# 496edo

 ← 495edo 496edo 497edo →
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 496ed2), also called 496-tone equal temperament (496tet) or 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 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 (%) -14.1 +32.4 -44.8 -28.3 +12.2 -41.8 +18.2 -38.2 +2.8 +41.1 +31.3
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.