3566edo

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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

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 2^1/3566, or the 3566th root of 2.

3566edo is a very strong 7-limit system, and is twice 1783edo, which is a very strong 5-limit edo. As an equal temperament, 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 (¢)	+0.000	+0.008	+0.001	-0.009	-0.112	+0.078	+0.036	-0.037	-0.007	+0.148	+0.113
	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)