513edo: Difference between revisions
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Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories |
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{{EDO intro|513}} | |||
[[ | 513edo divides the steps of [[171edo]] into three. It is [[consistent]] to the [[11-odd-limit]], [[tempering out]] [[4000/3993]], 12005/11979, and 46656/46585 using the [[patent val]]. Using the alternative 513e [[val]], 35937/35840, 42592/42525, and 166375/165888 are tempered out in the 11-limit. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|513}} | |||
=== Subsets and supersets === | |||
Since 513 factors into 3<sup>3</sup> × 19, 513edo has subset edos {{EDOs| 3, 9, 19, 27, 57, and 171 }}. | |||
Revision as of 11:48, 29 October 2023
| ← 512edo | 513edo | 514edo → |
513edo divides the steps of 171edo into three. It is consistent to the 11-odd-limit, tempering out 4000/3993, 12005/11979, and 46656/46585 using the patent val. Using the alternative 513e val, 35937/35840, 42592/42525, and 166375/165888 are tempered out in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.20 | -0.35 | -0.40 | +0.73 | -0.76 | +0.31 | -0.44 | +0.97 | -0.34 | +1.16 |
| Relative (%) | +0.0 | -8.6 | -14.9 | -17.3 | +31.2 | -32.6 | +13.2 | -18.7 | +41.3 | -14.4 | +49.7 | |
| Steps (reduced) |
513 (0) |
813 (300) |
1191 (165) |
1440 (414) |
1775 (236) |
1898 (359) |
2097 (45) |
2179 (127) |
2321 (269) |
2492 (440) |
2542 (490) | |
Subsets and supersets
Since 513 factors into 33 × 19, 513edo has subset edos 3, 9, 19, 27, 57, and 171.