578edo: Difference between revisions

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578edo is [[~~contorted~~]] in the [[5-limit]], tempering out [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out ~~10976~~/~~10935~~ (~~[[hemimage comma]]~~) ~~and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[bisupermajor]], the 22 & 118 temperament, and 119098/117649~~ which together with the schisma gives 7-limit [[pogo]] temperament, the 94 & ~~130~~ temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.

578edo is [[enfactoring|enfactored]] in the [[5-limit]], [[tempering out]] [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 118098/117649 (stearnsma) which together with the schisma gives 7-limit [[pogo]] temperament, the 224 & 354 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.

578 ~~factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.~~

=== Prime harmonics ===

=== Subsets and supersets ===

578 factors as {{factorization|578}}, with divisors {{EDOs| 2, 17, 34, and 289 }}.

~~[[Category:Equal divisions of the octave|###]] ~~

[[Category:Swetismic]]

[[Category:Hades]]

[[Category:Pogo]]

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-{{EDO intro|578}}
+{{Infobox ET}}
+{{ED intro}}
-edo is [[contorted]] in the [[5-limit]], tempering out [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 10976/10935 ([[hemimage comma]]) and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[bisupermajor]], the 22 & 118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[pogo]] temperament, the 94 & 130 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.
+edo is [[enfactoring|enfactored]] in the [[5-limit]], [[tempering out]] [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 118098/117649 (stearnsma) which together with the schisma gives 7-limit [[pogo]] temperament, the 224 & 354 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.
-factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.
+=== Prime harmonics ===
+{{Harmonics in equal|578|columns=11}}
-{{Harmonics in equal|578|columns=11}}
+=== Subsets and supersets ===
+factors as {{factorization|578}}, with divisors {{EDOs| 2, 17, 34, and 289 }}.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Swetismic]]
 [[Category:Hades]]
 [[Category:Pogo]]