# 308edo

 ← 307edo 308edo 309edo →
Prime factorization 22 × 7 × 11
Step size 3.8961¢
Fifth 180\308 (701.299¢) (→45\77)
Semitones (A1:m2) 28:24 (109.1¢ : 93.51¢)
Consistency limit 5
Distinct consistency limit 5

308 equal divisions of the octave (abbreviated 308edo or 308ed2), also called 308-tone equal temperament (308tet) or 308 equal temperament (308et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 308 equal parts of about 3.9 ¢ each. Each step represents a frequency ratio of 21/308, or the 308th root of 2.

## Theory

308edo only is consistent in the 5-odd-limit. Ignoring the harmonics 7, 11 and 13, it is strong in the 2.3.5.17.19.23.29.31 subgroup.

Using the patent val nonetheless, the equal temperament tempers out 19683/19600, 65625/65536, and 390625/388962 in the 7-limit, and 243/242, 1375/1372, 6250/6237, 9801/9800, and 14700/14641 in the 11-limit.

Using the 308d val, it supports unidec and gammic.

### Prime harmonics

Approximation of prime harmonics in 308edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.66 -0.60 +1.30 +1.93 +1.03 +0.24 -1.41 -1.00 -1.01 +0.42
Relative (%) +0.0 -16.8 -15.4 +33.5 +49.5 +26.5 +6.1 -36.2 -25.7 -25.8 +10.8
Steps
(reduced)
308
(0)
488
(180)
715
(99)
865
(249)
1066
(142)
1140
(216)
1259
(27)
1308
(76)
1393
(161)
1496
(264)
1526
(294)

### Subsets and supersets

Since 308 factors into 22 × 7 × 11, 308edo has subset edos 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-122 77 [308 488]] 0.2070 0.2071 5.32
2.3.5 [-36 11 8, [-7 22 -12 [308 488 715]] 0.2241 0.1708 4.38

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 9\308 35.06 128/125 Gammic (308d)
28 128\308
(4\308)
498.70
(15.58)
4/3
(126/125)
Oquatonic (308)

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