1edo: Difference between revisions

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{{interwiki

| de = ~~1edo~~

| de = 1-EDO

| en = 1edo

| es = 1-EDO

| ja =

| ro = 1DEO

}}

'''1 equal ~~division~~ of the octave''' ('''1edo''') is the [[tuning system]] that contains a single ~~note~~ and ~~the~~ [[octave]]s above and below that ~~note~~.

'''1 equal divisions of the octave''' (abbreviated '''1edo'''), '''1-tone equal temperament''' ('''1tet'''), or '''1 equal temperament''' ('''1et'''), when viewed under a [[regular temperament]] perspective, is the [[tuning system]] that contains a single pitch and pitches any whole number of [[octave]]s above and below that pitch. Each step of 1edo represents a frequency ratio of [[2/1]], or exactly the octave.

== Theory ==

One note repeated in octaves is an example of a [[trivial temperament]], it is ~~even a system that demonstrates~~ trivial ~~examples~~ of [[~~telicity~~]]. That said, it ~~is actually useful in~~ some ~~cases from a~~ musical ~~standpoint~~, particularly as a subset of ~~larger EDOs~~.

One note repeated in octaves is an example of a [[trivial temperament]] (specifically, it is the trivial temperament of the [[2-limit]]); most existing styles of music would find little use for a single set of octaves. That said, it does retain some musical value, particularly as 1edo is contained as a subset of every [[edo]]. In terms of [[JI]] representation, all [[prime harmonic]]s but 2 are tempered to some amount of octaves.

The first piece of ''Musica ricercata'' by György Ligeti simulates 1edo by playing only one pitch class (A) throughout different octaves on the piano, though the piano is not itself tuned to 1edo. The last chord of the piece uses another pitch class (D), breaking the pattern.

The first piece of ''Musica ricercata'' by {{w|György Ligeti}} simulates 1edo by playing only one pitch class (A) throughout different octaves on the piano, though the piano is not itself tuned to 1edo. The last chord of the piece uses another pitch class (D), breaking the pattern.

1edo is equivalent to the [[2-limit]], [[1-odd-limit]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO|1afdo]] and [[IFDO|1ifdo]]).

=== Odd harmonics ===

== Music ==

; [[Blendy Wave]]

* [https://www.youtube.com/watch?v=zHCvfgWA2Sg ''Octaves Only''] (2023)

* [https://www.youtube.com/watch?v=Fhv78-uO5vo ''PolyTech''] (2023)

; [[Francium]]

* [https://www.youtube.com/watch?v=qCYuoq2l6Qc ''E''] (2022)

; [[Frédéric Gagné]]

* ''Play "Do"'' (2021) – [[:File:0010 - Play Do.mp3|play]] | [https://musescore.com/fredg999/play-do score]

; [[User:Wendy_gunk|Wendy Gunk]]

* [https://www.youtube.com/watch?v=YpNh8CNS4tc ''1edo howard''] (2025)

~~'''[[User:Fredg999~~|~~Frédéric Gagné]]'''~~

{{Wikipedia|Musica ricercata #I. Sostenuto – Misurato – Prestissimo}}

* [[:File:0010 - Play Do.~~mp3|''Play "Do"'']] (2021) ([https://musescore.com/fredg999/play-do MuseScore.com])~~

~~'''György Ligeti''' (~~[[Wikipedia:György Ligeti|~~Wikipedia~~]])

; [[Wikipedia:György Ligeti|György Ligeti]]

* [https://soundcloud.com/elizamccarthy/ligeti-musica-ricercata-i ''Musica ricercata'': I. Sostenuto - Misurato - Prestissimo] (~~1951-1953) ([[Wikipedia:Musica ricercata#I. Sostenuto %E2%80%93 Misurato %E2%80%93 Prestissimo|Wikipedia]]~~)

* [https://soundcloud.com/elizamccarthy/ligeti-musica-ricercata-i ''Musica ricercata'': I. Sostenuto – Misurato – Prestissimo] (1951–1953)

'''~~Mandrake~~'''

; [[Mandrake]]

* [https://www.newgrounds.com/audio/listen/1114156 ~~''One Note To Tell A Story''~~] ~~(2022) (~~[https://www.youtube.com/watch?v=mDSj8SwBHRk YouTube])

* ''One Note To Tell A Story'' (2022) – [https://www.newgrounds.com/audio/listen/1114156 Newgrounds] | [https://www.youtube.com/watch?v=mDSj8SwBHRk YouTube]

~~'''~~NullPointerException Music~~'''~~

; [[NullPointerException Music]]

* [https://youtu.be/kRMU-dNOs-w "Cohesion"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)

~~'''STC_1001'''~~

; [[User:Phanomium|Phanomium]]

* [https://~~soundcloud~~.com/~~sexytoadsandfrogsfriendcircle/1-stc-s1001-neainaz~~ "Neainaz Antithetica, Theme"], from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''] (2021) [https://sexytoadsandfrogsfriendcircle.bandcamp.com/track/1-neainaz-antithetica-theme (~~Bandcamp~~)]

* [https://www.youtube.com/watch?v=A1XppPdwGJc ''Singularity''] (2024)

; [[STC_1001]]

* "Neainaz Antithetica, Theme", from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''] (2021) – [https://soundcloud.com/sexytoadsandfrogsfriendcircle/1-stc-s1001-neainaz SoundCloud] | [https://sexytoadsandfrogsfriendcircle.bandcamp.com/track/1-neainaz-antithetica-theme Bandcamp]

; [[Chris Vaisvil]]

* [https://www.youtube.com/watch?v=EAutHhRv3Gg ''0-EDO for Orchestra''] (2021) (despite the title, actually in 1edo)

== See also ==

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* [[Octave]]

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

[[Category:Trivial temperaments]]

[[Category:2-limit]]

[[Category:~~Macrotonal~~]]

[[Category:1-odd-limit]]

[[Category:~~Unison~~]]

[[Category:Just intonation scales]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{interwiki
-| de = 1edo
+| de = 1-EDO
 | en = 1edo
 | es = 1-EDO
 | ja =
+| ro = 1DEO
 }}
 {{Infobox ET}}
-'''1 equal division of the octave''' ('''1edo''') is the [[tuning system]] that contains a single note and the [[octave]]s above and below that note.
+'''1 equal divisions of the octave''' (abbreviated '''1edo'''), '''1-tone equal temperament''' ('''1tet'''), or '''1 equal temperament''' ('''1et'''), when viewed under a [[regular temperament]] perspective, is the [[tuning system]] that contains a single pitch and pitches any whole number of [[octave]]s above and below that pitch. Each step of 1edo represents a frequency ratio of [[2/1]], or exactly the octave.
 == Theory ==
-One note repeated in octaves is an example of a [[trivial temperament]], it is even a system that demonstrates trivial examples of [[telicity]]. That said, it is actually useful in some cases from a musical standpoint, particularly as a subset of larger EDOs.
+One note repeated in octaves is an example of a [[trivial temperament]] (specifically, it is the trivial temperament of the [[2-limit]]); most existing styles of music would find little use for a single set of octaves. That said, it does retain some musical value, particularly as 1edo is contained as a subset of every [[edo]]. In terms of [[JI]] representation, all [[prime harmonic]]s but 2 are tempered to some amount of octaves.
-The first piece of ''Musica ricercata'' by György Ligeti simulates 1edo by playing only one pitch class (A) throughout different octaves on the piano, though the piano is not itself tuned to 1edo. The last chord of the piece uses another pitch class (D), breaking the pattern.
+The first piece of ''Musica ricercata'' by {{w|György Ligeti}} simulates 1edo by playing only one pitch class (A) throughout different octaves on the piano, though the piano is not itself tuned to 1edo. The last chord of the piece uses another pitch class (D), breaking the pattern.
+edo is equivalent to the [[2-limit]], [[1-odd-limit]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO|1afdo]] and [[IFDO|1ifdo]]).
+=== Odd harmonics ===
+{{Harmonics in equal|1}}
 == Music ==
-{{See also|:Category:1edo tracks}}
+{{Catrel|1edo tracks}}
+; [[Blendy Wave]]
+* [https://www.youtube.com/watch?v=zHCvfgWA2Sg ''Octaves Only''] (2023)
+* [https://www.youtube.com/watch?v=Fhv78-uO5vo ''PolyTech''] (2023)
+; [[Francium]]
+* [https://www.youtube.com/watch?v=qCYuoq2l6Qc ''E''] (2022)
+; [[Frédéric Gagné]]
+* ''Play "Do"'' (2021) – [[:File:0010 - Play Do.mp3|play]] | [https://musescore.com/fredg999/play-do score]
+; [[User:Wendy_gunk|Wendy Gunk]]
+* [https://www.youtube.com/watch?v=YpNh8CNS4tc ''1edo howard''] (2025)
-'''[[User:Fredg999|Frédéric Gagné]]'''
+{{Wikipedia|Musica ricercata #I. Sostenuto – Misurato – Prestissimo}}
-* [[:File:0010 - Play Do.mp3|''Play "Do"'']] (2021) ([https://musescore.com/fredg999/play-do MuseScore.com])
-'''György Ligeti''' ([[Wikipedia:György Ligeti|Wikipedia]])
+; [[Wikipedia:György Ligeti|György Ligeti]]
-* [https://soundcloud.com/elizamccarthy/ligeti-musica-ricercata-i ''Musica ricercata'': I. Sostenuto - Misurato - Prestissimo] (1951-1953) ([[Wikipedia:Musica ricercata#I. Sostenuto %E2%80%93 Misurato %E2%80%93 Prestissimo|Wikipedia]])
+* [https://soundcloud.com/elizamccarthy/ligeti-musica-ricercata-i ''Musica ricercata'': I. Sostenuto – Misurato – Prestissimo] (1951–1953)
-'''Mandrake'''
+; [[Mandrake]]
-* [https://www.newgrounds.com/audio/listen/1114156 ''One Note To Tell A Story''] (2022) ([https://www.youtube.com/watch?v=mDSj8SwBHRk YouTube])
+* ''One Note To Tell A Story'' (2022) – [https://www.newgrounds.com/audio/listen/1114156 Newgrounds] | [https://www.youtube.com/watch?v=mDSj8SwBHRk YouTube]
-'''NullPointerException Music'''
+; [[NullPointerException Music]]
 * [https://youtu.be/kRMU-dNOs-w "Cohesion"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
-'''STC_1001'''
+; [[User:Phanomium|Phanomium]]
-* [https://soundcloud.com/sexytoadsandfrogsfriendcircle/1-stc-s1001-neainaz "Neainaz Antithetica, Theme"], from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''] (2021) [https://sexytoadsandfrogsfriendcircle.bandcamp.com/track/1-neainaz-antithetica-theme (Bandcamp)]
+* [https://www.youtube.com/watch?v=A1XppPdwGJc ''Singularity''] (2024)
+; [[STC_1001]]
+* "Neainaz Antithetica, Theme", from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''] (2021) – [https://soundcloud.com/sexytoadsandfrogsfriendcircle/1-stc-s1001-neainaz SoundCloud] | [https://sexytoadsandfrogsfriendcircle.bandcamp.com/track/1-neainaz-antithetica-theme Bandcamp]
+; [[Chris Vaisvil]]
+* [https://www.youtube.com/watch?v=EAutHhRv3Gg ''0-EDO for Orchestra''] (2021) (despite the title, actually in 1edo)
 == See also ==
@@ Line 35: / Line 59: @@
 * [[Octave]]
-[[Category:Equal divisions of the octave|#]] <!-- 1-digit number -->
+[[Category:Trivial temperaments]]
 [[Category:2-limit]]
-[[Category:Macrotonal]]
+[[Category:1-odd-limit]]
-[[Category:Unison]]
+[[Category:Just intonation scales]]
+[[Category:Listen]]