532edo

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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 (abbreviated 532edo or 532ed2), also called 532-tone equal temperament (532tet) or 532 equal temperament (532et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 532 equal parts of about 2.26 ¢ each. Each step represents a frequency ratio of 2^1/532, or the 532nd root of 2.

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 (%)	+0.0	-20.0	-26.6	+48.7	-41.8	+36.6	+47.0	+10.3	+46.5	-44.6	+36.8
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.