20567edo

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20567edo

20568edo →

Prime factorization	131 × 157
Step size	0.0583459¢
Fifth	12031\20567 (701.959¢)
Semitones (A1:m2)	1949:1546 (113.7¢ : 90.2¢)
Consistency limit	57
Distinct consistency limit	57

20567 equal divisions of the octave (abbreviated 20567edo or 20567ed2), also called 20567-tone equal temperament (20567tet) or 20567 equal temperament (20567et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 20567 equal parts of about 0.0583 ¢ each. Each step represents a frequency ratio of 2^1/20567, or the 20567th root of 2.

20567edo is a remarkable very high-limit system, distinctly consistent through the 57-odd-limit, with a lower relative error than any previous equal temperaments in the 43-limit. It tempers out 33814/33813, 35344/35343, 37180/37179, 42484/42483, 42688/42687, 47125/47124, 48504/48503, 67915/67914, 70500/70499, 91885/91884, 126225/126224, 156520/156519, 194580/194579, 206800/206793, and 561925/561924 in the 53-limit.

Prime harmonics

Approximation of prime harmonics in 20567edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	+0.0000	+0.0044	-0.0056	+0.0077	-0.0076	+0.0033	+0.0089	-0.0073	-0.0058	-0.0056	+0.0026
	relative (%)	+0	+8	-10	+13	-13	+6	+15	-13	-10	-10	+4
Steps (reduced)		20567 (0)	32598 (12031)	47755 (6621)	57739 (16605)	71150 (9449)	76107 (14406)	84067 (1799)	87367 (5099)	93036 (10768)	99914 (17646)	101893 (19625)