532edo: Difference between revisions

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~~==Theory==~~

~~{{harmonics in equal|532}}~~

Since 532 = 19 x 28, 532edo tempers out both the [[enneadeca]], which sets 6/5 to be 5\19 of the octave, and the [[oquatonic comma]], which sets 5/4 to be 9\28 of the octave. 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.

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.

~~Its 7th harmonic is halfway between two notes. In the~~ patent val~~, 532edo~~ tempers out 65625/65536 and ~~the~~ [[dimcomp comma]]. ~~In the~~ 532d val it tempers out 4375/4374 and the [[~~meter~~]].

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.

~~In the 11-limit, 532d val supports the [[hemienneadecal]] temperament.~~

=== Prime harmonics ===

~~[[Category:Equal divisions of the octave~~|~~###]]~~ <~~!-- 3-digit number --~~>

=== Subsets and supersets ===

Since 532 factors into 2<sup>2</sup> × 7 × 19, 532edo has subset edos {{EDOs| 2, 4, 7, 14, 19, 28, 38, 76, 133, and 266 }}.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|532}}
-==Theory==
-{{harmonics in equal|532}}
-Since 532 = 19 x 28, 532edo tempers out both the [[enneadeca]], which sets 6/5 to be 5\19 of the octave, and the [[oquatonic comma]], which sets 5/4 to be 9\28 of the octave. 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.
+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.
-Its 7th harmonic is halfway between two notes. In the patent val, 532edo tempers out 65625/65536 and the [[dimcomp comma]]. In the 532d val it tempers out 4375/4374 and the [[meter]].
+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.
-In the 11-limit, 532d val supports the [[hemienneadecal]] temperament.
+=== Prime harmonics ===
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+{{Harmonics in equal|532}}
+=== Subsets and supersets ===
+Since 532 factors into 2<sup>2</sup> × 7 × 19, 532edo has subset edos {{EDOs| 2, 4, 7, 14, 19, 28, 38, 76, 133, and 266 }}.