228edo: Difference between revisions
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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 [[support]]s 7-limit [[Pythagorean_family|compton temperament]] and in fact provides the [[Optimal_patent_val|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. | 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 [[support]]s 7-limit [[Pythagorean_family|compton temperament]] and in fact provides the [[Optimal_patent_val|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. | ||
{{Infobox ET | |||
| Prime factorization = 19 × 3 × 2<sup>2</sup> | |||
| Step size = 5.26316¢ | |||
| Fifth = 133\228 (700¢) | |||
| Major 2nd = 38\228 (200¢) | |||
| Semitones = (100¢:100¢) | |||
| Consistency = 5 | |||
}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 15:40, 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 → |