12276edo
| ← 12275edo | 12276edo | 12277edo → |
(semiconvergent)
12276 is a strong 11-limit system, with a lower 11-limit relative error than any lower division aside from 6691. 12276 tempers out the atom, so that the Pythagorean and syntonic commas an be approximated by 12 and 11 schismas respectively. In addition, 12276edo tempers out the septimal ruthenia, meaning that 64/63 is exactly 1/44 of the octave, or 279 primas.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0000 | +0.0010 | -0.0087 | +0.0017 | +0.0393 | +0.0299 | +0.0432 | -0.0241 | +0.0416 | +0.0280 |
| Relative (%) | +0.0 | +0.0 | +1.1 | -8.9 | +1.7 | +40.2 | +30.6 | +44.2 | -24.7 | +42.5 | +28.6 | |
| Steps (reduced) |
12276 (0) |
19457 (7181) |
28504 (3952) |
34463 (9911) |
42468 (5640) |
45427 (8599) |
50178 (1074) |
52148 (3044) |
55531 (6427) |
59637 (10533) |
60818 (11714) | |
Interval size measure
12276edo factors as 22 × 32 × 11 × 31, and among its divisors are 12, 22, 31, 99 and 198. This creates a unit known as the prima, useful for measurement of 11-limit intervals and commas. The Pythagorean comma is represented by 240 prima, and the syntonic comma by 220. A prima is almost exactly three tuning units.