532edo: Difference between revisions

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-Tempering both [[enneadeca]] and [[oquatonic comma]] sends to 532edo since 19×28.
+{{Infobox ET}}
-{{Infobox ET
+{{ED intro}}
-| Prime factorization = 19 × 7 × 2<sup>2</sup>
-| Step size = 2.25564¢
-| Fifth = 311\532 (701.504¢)
-| Major 2nd = 90\532 (203.008¢)
-| Semitones = 49:41 (110.526¢:92.481¢)
-| Consistency = 5
-}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+edo 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 }}.