1224edo
Jump to navigation
Jump to search
Prime factorization
23 × 32 × 17
Step size
0.980392¢
Fifth
716\1224 (701.961¢) (→179\306)
Semitones (A1:m2)
116:92 (113.7¢ : 90.2¢)
Consistency limit
21
Distinct consistency limit
21
| ← 1223edo | 1224edo | 1225edo → |
1224 equal divisions of the octave (1224edo), or 1224-tone equal temperament (1224tet), 1224 equal temperament (1224et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1224 equal parts of about 0.98 ¢ each.
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 | +1 | -4 | -20 | -34 | -34 | -5 | -46 | +16 | -17 | +6 | |
| 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.