3578edo
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Prime factorization
2 × 1789
Step size
0.335383¢
Fifth
2093\3578 (701.956¢)
Semitones (A1:m2)
339:269 (113.7¢ : 90.22¢)
Consistency limit
21
Distinct consistency limit
21
| ← 3577edo | 3578edo | 3579edo → |
3578 equal divisions of the octave (abbreviated 3578edo or 3578ed2), also called 3578-tone equal temperament (3578tet) or 3578 equal temperament (3578et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3578 equal parts of about 0.335 ¢ each. Each step represents a frequency ratio of 21/3578, or the 3578th root of 2.
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) | |