296edo: Difference between revisions

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~~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 ([[ragisma]]), 16875/16807 (mirkwai), and 118098/117649 (stearnsma), [[support~~|supporting~~]] 7-limit [[octoid]] ~~temperament~~. In the 11-limit, [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[6250/6237]] and [[9801/9800]]; in the 13-limit, [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], and [[6656/6655]], so that it also supports the 11- and 13-limit versions of octoid. It allows [[swetismic chords]] and [[squbemic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.

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 ([[ragisma]]), 16875/16807 (mirkwai), and 118098/117649 (stearnsma), [[support]]ing 7-limit [[octoid]] and [[sabric]]. In the 11-limit, [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[6250/6237]] and [[9801/9800]]; in the 13-limit, [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], and [[6656/6655]], so that it also supports the 11- and 13-limit versions of octoid. It allows [[swetismic chords]] and [[squbemic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.

~~296 is divisible by {{EDOs| 2, 4, 8, 37, 74 and 148 }}~~.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 296 factors into 23 × 37, 296edo has subset edos {{EDOs| 2, 4, 8, 37, 74 and 148 }}.

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" | Subgroup

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~stretch~~ (¢)

! rowspan="2" | Optimal 8ve Stretch (¢)

! colspan="2" | Tuning ~~error~~

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

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|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

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| 182.43

| 10/9

| [[~~Minortone]] / [[mitonic~~]]

| [[Mitonic]]

|-

| 1

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| 271.62

| 75/64

| [[~~Orson]] / [[sabric~~]]

| [[Sabric]]

|-

| 1

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Line 104:

|}

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

[[Category:Sabric]]

~~[[Category:Orson~~]]

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 {{Infobox ET}}
-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.
+{{EDO intro|296}}
 == 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 ([[ragisma]]), 16875/16807 (mirkwai), and 118098/117649 (stearnsma), [[support|supporting]] 7-limit [[octoid]] temperament. In the 11-limit, [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[6250/6237]] and [[9801/9800]]; in the 13-limit, [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], and [[6656/6655]], so that it also supports the 11- and 13-limit versions of octoid. It allows [[swetismic chords]] and [[squbemic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.
+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 ([[ragisma]]), 16875/16807 (mirkwai), and 118098/117649 (stearnsma), [[support]]ing 7-limit [[octoid]] and [[sabric]]. In the 11-limit, [[540/539]], 1375/1372, [[3025/3024]], [[4000/3993]], [[6250/6237]] and [[9801/9800]]; in the 13-limit, [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], and [[6656/6655]], so that it also supports the 11- and 13-limit versions of octoid. It allows [[swetismic chords]] and [[squbemic chords]] in the 13-odd-limit, in addition to [[nicolic chords]] in the 15-odd-limit.
-is divisible by {{EDOs| 2, 4, 8, 37, 74 and 148 }}.
 === Prime harmonics ===
 {{Harmonics in equal|296|columns=11}}
+=== Subsets and supersets ===
+Since 296 factors into 2<sup>3</sup> × 37, 296edo has subset edos {{EDOs| 2, 4, 8, 37, 74 and 148 }}.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Comma list|Comma List]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve stretch (¢)
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
-! colspan="2" | Tuning error
+! colspan="2" | Tuning Error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 61: / Line 62: @@
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
@@ Line 70: / Line 71: @@
 | 182.43
 | 10/9
-| [[Minortone]] / [[mitonic]]
+| [[Mitonic]]
 |-
 | 1
@@ Line 76: / Line 77: @@
 | 271.62
 | 75/64
-| [[Orson]] / [[sabric]]
+| [[Sabric]]
 |-
 | 1
@@ Line 103: / Line 104: @@
 |}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+[[Category:Sabric]]
-[[Category:Orson]]