534edo

← 533edo

534edo

535edo →

Prime factorization	2 × 3 × 89
Step size	2.24719 ¢
Fifth	312\534 (701.124 ¢) (→ 52\89)
Semitones (A1:m2)	48:42 (107.9 ¢ : 94.38 ¢)
Dual sharp fifth	313\534 (703.371 ¢)
Dual flat fifth	312\534 (701.124 ¢) (→ 52\89)
Dual major 2nd	91\534 (204.494 ¢)
Consistency limit	7
Distinct consistency limit	7

534 equal divisions of the octave (abbreviated 534edo or 534ed2), also called 534-tone equal temperament (534tet) or 534 equal temperament (534et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 534 equal parts of about 2.25 ¢ each. Each step represents a frequency ratio of 2^1/534, or the 534th root of 2.

534edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. The patent val tempers out 2401/2400 and 19683/19600 in the 7-limit and provides the optimal patent val for 7-limit harry temperament.

Odd harmonics

Approximation of odd harmonics in 534edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.831	+0.203	-0.287	+0.584	-0.756	-0.078	-0.628	+0.663	-0.884	-1.118	+0.939
	Relative (%)	-37.0	+9.0	-12.8	+26.0	-33.6	-3.5	-28.0	+29.5	-39.3	-49.8	+41.8
Steps (reduced)		846 (312)	1240 (172)	1499 (431)	1693 (91)	1847 (245)	1976 (374)	2086 (484)	2183 (47)	2268 (132)	2345 (209)	2416 (280)

Subsets and supersets

Since 534 factors into 2 × 3 × 89, 534edo has subset edos 2, 3, 6, 89, 178, and 267.