228edo: Difference between revisions

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| Major 2nd = 38\228 (200¢)
| Major 2nd = 38\228 (200¢)
| Semitones = 38:38 (100¢:100¢)
| Semitones = 38:38 (100¢:100¢)
| Consistency = 5
| Consistency = 7
}}
}}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Revision as of 15:43, 12 September 2022

The 228 equal division divides the octave into 228 equal parts of 5.263 cents each. 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.

← 227edo 228edo 229edo →
Prime factorization 19 × 3 × 22
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