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{{interwiki
{{interwiki
| de = 1edo
| de = 1-EDO
| en = 1edo
| en = 1edo
| es = 1-EDO
| es = 1-EDO
| ja =  
| 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.
{{Infobox ET}}
'''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 ==
== 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 ===
{{Harmonics in equal|1}}


== Music ==
== Music ==
{{See also|:Category:1edo tracks}}
{{Catrel|1edo tracks}}
{| class="wikitable sortable"
 
!Title
; [[Blendy Wave]]
!Composer
* [https://www.youtube.com/watch?v=zHCvfgWA2Sg ''Octaves Only''] (2023)
!Year
* [https://www.youtube.com/watch?v=Fhv78-uO5vo ''PolyTech''] (2023)
!Genre
 
!Additional links
; [[Francium]]
|-
* [https://www.youtube.com/watch?v=qCYuoq2l6Qc ''E''] (2022)
|[https://soundcloud.com/elizamccarthy/ligeti-musica-ricercata-i ''Musica ricercata'': I. Sostenuto - Misurato - Prestissimo]
 
|[[wikipedia:György_Ligeti|György Ligeti]]
; [[Frédéric Gagné]]
|1951-1953
* ''Play "Do"'' (2021) – [[:File:0010 - Play Do.mp3|play]] | [https://musescore.com/fredg999/play-do score]
|Classical
 
|[[wikipedia:Musica_ricercata#I._Sostenuto_%E2%80%93_Misurato_%E2%80%93_Prestissimo|Analysis (Wikipedia)]]
; [[User:Wendy_gunk|Wendy Gunk]]
|-
* [https://www.youtube.com/watch?v=YpNh8CNS4tc ''1edo howard''] (2025)
|[https://youtu.be/kRMU-dNOs-w "Cohesion"] (from ''[https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn Edolian]'')
 
|NullPointerException Music
{{Wikipedia|Musica ricercata #I. Sostenuto – Misurato – Prestissimo}}
|2020
 
|Classical
; [[Wikipedia:György Ligeti|György Ligeti]]
|
* [https://soundcloud.com/elizamccarthy/ligeti-musica-ricercata-i ''Musica ricercata'': I. Sostenuto – Misurato – Prestissimo] (1951–1953)
|-
 
|[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]'')
; [[Mandrake]]
|STC_1001
* ''One Note To Tell A Story'' (2022) – [https://www.newgrounds.com/audio/listen/1114156 Newgrounds] | [https://www.youtube.com/watch?v=mDSj8SwBHRk YouTube]
|2021
 
|Electronic
; [[NullPointerException Music]]
|[https://sexytoadsandfrogsfriendcircle.bandcamp.com/album/staffcirc-vol-7-terra-octava Album (Bandcamp)]
* [https://youtu.be/kRMU-dNOs-w "Cohesion"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
|-
 
|[[:File:0010 - Play Do.mp3|''Play "Do"'']]
; [[User:Phanomium|Phanomium]]
|[[User:Fredg999|Frédéric Gagné]]
* [https://www.youtube.com/watch?v=A1XppPdwGJc ''Singularity''] (2024)
|2021
 
|Classical
; [[STC_1001]]
|[https://musescore.com/fredg999/play-do Score (MuseScore)]
* "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]
|-
 
|[https://www.newgrounds.com/audio/listen/1114156 One Note To Tell A Story]
; [[Chris Vaisvil]]
|Mandrake
* [https://www.youtube.com/watch?v=EAutHhRv3Gg ''0-EDO for Orchestra''] (2021) (despite the title, actually in 1edo)
|2022
|Electronic
|[https://www.youtube.com/watch?v=mDSj8SwBHRk Video (YouTube)]
|}


== See also ==
== See also ==
Line 56: Line 59:
* [[Octave]]
* [[Octave]]


[[Category:Equal divisions of the octave|#]] <!-- 1-digit number -->
[[Category:Trivial temperaments]]
[[Category:2-limit]]
[[Category:2-limit]]
[[Category:Macrotonal]]
[[Category:1-odd-limit]]
[[Category:Unison]]
[[Category:Just intonation scales]]
[[Category:Listen]]
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