308edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 40: | Line 31: | ||
| 0.1708 | | 0.1708 | ||
| 4.38 | | 4.38 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 63: | Line 47: | ||
| 4/3<br />(126/125) | | 4/3<br />(126/125) | ||
| [[Oquatonic]] (308) | | [[Oquatonic]] (308) | ||
{{rank-2 end}} | |||
{{orf}} | {{orf}} | ||
Revision as of 01:49, 16 November 2024
| ← 307edo | 308edo | 309edo → |
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
| 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