# 1308edo

 ← 1307edo 1308edo 1309edo →
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.