532edo
| ← 531edo | 532edo | 533edo → |
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 2.256 ¢ each. Each step represents a frequency ratio of 21/532, 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
| 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.