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&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.		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&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]], 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 729/729, 1575/1573, 1716/1715 and 2080/2079, and provides the optimal patent val for 13-limit pogo. 578 factors as 2 * 17^2.