# 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 (308edo), or 308-tone equal temperament (308tet), 308 equal temperament (308et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 308 equal parts of about 3.9 ¢ each.

## Theory

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

308et tempers out following commas:

7-limit commas: 4096000/4084101, 390625/388962, 26873856/26796875, 19683/19600, 78125000/78121827, 65625/65536, 1640558367/1638400000

11-limit commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375, 243/242, 131072/130977, 6250/6237, 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883, 9801/9800, 539055/537824, 202397184/201768035

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 -17 -15 +33 +50 +26 +6 -36 -26 -26 +11
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

308 factors into 22 x 7 x 11, with 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
(Reduced)
Cents
(Reduced)
Associated
Ratio
Temperaments
1 9\308 35.06 128/125 Gammic (308d)
28 128\308
(4\308)
498.70
(15.58)
4/3
(2048/2025)
Oquatonic