499edo

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← 498edo499edo500edo →
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 499-tone equal temperament (499tet), 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 of 499edo 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 +10 +36 +13 -26 +48 +36 +28 -26 -13 -14
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
1 23\499 55.311 16875/16384 Escapade
1 126\499 303.006 25/21 Quinmite
1 146\499 351.102 49/40 Newt
1 178\499 428.056 2800/2187 Osiris

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Music

Francium