312edo: Difference between revisions
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{{EDO intro|312}} | {{EDO intro|312}} | ||
This edo is the first multiple of 12 to have a [[patent val]] [[perfect fifth|fifth]] that does not correspond to the [[12edo]] fifth of 700 cents. It is strong in the 2.9.15.7 [[subgroup]]. Beyond that, it is harmonic quality is quite poor for its size. | |||
This | |||
=== Odd harmonics === | |||
{{Harmonics in equal|312|columns=12}} | |||
{{ | === Subsets and supersets === | ||
Since 312 factors into {{factorization|312}}, 312edo has subset edos {{EDOs| 2, 3, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, and 156 }}. [[624edo]], which doubles it, provides the much needed correction to many of the lower harmonics. | |||
Revision as of 10:32, 21 February 2024
| ← 311edo | 312edo | 313edo → |
This edo is the first multiple of 12 to have a patent val fifth that does not correspond to the 12edo fifth of 700 cents. It is strong in the 2.9.15.7 subgroup. Beyond that, it is harmonic quality is quite poor for its size.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.89 | -1.70 | +0.40 | -0.06 | -1.32 | +1.78 | +0.19 | -1.11 | -1.36 | -1.55 | -1.35 | +0.45 |
| Relative (%) | +49.2 | -44.2 | +10.5 | -1.7 | -34.3 | +46.3 | +5.0 | -28.8 | -35.3 | -40.3 | -35.1 | +11.7 | |
| Steps (reduced) |
495 (183) |
724 (100) |
876 (252) |
989 (53) |
1079 (143) |
1155 (219) |
1219 (283) |
1275 (27) |
1325 (77) |
1370 (122) |
1411 (163) |
1449 (201) | |
Subsets and supersets
Since 312 factors into 23 × 3 × 13, 312edo has subset edos 2, 3, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, and 156. 624edo, which doubles it, provides the much needed correction to many of the lower harmonics.