296edo: Difference between revisions

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The '''296 equal temperament''' ~~divides~~ the octave into 296 ~~equal~~ parts of 4.~~054 cents~~ each.

{{Infobox ET

| Prime factorization = 2<sup>3</sup> × 37

| Step size = 4.05405¢

| Fifth = 173\296 (702.35¢)

| Semitones = 27:23 (109.46¢ : 93.24¢)

| Consistency = 15

}}

The '''296 equal divisions of the octave''' ('''296edo'''), or the '''296(-tone) equal temperament''' ('''296tet''', '''296et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 296 parts of about 4.05 [[cent]]s each.

== Theory ==

In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo| -16 35 -17 }}. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out [[4375/4374]] and 16875/16807, supporting 7-limit [[octoid]] temperament. In the 11-limit, it tempers out 1375/1372, [[6250/6237]], [[540/539]], [[4000/3993]] and [[3025/3024]], and in the 13-limit [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], so that it also supports the 11- and 13-limit versions of octoid.

@@ Line 1: / Line 1: @@
-The '''296 equal temperament''' divides the octave into 296 equal parts of 4.054 cents each.
+{{Infobox ET
+| Prime factorization = 2<sup>3</sup> × 37
+| Step size = 4.05405¢
+| Fifth = 173\296 (702.35¢)
+| Semitones = 27:23 (109.46¢ : 93.24¢)
+| Consistency = 15
+}}
+The '''296 equal divisions of the octave''' ('''296edo'''), or the '''296(-tone) equal temperament''' ('''296tet''', '''296et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 296 parts of about 4.05 [[cent]]s each.
+== Theory ==
 In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo| -16 35 -17 }}. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out [[4375/4374]] and 16875/16807, supporting 7-limit [[octoid]] temperament. In the 11-limit, it tempers out 1375/1372, [[6250/6237]], [[540/539]], [[4000/3993]] and [[3025/3024]], and in the 13-limit [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], so that it also supports the 11- and 13-limit versions of octoid.