3566edo
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Prime factorization
2 × 1783
Step size
0.336511¢
Fifth
2086\3566 (701.963¢) (→1043\1783)
Semitones (A1:m2)
338:268 (113.7¢ : 90.19¢)
Consistency limit
11
Distinct consistency limit
11
Special properties
| ← 3565edo | 3566edo | 3567edo → |
3566 equal divisions of the octave (abbreviated 3566edo or 3566ed2), also called 3566-tone equal temperament (3566tet) or 3566 equal temperament (3566et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3566 equal parts of about 0.337 ¢ each. Each step represents a frequency ratio of 21/3566, or the 3566th root of 2. It is a very strong 7-limit system, and is twice 1783edo, which is a very strong 5-limit edo. It tempers out the lakisma and supports a number of very high accuracy 7-limit rank-3 temperaments. It is a zeta peak integer edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0080 | +0.0015 | -0.0093 | -0.1121 | +0.0781 | +0.0362 | -0.0369 | -0.0074 | +0.1480 | +0.1131 |
| Relative (%) | +0.0 | +2.4 | +0.4 | -2.8 | -33.3 | +23.2 | +10.8 | -11.0 | -2.2 | +44.0 | +33.6 | |
| Steps (reduced) |
3566 (0) |
5652 (2086) |
8280 (1148) |
10011 (2879) |
12336 (1638) |
13196 (2498) |
14576 (312) |
15148 (884) |
16131 (1867) |
17324 (3060) |
17667 (3403) | |