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.

{{Infobox ET

| Prime factorization = 19 × 3 × 2<sup>2</sup>

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| Consistency = 7

}}

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]]. 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 ===

[[Category:Equal divisions of the octave|###]]

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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.
 {{Infobox ET
 | Prime factorization = 19 × 3 × 2<sup>2</sup>
@@ Line 8: / Line 7: @@
 | Consistency = 7
 }}
+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]]. 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 ===
+{{Harmonics in equal|228}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->