Septiennealimmal clan: Difference between revisions
+tunings |
→No-five septiennealimmal: add natural but less accurate 2.3.7.13 subgroup extension (the 11 increases badness significantly due to being found at more than 1 gen, and the 5 has two possible mappings (36c and 36)) |
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| Line 21: | Line 21: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2592/2401 = 133. | * [[CTE]]: ~2592/2401 = 133.33... = 1\9, ~3/2 = 702.0044 | ||
: [[error map]]: {{val| 0.0000 +0.0494 -0.1549 }} | : [[error map]]: {{val| 0.0000 +0.0494 -0.1549 }} | ||
* [[POTE]]: ~2592/2401 = 133. | * [[POTE]]: ~2592/2401 = 133.33... = 1\9, ~3/2 = 701.9649 | ||
: error map: {{val| 0.0000 +0.0099 -0.1944 }} | : error map: {{val| 0.0000 +0.0099 -0.1944 }} | ||
{{Optimal ET sequence|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, …, 8397dd, 8703dd }} | {{Optimal ET sequence|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, …, 8397dd, 8703dd }} | ||
[[Badness]] (Dirichlet): 0. | === Septiennealic === | ||
Septiennealic finds a somewhat high-damage but very simple/intuitive mapping of prime 13 via explaining ~7/6 = 2\9 as a consequence of ~14/13~13/12 = 1\9. A notable tuning of septiennealic not appearing in the optimal ET sequence is [[63edo]]. | |||
[[Subgroup]]: 2.3.7.13 | |||
[[Comma list]]: [[169/168]], [[31213/31104]] | |||
{{Mapping|legend=2| 9 0 11 19 | 0 1 1 1 }} | |||
[[Optimal tuning]] ([[CTE]]): ~13/12 = 133.33... = 1\9, ~3/2 = 702.638 | |||
{{Optimal ET sequence|legend=1| 27, 36, 99, 135f, 171f }} | |||
[[Badness]] (Dirichlet): 0.540 | |||
=== Ennea === | === Ennea === | ||