532edo

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← 531edo532edo533edo →
Prime factorization 22 × 7 × 19
Step size 2.25564¢
Fifth 311\532 (701.504¢)
Semitones (A1:m2) 49:41 (110.5¢ : 92.48¢)
Consistency limit 5
Distinct consistency limit 5

532 equal divisions of the octave (532edo), or 532-tone equal temperament (532tet), 532 equal temperament (532et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 532 equal parts of about 2.26 ¢ each.

Theory

Approximation of prime harmonics in 532edo
Harmonic 2 3 5 7 11 13 17 19 23 29
Error absolute (¢) +0.000 -0.451 -0.599 +1.099 -0.942 +0.826 +1.060 +0.231 +1.049 -1.006
relative (%) +0 -20 -27 +49 -42 +37 +47 +10 +47 -45
Steps
(reduced)
532
(0)
843
(311)
1235
(171)
1494
(430)
1840
(244)
1969
(373)
2175
(47)
2260
(132)
2407
(279)
2584
(456)

Since 532 = 19 x 28, 532edo tempers out both the enneadeca, which sets 6/5 to be 5\19 of the octave, and the oquatonic comma, which sets 5/4 to be 9\28 of the octave. Therefore, it can be conceptualized as superset of 19edo and 28edo.

In addition to the enneadecal and oquatonic, it also supports untriton in the 5-limit.

Its 7th harmonic is halfway between two notes. In the patent val, 532edo tempers out 65625/65536 and the dimcomp comma. In the 532d val it tempers out 4375/4374 and the meter.

In the 11-limit, 532d val supports the hemienneadecal temperament.