# 532edo

 ← 531edo 532edo 533edo →
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.

532edo is only consistent to the 5-odd-limit since harmonic 7 is about halfway between its steps. As 532 = 19 × 28, 532edo tempers out both the enneadeca, which sets 6/5 to 5\19, and the oquatonic comma, which sets 5/4 to 9\28. 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.

The patent val tempers out 65625/65536 (horwell comma) and 390625/388962 (dimcomp comma) in the 7-limit. The 532d val tempers out 4375/4374 (ragisma) and 703125/702464 (meter). In the 11-limit, 532d val supports the hemienneadecal temperament.

### Prime harmonics

Approximation of prime harmonics in 532edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 -0.451 -0.599 +1.099 -0.942 +0.826 +1.060 +0.231 +1.049 -1.006 +0.829
relative (%) +0 -20 -27 +49 -42 +37 +47 +10 +47 -45 +37
Steps
(reduced)
532
(0)
843
(311)
1235
(171)
1494
(430)
1840
(244)
1969
(373)
2175
(47)
2260
(132)
2407
(279)
2584
(456)
2636
(508)

### Subsets and supersets

Since 532 factors into 22 × 7 × 19, 532edo has subset edos 2, 4, 7, 14, 19, 28, 38, 76, 133, and 266.