512edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 512edo factors into | Since 512edo factors into {{factorization|512}}, 512edo has subset edos {{EDOs| 2, 4, 8, 16, 32, 64, 128, and 256 }}. | ||
Revision as of 13:49, 2 November 2023
| ← 511edo | 512edo | 513edo → |
(semiconvergent)
With only a consistency limit of 5, this 9th-power-of-two edo does not have a whole lot to offer in terms of lower harmonics. Harmonic 3 is about halfway between its steps, making it suitable for a 2.9.5.21.17.19.23 subgroup interpretation, with optional addition of either 11 or 13.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.17 | +0.41 | -0.86 | -0.00 | -0.54 | +0.88 | -0.77 | +0.51 | +0.14 | +0.31 | -0.15 |
| Relative (%) | +49.9 | +17.3 | -36.6 | -0.2 | -22.9 | +37.5 | -32.8 | +21.9 | +6.1 | +13.3 | -6.4 | |
| Steps (reduced) |
812 (300) |
1189 (165) |
1437 (413) |
1623 (87) |
1771 (235) |
1895 (359) |
2000 (464) |
2093 (45) |
2175 (127) |
2249 (201) |
2316 (268) | |
Subsets and supersets
Since 512edo factors into 29, 512edo has subset edos 2, 4, 8, 16, 32, 64, 128, and 256.