578edo

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← 577edo

578edo

579edo →

Prime factorization	2 × 172
Step size	2.07612 ¢
Fifth	338\578 (701.73 ¢) (→ 169\289)
Semitones (A1:m2)	54:44 (112.1 ¢ : 91.35 ¢)
Consistency limit	7
Distinct consistency limit	7

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 × 17², with divisors 2, 17, 34, and 289.

Approximation of prime harmonics in 578edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.225	-0.155	+0.724	+0.931	+0.303	+0.927	-0.627	+0.791	+0.181	+0.985
	Relative (%)	+0.0	-10.8	-7.4	+34.9	+44.9	+14.6	+44.6	-30.2	+38.1	+8.7	+47.5
Steps (reduced)		578 (0)	916 (338)	1342 (186)	1623 (467)	2000 (266)	2139 (405)	2363 (51)	2455 (143)	2615 (303)	2808 (496)	2864 (552)