103edo: Difference between revisions

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~~The '''103 equal divisions of the octave''' ('''103edo'''), or the '''103(-tone) equal temperament''' ('''103tet''', '''103et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO|~~equal division of the octave]] into~~ 103 ~~steps of about 11.7 [[cent]]s each.~~

== Theory ==

103edo is a good [[miracle]] tuning, especially for the [[7-limit|7-]] and ~~[[13-limit]] and~~ [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite.

103edo is a good [[miracle]] tuning, especially for the [[7-limit|7-]], and for [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite.

103edo ~~is the 27th [[prime numbers|prime]] edo.~~

In 103edo, all intervals within the 17-odd-limit are [[consistent]], with the sole exception of 9/8 and its octave complement 16/9, which barely miss.

~~In 103-EDO~~, all intervals within the 17-odd-limit are consistent, with the sole exception of 9/8 and its octave complement 16/9, which barely miss.

=== Prime harmonics ===

=== Subsets and supersets ===

103edo is the 27th [[prime edo]].

== Intervals ==

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== 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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| [[Phicordial]]

|-

|1

| 1

|37\103

| 37\103

|431.06

| 431.06

|77/60

| 77/60

|[[Lockerbie]]

| [[Lockerbie]]

|-

| 1

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| 442.708

| 162/125

| [[~~Sensipent]] / [[sensei~~]]

| [[Sensei]]

|-

| 1

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{| class="wikitable"

|+

! colspan="3" |Marvel and Benediction

! colspan="3" | Marvel and Benediction

! colspan="3" |Hemisecordite

! colspan="3" | Hemisecordite

|-

!Degree

! Degree

!cents

! cents

!Difference from 72edo

! Difference from 72edo

!Degree

! Degree

!cents

! cents

!Difference from 62edo

! Difference from 62edo

|-

|1

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== Music ==

* [https://www.youtube.com/watch?v=5pbnmzXAFcM Forest Tribe Dance] by [[User:Francium|Francium]]

* [https://www.youtube.com/watch?v=5pbnmzXAFcM ''Forest Tribe Dance''] by [[User:Francium|Francium]]

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

[[Category:Benediction]]

[[Category:Miracle]]

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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''103 equal divisions of the octave''' ('''103edo'''), or the '''103(-tone) equal temperament''' ('''103tet''', '''103et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 103 steps of about 11.7 [[cent]]s each.
+{{EDO intro|103}}
 == Theory ==
-edo is a good [[miracle]] tuning, especially for the [[7-limit|7-]] and [[13-limit]] and [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite.
+edo is a good [[miracle]] tuning, especially for the [[7-limit|7-]], and for [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite.
-edo is the 27th [[prime numbers|prime]] edo.
+In 103edo, all intervals within the 17-odd-limit are [[consistent]], with the sole exception of 9/8 and its octave complement 16/9, which barely miss.
-In 103-EDO, all intervals within the 17-odd-limit are consistent, with the sole exception of 9/8 and its octave complement 16/9, which barely miss.
 === Prime harmonics ===
 {{Harmonics in equal|103|intervals=prime}}
+=== Subsets and supersets ===
+edo is the 27th [[prime edo]].
 == Intervals ==
@@ Line 231: / Line 232: @@
 == 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 286: / Line 287: @@
 {| 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 346: / Line 347: @@
 | [[Phicordial]]
 |-
-|1
+| 1
-|37\103
+| 37\103
-|431.06
+| 431.06
-|77/60
+| 77/60
-|[[Lockerbie]]
+| [[Lockerbie]]
 |-
 | 1
@@ Line 356: / Line 357: @@
 | 442.708
 | 162/125
-| [[Sensipent]] / [[sensei]]
+| [[Sensei]]
 |-
 | 1
@@ Line 405: / Line 406: @@
 {| class="wikitable"
 |+
-! colspan="3" |Marvel and Benediction
+! colspan="3" | Marvel and Benediction
-! colspan="3" |Hemisecordite
+! colspan="3" | Hemisecordite
 |-
-!Degree
+! Degree
-!cents
+! cents
-!Difference from 72edo
+! Difference from 72edo
-!Degree
+! Degree
-!cents
+! cents
-!Difference from 62edo
+! Difference from 62edo
 |-
 |1
@@ Line 914: / Line 915: @@
 == Music ==
-* [https://www.youtube.com/watch?v=5pbnmzXAFcM Forest Tribe Dance] by [[User:Francium|Francium]]
+* [https://www.youtube.com/watch?v=5pbnmzXAFcM ''Forest Tribe Dance''] by [[User:Francium|Francium]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Benediction]]
 [[Category:Miracle]]
-[[Category:Prime EDO]]