534edo

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← 533edo534edo535edo →
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 21/534, 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.