246edo

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← 245edo246edo247edo →
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.

Scales

cata_246edo.jpg
Cata in 246edo