1edo: Difference between revisions
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'''1 equal divisions of the octave''' (abbreviated '''1edo'''), | '''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]] | 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 {{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. | 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 [[AFDO|1afdo]] and [[IFDO|1ifdo]]. | 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 === | === Odd harmonics === | ||
| Line 29: | Line 30: | ||
; [[Frédéric Gagné]] | ; [[Frédéric Gagné]] | ||
* [[:File:0010 - Play Do.mp3| | * ''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) | |||
{{Wikipedia|Musica ricercata #I. Sostenuto – Misurato – Prestissimo}} | |||
; [[Wikipedia:György Ligeti|György Ligeti]] | ; [[Wikipedia:György Ligeti|György Ligeti]] | ||
* [https://soundcloud.com/elizamccarthy/ligeti-musica-ricercata-i ''Musica ricercata'': I. Sostenuto | * [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.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) | * [https://youtu.be/kRMU-dNOs-w "Cohesion"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020) | ||
; [[User:Phanomium|Phanomium]] | |||
* [https://www.youtube.com/watch?v=A1XppPdwGJc ''Singularity''] (2024) | |||
; [[STC_1001]] | ; [[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 == | == See also == | ||
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* [[Octave]] | * [[Octave]] | ||
[[Category:Trivial temperaments]] | |||
[[Category:2-limit]] | [[Category:2-limit]] | ||
[[Category: | [[Category:1-odd-limit]] | ||
[[Category:Just intonation scales]] | [[Category:Just intonation scales]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Latest revision as of 03:39, 17 May 2026
| ← 0edo | 1edo | 2edo → |
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 octaves 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 (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 harmonics 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.
1edo is equivalent to the 2-limit, 1-odd-limit, and 1-p-fdo with arbitrary value of p (including 1afdo and 1ifdo).
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +498 | -386 | +231 | -204 | -551 | +359 | +112 | -105 | -298 | -471 | +572 |
| Relative (%) | +41.5 | -32.2 | +19.3 | -17.0 | -45.9 | +30.0 | +9.3 | -8.7 | -24.8 | -39.2 | +47.6 | |
| Step | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | |
Music
- See also: Category:1edo tracks
- Octaves Only (2023)
- PolyTech (2023)
- E (2022)
- 1edo howard (2025)
- One Note To Tell A Story (2022) – Newgrounds | YouTube
- "Cohesion", from Edolian (2020)
- Singularity (2024)
- "Neainaz Antithetica, Theme", from STAFFcirc vol. 7 (2021) – SoundCloud | Bandcamp
- 0-EDO for Orchestra (2021) (despite the title, actually in 1edo)