308edo

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← 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

Template:EDO intro

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

Template:Comma basis begin |- | 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 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 9\308 | 35.06 | 128/125 | Gammic (308d) |- | 28 | 128\308
(4\308) | 498.70
(15.58) | 4/3
(126/125) | Oquatonic (308) Template:Rank-2 end Template:Orf