532edo: Difference between revisions
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In addition to the enneadecal and oquatonic, it also supports [[untriton]] in the 5-limit. | 532edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. As 532 = 19 × 28, 532edo [[tempering out|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 === | |||
{{Harmonics in equal|532}} | |||
=== Subsets and supersets === | |||
Since 532 factors into {{factorization|532}}, 532edo has subset edos {{EDOs| 2, 4, 7, 14, 19, 28, 38, 76, 133, and 266 }}. | |||
Latest revision as of 23:00, 20 February 2025
| ← 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 2.26 ¢ 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 (%) | +0.0 | -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.