228edo
Jump to navigation
Jump to search
Prime factorization
22 × 3 × 19
Step size
5.26316¢
Fifth
133\228 (700¢) (→7\12)
Semitones (A1:m2)
19:19 (100¢ : 100¢)
Dual sharp fifth
134\228 (705.263¢) (→67\114)
Dual flat fifth
133\228 (700¢) (→7\12)
Dual major 2nd
39\228 (205.263¢) (→13\76)
Consistency limit
7
Distinct consistency limit
7
| ← 227edo | 228edo | 229edo → |
The 228 equal division divides the octave into 228 equal parts of 5.263 cents each. It is the first merger of 12edo and 19edo, and its step size is the difference between 12edo's and 19edo's fifths. It 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 | -40 | -8 | +26 | +25 | +30 | +23 | +6 | +47 | -45 | -37 | |
| Steps (reduced) |
361 (133) |
529 (73) |
640 (184) |
723 (39) |
789 (105) |
844 (160) |
891 (207) |
932 (20) |
969 (57) |
1001 (89) |
1031 (119) | |