539edo: Difference between revisions
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Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|539}} | |||
[[ | 539edo is in[[consistent]] to the [[5-odd-limit]]. If [[harmonic]] [[5/1|5]] is used at all, the 539c [[val]] has better overall accuracy than the [[patent val]]. Meanwhile, the patent val [[tempering out|tempers out]] the [[sensipent comma]], 78732/78125, and provides the [[optimal patent val]] for the 5-limit [[sensipent]] temperament, tuning it more accurate than 65et by a tiny margin. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|539}} | |||
=== Subsets and supersets === | |||
Since 539 factors into 7<sup>2</sup> × 11, 539edo has subset edos {{EDOs| 7, 11, 49, and 77 }}. | |||
[[Category:Sensipent]] | |||
Revision as of 11:13, 29 October 2023
| ← 538edo | 539edo | 540edo → |
539edo is inconsistent to the 5-odd-limit. If harmonic 5 is used at all, the 539c val has better overall accuracy than the patent val. Meanwhile, the patent val tempers out the sensipent comma, 78732/78125, and provides the optimal patent val for the 5-limit sensipent temperament, tuning it more accurate than 65et by a tiny margin.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.656 | +1.070 | -0.366 | +0.914 | +0.816 | +1.031 | +0.414 | -0.317 | +0.817 | -1.022 | -0.445 |
| Relative (%) | -29.5 | +48.1 | -16.4 | +41.0 | +36.6 | +46.3 | +18.6 | -14.2 | +36.7 | -45.9 | -20.0 | |
| Steps (reduced) |
854 (315) |
1252 (174) |
1513 (435) |
1709 (92) |
1865 (248) |
1995 (378) |
2106 (489) |
2203 (47) |
2290 (134) |
2367 (211) |
2438 (282) | |
Subsets and supersets
Since 539 factors into 72 × 11, 539edo has subset edos 7, 11, 49, and 77.