130edo: Difference between revisions

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{{Infobox ET

| Prime factorization = 2 × 5 × 13

| Step size = 9.~~23077¢~~

| Step size = 9.231¢

| Fifth = 76\130 (701.~~54¢~~) (→ [[65edo|38\65]])

| Fifth = 76\130 (701.538¢) (→ [[65edo|38\65]])

| Major 2nd = 22\130 (203¢)

| ~~Minor 2nd~~ = 10~~\130~~ (92¢)

| Semitones = 12:10 (111¢ : 92¢)

| ~~Augmented 1sn~~ = ~~12\130 (111¢)~~

| Consistency = 15

}}

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== Theory ==

130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the rank-three temperament [[~~Breed family #Jove|~~jove]], tempering out [[243/242]] and [[441/440]], plus [[364/363]] for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic temperaments #Harry|harry]] temperaments.

130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the rank-three temperament [[jove]], tempering out [[243/242]] and [[441/440]], plus [[364/363]] for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic temperaments #Harry|harry]] temperaments.

=== Prime harmonics ===

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== Intervals ==

{| class="wikitable center-all right-2 left-3"

|-

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== Scales ==

{| class="wikitable"

|+14-tone temperament of "Narrative Wars"<br>as an example of using ~~130-EDO~~:

|+14-tone temperament of "Narrative Wars"<br>as an example of using 130edo:

! Step

! Cents

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== Music ==

* [http://www.archive.org/details/TheParadiseOfCantor The Paradise of Cantor] [http://www.archive.org/download/TheParadiseOfCantor/cantor.mp3 play] by [[Gene Ward Smith]]

* [https://youtu.be/30UQVYWnsDU "Narrative Wars"] by Sevish (uses a 14-tone (13 7 9 9 9 7 13 9 7 13 5 13 7 9) subset of ~~130-EDO~~, from the 2016 compilation album "Next Xen")

* [https://youtu.be/30UQVYWnsDU "Narrative Wars"] by Sevish (uses a 14-tone (13 7 9 9 9 7 13 9 7 13 5 13 7 9) subset of 130edo, from the 2016 compilation album "Next Xen")

[[Category:Equal divisions of the octave]]

[[Category:Harry]]

[[Category:~~Hemischismic~~]]

[[Category:Hemischis]]

[[Category:Hemiwürschmidt]]

~~[[Category:Listen]]~~

[[Category:Sesquiquartififths]]

[[Category:Zeta]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET
 | Prime factorization = 2 × 5 × 13
-| Step size = 9.23077¢
+| Step size = 9.231¢
-| Fifth = 76\130 (701.54¢) (→ [[65edo|38\65]])
+| Fifth = 76\130 (701.538¢) (→ [[65edo|38\65]])
 | Major 2nd = 22\130 (203¢)
-| Minor 2nd = 10\130 (92¢)
+| Semitones = 12:10 (111¢ : 92¢)
-| Augmented 1sn = 12\130  (111¢)
+| Consistency = 15
 }}
@@ Line 11: / Line 11: @@
 == Theory ==
-edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the rank-three temperament [[Breed family #Jove|jove]], tempering out [[243/242]] and [[441/440]], plus [[364/363]] for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic temperaments #Harry|harry]] temperaments.
+edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischis]]. It also can be used to tune the rank-three temperament [[jove]], tempering out [[243/242]] and [[441/440]], plus [[364/363]] for the 13-limit and [[595/594]] for the 17-limit. It gives the [[optimal patent val]] for 11-limit [[hemiwürschmidt]] and [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic temperaments #Harry|harry]] temperaments.
 === Prime harmonics ===
@@ Line 17: / Line 17: @@
 == Intervals ==
 {| class="wikitable center-all right-2 left-3"
 |-
@@ Line 430: / Line 429: @@
 == Scales ==
 {| class="wikitable"
-|+14-tone temperament of "Narrative Wars"<br>as an example of using 130-EDO:
+|+14-tone temperament of "Narrative Wars"<br>as an example of using 130edo:
 ! Step
 ! Cents
@@ Line 494: / Line 493: @@
 == Music ==
 * [http://www.archive.org/details/TheParadiseOfCantor The Paradise of Cantor] [http://www.archive.org/download/TheParadiseOfCantor/cantor.mp3 play] by [[Gene Ward Smith]]
-* [https://youtu.be/30UQVYWnsDU "Narrative Wars"] by Sevish (uses a 14-tone (13 7 9 9 9 7 13 9 7 13 5 13 7 9) subset of 130-EDO, from the 2016 compilation album "Next Xen")
+* [https://youtu.be/30UQVYWnsDU "Narrative Wars"] by Sevish (uses a 14-tone (13 7 9 9 9 7 13 9 7 13 5 13 7 9) subset of 130edo, from the 2016 compilation album "Next Xen")
 [[Category:Equal divisions of the octave]]
 [[Category:Harry]]
-[[Category:Hemischismic]]
+[[Category:Hemischis]]
 [[Category:Hemiwürschmidt]]
-[[Category:Listen]]
 [[Category:Sesquiquartififths]]
 [[Category:Zeta]]
+[[Category:Listen]]