578edo: Difference between revisions

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~~The ''578 equal division'' divides the octave into 578 equal parts of 2.076 cents each. It~~ is ~~contorted~~ in the 5-limit, tempering out 32805/32768 with the same tuning as 289edo. It tempers out ~~10976/10935 and 65625/65536 in the 7-limit, supporting the 22&118 temperament, and 119098~~/117649 which together with the schisma gives 7-limit [[~~Schismatic_family#Pogo|~~pogo ~~temperament~~]], the 94&~~amp;130~~ temperament. In the 11-limit it tempers out 540/539 and 4000/3993 and provides the [[~~Optimal_patent_val|~~optimal patent val]] for 11-limit pogo and the planar temperament [[~~Swetismic_temperaments#Hades|~~hades]]. In the 13-limit, it tempers out 729/~~729~~, 1575/1573, 1716/1715 and 2080/2079, and provides the optimal patent val for 13-limit pogo~~, as well as other temperaments tempering out 1716/1715, the rank five temperament for which it also provides the optimal patent val~~. 578 factors as 2 * 17^2.

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.

=== Prime harmonics ===

=== Subsets and supersets ===

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

[[Category:Swetismic]]

[[Category:Hades]]

[[Category:Pogo]]

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-The ''578 equal division'' divides the octave into 578 equal parts of 2.076 cents each. It is contorted in the 5-limit, tempering out 32805/32768 with the same tuning as 289edo. It tempers out 10976/10935 and 65625/65536 in the 7-limit, supporting the 22&amp;118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[Schismatic_family#Pogo|pogo temperament]], the 94&amp;130 temperament. In the 11-limit it tempers out 540/539 and 4000/3993 and provides the [[Optimal_patent_val|optimal patent val]] for 11-limit pogo and the planar temperament [[Swetismic_temperaments#Hades|hades]]. In the 13-limit, it tempers out 729/729, 1575/1573, 1716/1715 and 2080/2079, and provides the optimal patent val for 13-limit pogo, as well as other temperaments tempering out 1716/1715, the rank five temperament for which  it also provides the optimal patent val. 578 factors as 2 * 17^2.
+{{Infobox ET}}
+{{ED intro}}
+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.
+=== Prime harmonics ===
+{{Harmonics in equal|578|columns=11}}
+=== Subsets and supersets ===
+factors as {{factorization|578}}, with divisors {{EDOs| 2, 17, 34, and 289 }}.
+[[Category:Swetismic]]
+[[Category:Hades]]
+[[Category:Pogo]]