308edo
← 307edo | 308edo | 309edo → |
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
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
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 |