228edo: Difference between revisions

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{{Infobox ET

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

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

| Step size = 5.26316¢

| ~~Fifth~~ = 133\228 (~~700¢~~) (→7\12)

| Sharp fifth = 134\228 (705.26¢)

| Major 2nd = 38\228 (~~200¢)~~

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

~~| Semitones = 38:38 (100¢:100¢~~)

| 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 [[~~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.

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 ===

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

[[Category:Compton]]

@@ Line 1: / Line 1: @@
 {{Infobox ET
-| Prime factorization = 19 × 3 × 2<sup>2</sup>
+| Prime factorization = 2<sup>2</sup> × 3 × 19
 | Step size = 5.26316¢
-| Fifth = 133\228 (700¢) (→7\12)
+| Sharp fifth = 134\228 (705.26¢)
-| Major 2nd = 38\228 (200¢)
+| Flat fifth = 133\228 (700.00¢) (→ [[12edo|7\12]])
-| Semitones = 38:38 (100¢:100¢)
+| 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 [[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.
+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 ===
@@ Line 13: / Line 13: @@
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Compton]]