6</sup> | |||
=== Commas 540/539, 847/845 === | === Commas 540/539, 847/845 === | ||
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{{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }} | {{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }} | ||
[[Badness]]: 3.97 × 10<sup>-6</sup> | |||
=== Commas 540/539, 625/624 === | === Commas 540/539, 625/624 === | ||
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{{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }} | {{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }} | ||
[[Badness]]: 3.59 × 10<sup>-6</sup> | |||
=== Commas 540/539, 676/675 === | === Commas 540/539, 676/675 === | ||
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{{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }} | {{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }} | ||
[[Badness]]: 3.06 × 10<sup>-6</sup> | |||
== Pentacircle (896/891) == | == Pentacircle (896/891) == | ||