3566edo

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← 3565edo3566edo3567edo →
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

3566 equal divisions of the octave (abbreviated 3566edo), or 3566-tone equal temperament (3566tet), 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 of 3566edo 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

Approximation of prime harmonics in 3566edo
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 +2 +0 -3 -33 +23 +11 -11 -2 +44 +34
Steps
(reduced)
3566
(0)
5652
(2086)
8280
(1148)
10011
(2879)
12336
(1638)
13196
(2498)
14576
(312)
15148
(884)
16131
(1867)
17324
(3060)
17667
(3403)