228edo: Difference between revisions

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{{Infobox ET

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

~~| Step size = 5.26316¢~~

~~| Sharp fifth = 134\228 (705.26¢)~~

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.

~~| Flat fifth = 133\228 (700.00¢) (→~~ [[12edo~~|7\12~~]])

~~| Major 2nd = 39\228 (205~~.~~26¢)~~

~~| 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 [[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|###]] ~~

[[Category:Compton]]

@@ Line 1: / Line 1: @@
-{{Infobox ET
+{{Infobox ET}}
-| Prime factorization = 2<sup>2</sup> × 3 × 19
+{{ED intro}}
-| Step size = 5.26316¢
-| Sharp fifth = 134\228 (705.26¢)
+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.
-| Flat fifth = 133\228 (700.00¢) (→ [[12edo|7\12]])
-| Major 2nd = 39\228 (205.26¢)
-| 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 [[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 -->
 [[Category:Compton]]