# 499edo

 ← 498edo 499edo 500edo →
Prime factorization 499 (prime)
Step size 2.40481¢
Fifth 292\499 (702.204¢)
Semitones (A1:m2) 48:37 (115.4¢ : 88.98¢)
Consistency limit 9
Distinct consistency limit 9

499 equal divisions of the octave (abbreviated 499edo or 499ed2), also called 499-tone equal temperament (499tet) or 499 equal temperament (499et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 499 equal parts of about 2.4 ¢ each. Each step represents a frequency ratio of 21/499, or the 499th root of 2.

## Theory

499et tempers out 33554432/33480783, 359661568/358722675 and 2401/2400 in the 7-limit; 100663296/100656875, 2097152/2096325, 536870912/535869675, 151263/151250, 104857600/104825259, 131072/130977, 200704/200475, 17537553/17500000, 19712/19683, 1479016/1476225, 3025/3024, 41503/41472, 532400/531441 and 67110351/67108864 in the 11-limit.

### Prime harmonics

Approximation of prime harmonics in 499edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.25 +0.86 +0.31 -0.62 +1.16 +0.86 +0.68 -0.62 -0.32 -0.35
Relative (%) +0.0 +10.4 +35.8 +13.0 -25.6 +48.1 +35.6 +28.4 -25.7 -13.3 -14.4
Steps
(reduced)
499
(0)
791
(292)
1159
(161)
1401
(403)
1726
(229)
1847
(350)
2040
(44)
2120
(124)
2257
(261)
2424
(428)
2472
(476)

### Subsets and supersets

499edo is the 95th prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [791 -499 499 791] -0.0787 0.0787 3.27
2.3.5 [32 -7 -9, [1 36 -25 499 791 1159] -0.1760 0.1519 6.32
2.3.5.7 2401/2400, 1959552/1953125, 26873856/26796875 499 791 1159 1401] -0.1598 0.1345 5.59

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments