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]] (schisma) with the same tuning as [[289edo]]. It tempers out 10976/10935 ([[hemimage comma]]) and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[~~Hemimage temperaments #Bisupermajor|~~bisupermajor]], the 22&118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[~~Schismatic family #Pogo|~~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 [[~~Swetismic temperaments #Hades|~~hades]], as well as other temperaments tempering out 540/539, the rank ~~four~~ 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 [[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.

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

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

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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]] (schisma) with the same tuning as [[289edo]]. It tempers out 10976/10935 ([[hemimage comma]]) and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[Hemimage temperaments #Bisupermajor|bisupermajor]], the 22&118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[Schismatic family #Pogo|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 [[Swetismic temperaments #Hades|hades]], as well as other temperaments tempering out 540/539, the rank four 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 intro|578}}
+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.
 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.
+{{Harmonics in equal|578|columns=11}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->