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 21/578, 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 (%) +0.0 -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)

Subsets and supersets

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