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 | 1224edo is [[Enfactoring|enfactored]] in the 11-limit, with the same tuning as [[612edo]], but it corrects the [[harmonic]]s [[13/1|13]] and [[17/1|17]] to work better with the flat tendency of the lower harmonics. It provides the [[optimal patent val]] for the 19-limit semihemiennealimmal temperament with fine tunes of [[23/1|23]], [[29/1|29]] and [[31/1|31]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 1224 factors into | Since 1224 factors into {{factorization|1224}}, 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 10:03, 31 October 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 flat tendency of the lower 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.