1224edo
| ← 1223edo | 1224edo | 1225edo → |
1224 equal divisions of the octave (abbreviated 1224edo or 1224ed2), also called 1224-tone equal temperament (1224tet) or 1224 equal temperament (1224et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1224 equal parts of about 0.98 ¢ each. Each step represents a frequency ratio of 21/1224, or the 1224th root of 2.
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 | +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.