1308edo

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← 1307edo1308edo1309edo →
Prime factorization 22 × 3 × 109
Step size 0.917431¢ 
Fifth 765\1308 (701.835¢) (→255\436)
Semitones (A1:m2) 123:99 (112.8¢ : 90.83¢)
Consistency limit 21
Distinct consistency limit 21
Special properties

1308 equal divisions of the octave (abbreviated 1308edo or 1308ed2), also called 1308-tone equal temperament (1308tet) or 1308 equal temperament (1308et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1308 equal parts of about 0.917 ¢ each. Each step represents a frequency ratio of 21/1308, or the 1308th root of 2.

1308edo is distinctly consistent to the 21-odd-limit, and is the 15th zeta gap edo. With 23/17 barely missing the line, it has reasonable approximations up to the 37-limit.

The equal temperament tempers out [37 25 -33 (whoosh comma) and [-46 51 -15 (171 & 1137 comma) in the 5-limit; 250047/250000, 2460375/2458624, and [47 4 0 -19 in the 7-limit; 9801/9800, 151263/151250, 234375/234256, and 67110351/67108864 in the 11-limit; 4225/4224, 6656/6655, 50193/50176, 91125/91091, and 655473/655360 in the 13-limit; 2601/2600, 5832/5831, 11016/11011, 11271/11264, 12376/12375, and 108086/108045 in the 17-limit; 5491/5488, 5776/5775, 5985/5984, 6175/6174, 10241/10240, and 10830/10829 in the 19-limit.

Prime harmonics

Approximation of prime harmonics in 1308edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31 37
Error Absolute (¢) +0.000 -0.120 -0.075 -0.019 +0.058 -0.161 -0.368 -0.265 +0.166 -0.219 -0.081 +0.032
Relative (%) +0.0 -13.1 -8.2 -2.0 +6.3 -17.5 -40.1 -28.9 +18.1 -23.9 -8.9 +3.5
Steps
(reduced)
1308
(0)
2073
(765)
3037
(421)
3672
(1056)
4525
(601)
4840
(916)
5346
(114)
5556
(324)
5917
(685)
6354
(1122)
6480
(1248)
6814
(274)

Subsets and supersets

Since 1308 factors into 22 × 3 × 109, 1308edo has subset edos 2, 3, 4, 6, 12, 109, 218, 327, 436, and 654.