308edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 308 factors into 2<sup>2</sup> × 7 × 11, 308edo has subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}. | Since 308 factors into {{nowrap|2<sup>2</sup> × 7 × 11}}, 308edo has subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 30: | Line 30: | ||
| {{monzo| -122 77 }} | | {{monzo| -122 77 }} | ||
| {{mapping| 308 488 }} | | {{mapping| 308 488 }} | ||
| 0.2070 | | +0.2070 | ||
| 0.2071 | | 0.2071 | ||
| 5.32 | | 5.32 | ||
| Line 37: | Line 37: | ||
| {{monzo| -36 11 8 }}, {{monzo| -7 22 -12 }} | | {{monzo| -36 11 8 }}, {{monzo| -7 22 -12 }} | ||
| {{mapping| 308 488 715 }} | | {{mapping| 308 488 715 }} | ||
| 0.2241 | | +0.2241 | ||
| 0.1708 | | 0.1708 | ||
| 4.38 | | 4.38 | ||
| Line 64: | Line 64: | ||
| [[Oquatonic]] (308) | | [[Oquatonic]] (308) | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
Revision as of 16:53, 15 January 2025
| ← 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
| 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* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 9\308 | 35.06 | 128/125 | Gammic (308d) |
| 28 | 128\308 (4\308) |
498.70 (15.58) |
4/3 (126/125) |
Oquatonic (308) |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct