228edo
| ← 227edo | 228edo | 229edo → |
It is the first merger of 12edo and 19edo, and its step size is the difference between 12edo's and 19edo's fifths. The equal temperament tempers out the Pythagorean comma, 531441/524288, in the 3-limit, and 225/224 and 250047/250000 in the 7-limit, so that it supports 7-limit compton temperament and in fact provides the optimal patent val. In the 11-limit it tempers out 225/224, 441/440, 1375/1372 and 4375/4356, so that it supports 11-limit compton. Aside from the Pythagorean comma, the 12-comma, it tempers out the enneadeca or 19-tone-comma, and this is reflected in the fact that 228 = 12 × 19.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.96 | -2.10 | -0.40 | +1.35 | +1.31 | +1.58 | +1.20 | +0.31 | +2.49 | -2.36 | -1.96 |
| Relative (%) | -37.1 | -40.0 | -7.7 | +25.7 | +25.0 | +30.0 | +22.9 | +5.8 | +47.3 | -44.8 | -37.2 | |
| Steps (reduced) |
361 (133) |
529 (73) |
640 (184) |
723 (39) |
789 (105) |
844 (160) |
891 (207) |
932 (20) |
969 (57) |
1001 (89) |
1031 (119) | |