# 246edo

 ← 245edo 246edo 247edo →
Prime factorization 2 × 3 × 41
Step size 4.87805¢
Fifth 144\246 (702.439¢) (→24\41)
Semitones (A1:m2) 24:18 (117.1¢ : 87.8¢)
Consistency limit 5
Distinct consistency limit 5

246 equal divisions of the octave (abbreviated 246edo or 246ed2), also called 246-tone equal temperament (246tet) or 246 equal temperament (246et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 246 equal parts of about 4.88 ¢ each. Each step represents a frequency ratio of 21/246, or the 246th root of 2.

## Theory

246 = 6 × 41, and 246edo shares its fifth with 41edo. It is only consistent to the 5-odd-limit, but the patent val offers excellent approximations (within half a cent) of prime harmonics 11, 19, and 29, and quite good approximations (within one cent) of 5 and 23. The same 11 and 19 are straight-up inherited by the monstrous 2460edo.

As an equal temperament, 246et tempers out 15625/15552 (kleisma) in the 5-limit; 5120/5103 and 118098/117649 in the 7-limit; and 540/539, 9801/9800 in the 11-limit; 325/324, 625/624 in the 13-limit. It provides the optimal patent val for cata, the 2.3.5.13 subgroup temperament tempering out 325/324 and 625/624. The 246d val supports tritikleismic. The 246ee val supports countercata. The 246f val supports supers.

### Prime harmonics

Approximation of prime harmonics in 246edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.48 -0.95 +1.91 -0.10 -1.50 +2.36 +0.05 +0.99 -0.31 +1.31
Relative (%) +0.0 +9.9 -19.4 +39.1 -2.0 -30.8 +48.4 +1.0 +20.4 -6.3 +26.8
Steps
(reduced)
246
(0)
390
(144)
571
(79)
691
(199)
851
(113)
910
(172)
1006
(22)
1045
(61)
1113
(129)
1195
(211)
1219
(235)

### Subsets and supersets

Since 246 factors into 2 × 3 × 41, 246edo has subset edos 2, 3, 6, 41, 82, and 123.

A step of 246edo is exactly 10 minas.

Cata in 246edo