1224edo: Difference between revisions
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{{EDO intro|1224}} | {{EDO intro|1224}} | ||
== | 1224edo is [[Enfactoring|enfactored]] in the 11-limit, with the same tuning as [[612edo]], but it corrects the harmonics [[13/1|13]] and [[17/1|17]] to work better with the other harmonics. It provides the [[optimal patent val]] for the 19-limit semihemiennealimmal temperament with fine tunes of 23, 29 and 31. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|1224}} | {{Harmonics in equal|1224}} | ||
1224edo | |||
=== Subsets and supersets === | |||
Since 1224 factors into 2<sup>3</sup> × 3<sup>2</sup> × 17, 1224edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, and 612 }}. | |||
Revision as of 06:49, 10 June 2023
| ← 1223edo | 1224edo | 1225edo → |
1224edo is enfactored in the 11-limit, with the same tuning as 612edo, but it corrects the harmonics 13 and 17 to work better with the other harmonics. It provides the optimal patent val for the 19-limit semihemiennealimmal temperament with fine tunes of 23, 29 and 31.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.006 | -0.039 | -0.198 | -0.338 | -0.332 | -0.053 | -0.454 | +0.157 | -0.165 | +0.062 |
| Relative (%) | +0.0 | +0.6 | -4.0 | -20.2 | -34.4 | -33.8 | -5.5 | -46.3 | +16.0 | -16.9 | +6.4 | |
| Steps (reduced) |
1224 (0) |
1940 (716) |
2842 (394) |
3436 (988) |
4234 (562) |
4529 (857) |
5003 (107) |
5199 (303) |
5537 (641) |
5946 (1050) |
6064 (1168) | |
Subsets and supersets
Since 1224 factors into 23 × 32 × 17, 1224edo has subset edos 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, and 612.