113edo: Difference between revisions

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~~The '''113 equal divisions of the octave''' ('''113edo'''), or the '''113(-tone) equal temperament''' ('''113tet''', '''113et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO|~~equal division of the octave]] into~~ 113 ~~parts of about 10.6 [[cent]]s each.~~

== Theory ==

113edo is distinctly [[consistent]] in the [[13-odd-limit]] with a flat tendency. As a temperament, it [[tempers out]] the [[amity comma]] and the [[ampersand]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and 1071875/1062882 in the [[7-limit]]; [[243/242]], [[385/384]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[325/324]], [[364/363]], [[729/728]], and 1625/1617 in the [[13-limit]]. It notably [[support]]s the 5-limit [[amity]] temperament, 7-limit [[amicable]] temperament, 7- and 11-limit [[miracle]] temperament, and 13-limit [[manna]] temperament.

~~113edo is the 30th [[prime EDO]].~~

=== Prime harmonics ===

=== ~~Prime harmonics~~ ===

=== Subsets and supersets ===

~~{{Primes in~~ edo~~|113}}~~

113edo is the 30th [[prime edo]].

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

|+Table of rank-2 temperaments by generator

! Periods per ~~octave~~

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

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| 339.82

| 243/200

| [[~~Amity]] / [[houborizic~~]]

| [[Houborizic]]

|-

| 1

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| [[Gaster temperament|Gaster]]

|}

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

~~[[Category:Prime EDO]]~~

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 {{Infobox ET}}
-The '''113 equal divisions of the octave''' ('''113edo'''), or the '''113(-tone) equal temperament''' ('''113tet''', '''113et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 113 parts of about 10.6 [[cent]]s each.
+{{EDO intro|113}}
 == Theory ==
 edo is distinctly [[consistent]] in the [[13-odd-limit]] with a flat tendency. As a temperament, it [[tempers out]] the [[amity comma]] and the [[ampersand]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and 1071875/1062882 in the [[7-limit]]; [[243/242]], [[385/384]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[325/324]], [[364/363]], [[729/728]], and 1625/1617 in the [[13-limit]]. It notably [[support]]s the 5-limit [[amity]] temperament, 7-limit [[amicable]] temperament, 7- and 11-limit [[miracle]] temperament, and 13-limit [[manna]] temperament.
-edo is the 30th [[prime EDO]].
+=== Prime harmonics ===
+{{Harmonics in equal|113}}
-=== Prime harmonics ===
+=== Subsets and supersets ===
-{{Primes in edo|113}}
+edo is the 30th [[prime edo]].
 == 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 60: / Line 61: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
@@ Line 118: / Line 119: @@
 | 339.82
 | 243/200
-| [[Amity]] / [[houborizic]]
+| [[Houborizic]]
 |-
 | 1
@@ Line 144: / Line 145: @@
 | [[Gaster temperament|Gaster]]
 |}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
-[[Category:Prime EDO]]