228edo: Difference between revisions

(12 intermediate revisions by 6 users not shown)

Line 1:

~~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 ~~240047~~/~~240000~~ in the 7-limit, so that it ~~supports~~ 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|~~enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 * 19.

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 [[tempering out|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 [[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:Compton]]

@@ Line 1: / Line 1: @@
-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 240047/240000 in the 7-limit, so that it supports 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|enneadeca]] or 19-tone-comma, and this is reflected in the fact that 228 = 12 * 19.
+{{Infobox ET}}
+{{ED intro}}
+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 [[tempering out|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 [[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:Compton]]