94edo: Difference between revisions

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~~The '''~~94 equal divisions of the octave''' ('''94edo'''), or the '''94(-tone) equal temperament''' ('''94tet''', '''94et''') when viewed from a [[regular temperament]] perspective, results from dividing the [[octave]] into 94 [[equal]]ly-sized steps, where each step is about 12.8 [[cent]]s.

== Theory ==

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The list of 23-limit commas it tempers out is huge, but it is worth noting that it tempers out [[32805/32768]] and is thus a [[schismatic]] system, that it tempers out [[225/224]] and [[385/384]] and so is a [[marvel]] system, and that it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[275/273]], and for a number of other temperaments, such as [[isis]].

94edo is an excellent ~~EDO~~ for [[Carlos Beta]] scale, since the difference between 5 steps of 94edo and 1 step of Carlos Beta is only -0.00314534 cents.

94edo is an excellent edo for [[Carlos Beta]] scale, since the difference between 5 steps of 94edo and 1 step of Carlos Beta is only -0.00314534 cents.

=== Prime harmonics ===

== Intervals ==

== 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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|}

94et is lower in relative error than any previous equal temperaments in the 23-limit, and the ~~next ET~~ that does better in this subgroup is 193.

94et is lower in relative error than any previous equal temperaments in the 23-limit, and the equal temperament that does better in this subgroup is 193.

=== Rank-2 temperaments ===

{| class="wikitable center-all right-3 left-5"

! Periods per ~~octave~~

! Periods per 8ve

! Generator

! Cents

! Associated ~~ratio~~

! Associated Ratio

! Temperament

|-

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* [[Garibaldi17]]

Since 94edo has a step of 12.766 cents, it also allows one to use its ~~MOS~~ scales as circulating temperaments and is the first edo to allows one to use a ~~Mohajira~~, ~~Pajara~~ or ~~Miracle MOS~~ scale a as circulating temperament{{clarify}}.

Since 94edo has a step of 12.766 cents, it also allows one to use its mos scales as circulating temperaments and is the first edo to allows one to use a nohajira, pajara or miracle mos scale a as circulating temperament{{clarify}}.

{| class="wikitable mw-collapsible mw-collapsed"

|+Circulating temperaments in 94edo

|+ style=white-space:nowrap | Circulating temperaments in 94edo

!Tones

!Pattern

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|}

~~[[Category:94edo| ]] ~~

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

[[Category:Garibaldi]]

[[Category:Marvel]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''94 equal divisions of the octave''' ('''94edo'''), or the '''94(-tone) equal temperament''' ('''94tet''', '''94et''') when viewed from a [[regular temperament]] perspective, results from dividing the [[octave]] into 94 [[equal]]ly-sized steps, where each step is about 12.8 [[cent]]s.
+{{EDO intro|94}}
 == Theory ==
@@ Line 7: / Line 7: @@
 The list of 23-limit commas it tempers out is huge, but it is worth noting that it tempers out [[32805/32768]] and is thus a [[schismatic]] system, that it tempers out [[225/224]] and [[385/384]] and so is a [[marvel]] system, and that it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[275/273]], and for a number of other temperaments, such as [[isis]].
-edo is an excellent EDO for [[Carlos Beta]] scale, since the difference between 5 steps of 94edo and 1 step of Carlos Beta is only -0.00314534 cents.
+edo is an excellent edo for [[Carlos Beta]] scale, since the difference between 5 steps of 94edo and 1 step of Carlos Beta is only -0.00314534 cents.
 === Prime harmonics ===
-{{Primes in edo|94|columns=11}}
+{{Harmonics in equal|94|columns=11}}
 == Intervals ==
-{{main| Table of 94edo intervals }}
+{{Main| Table of 94edo intervals }}
 == 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 83: / Line 83: @@
 |}
-et is lower in relative error than any previous equal temperaments in the 23-limit, and the next ET that does better in this subgroup is 193.
+et is lower in relative error than any previous equal temperaments in the 23-limit, and the equal temperament that does better in this subgroup is 193.
 === Rank-2 temperaments ===
 {| class="wikitable center-all right-3 left-5"
-! Periods<br>per octave
+! Periods<br>per 8ve
 ! Generator
 ! Cents
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperament
 |-
@@ Line 183: / Line 183: @@
 * [[Garibaldi17]]
-Since 94edo has a step of 12.766 cents, it also allows one to use its MOS scales as circulating temperaments and is the first edo to allows one to use a Mohajira, Pajara or Miracle MOS scale a as circulating temperament{{clarify}}.
+Since 94edo has a step of 12.766 cents, it also allows one to use its mos scales as circulating temperaments and is the first edo to allows one to use a nohajira, pajara or miracle mos scale a as circulating temperament{{clarify}}.
 {| class="wikitable mw-collapsible mw-collapsed"
-|+Circulating temperaments in 94edo
+|+ style=white-space:nowrap | Circulating temperaments in 94edo
 !Tones
 !Pattern
@@ Line 419: / Line 419: @@
 |}
-[[Category:94edo| ]] <!-- main article -->
-[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
 [[Category:Garibaldi]]
 [[Category:Marvel]]