Catalog of rank-4 temperaments: Difference between revisions
→Swetismic (540/539): we can't leave out the best extension (+729/728) |
→Trimitone (8019/8000): +obvious extension, a bit more complex |
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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 = 701.5449, ~5/4 = 386.7538, ~7/4 = 968.8259 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.4729, ~5/4 = 386.5374, ~7/4 = 968.6210 | |||
{{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }} | {{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }} | ||
[[Badness]]: 0.0820 × 10<sup>-6</sup> | |||
=== Commas 729/728, 1001/1000 === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 729/728, 1001/1000 | |||
{{Mapping|legend=1| 1 0 0 0 6 -3 | 0 1 0 0 -6 6 | 0 0 1 0 3 0 | 0 0 0 1 0 -1 }} | |||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.5537, ~5/4 = 386.7680, ~7/4 = 968.8144 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.4770, ~5/4 = 386.5437, ~7/4 = 968.6150 | |||
{{Optimal ET sequence|legend=1| 53, 58, 72, 111, 130, 183, 190, 243e, 248, 301, 373, 804, 1177be }} | |||
[[Badness]]: 3.33 × 10<sup>-6</sup> | |||
== Kalismic (9801/9800) == | == Kalismic (9801/9800) == | ||