3578edo: Difference between revisions
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{{Infobox ET}} | |||
{{EDO intro|3578}} | {{EDO intro|3578}} | ||
3578edo is consistent in the 21-odd-limit. It inherits the 2.5.11.13.29.31 subgroup mapping from [[1789edo]] and tempers out the [[jacobin comma]]. Although it significantly improves the 2.3.17.19 subgroup, it does have a pretty rough 7th harmonic, with the roughly the same relative error as in 1789edo and is best considered as a 2.3.5.11.13.17.29.29.31 subgroup tuning. | |||
=== Prime harmonics === | |||
{{harmonics in equal|3578}} | |||
Revision as of 20:08, 2 April 2023
| ← 3577edo | 3578edo | 3579edo → |
3578edo is consistent in the 21-odd-limit. It inherits the 2.5.11.13.29.31 subgroup mapping from 1789edo and tempers out the jacobin comma. Although it significantly improves the 2.3.17.19 subgroup, it does have a pretty rough 7th harmonic, with the roughly the same relative error as in 1789edo and is best considered as a 2.3.5.11.13.17.29.29.31 subgroup tuning.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.001 | +0.047 | +0.095 | +0.052 | -0.058 | +0.019 | -0.028 | -0.102 | +0.048 | -0.038 |
| Relative (%) | +0.0 | +0.4 | +14.1 | +28.4 | +15.4 | -17.3 | +5.8 | -8.5 | -30.5 | +14.4 | -11.4 | |
| Steps (reduced) |
3578 (0) |
5671 (2093) |
8308 (1152) |
10045 (2889) |
12378 (1644) |
13240 (2506) |
14625 (313) |
15199 (887) |
16185 (1873) |
17382 (3070) |
17726 (3414) | |