308edo

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← 307edo308edo309edo →
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