578edo

The 578 equal division divides the octave into 578 equal parts of 2.076 cents each. It is contorted (or enfactored) 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 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.

578 factors as 2 × 17², with divisors 2, 17, 34, and 289.