578edo

← 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

578 equal divisions of the octave (abbreviated 578edo or 578ed2), also called 578-tone equal temperament (578tet) or 578 equal temperament (578et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 578 equal parts of about 2.08 ¢ each. Each step represents a frequency ratio of 2^1/578, or the 578th root of 2.

578edo is 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

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	-11	-7	+35	+45	+15	+45	-30	+38	+9	+47
Steps (reduced)		578 (0)	916 (338)	1342 (186)	1623 (467)	2000 (266)	2139 (405)	2363 (51)	2455 (143)	2615 (303)	2808 (496)	2864 (552)

Subsets and supersets

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