496edo

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← 495edo496edo497edo →
Prime factorization 24 × 31
Step size 2.41935¢
Fifth 290\496 (701.613¢) (→145\248)
Semitones (A1:m2) 46:38 (111.3¢ : 91.94¢)
Consistency limit 5
Distinct consistency limit 5

496 equal divisions of the octave (abbreviated 496edo), or 496-tone equal temperament (496tet), 496 equal temperament (496et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 496 equal parts of about 2.42 ¢ each. Each step of 496edo represents a frequency ratio of 21/496, or the 496th root of 2.

496edo is enfactored in the 11-limit, with the same tuning as 248edo, but the patent vals differ on the mapping for 13. As such, in the 11-limit it supports a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, it tempers out 4225/4224.

496edo is good with the 2.3.11.19 subgroup. For higher limits, it has good approximations of 31, 37, and 47. In the 2.3.11.19 subgroup, it tempers out 131072/131043.

Odd harmonics

Approximation of odd harmonics in 496edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -0.34 +0.78 -1.08 -0.68 +0.29 -1.01 +0.44 -0.92 +0.07 +0.99 +0.76
relative (%) -14 +32 -45 -28 +12 -42 +18 -38 +3 +41 +31
Steps
(reduced)
786
(290)
1152
(160)
1392
(400)
1572
(84)
1716
(228)
1835
(347)
1938
(450)
2027
(43)
2107
(123)
2179
(195)
2244
(260)

Subsets and supersets

496 is the 3rd perfect number, factoring into 24 × 31. Its nontrivial divisors are 2, 4, 8, 16, 31, 62, 124, 248, the most notable being 31.