1edo: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES<~~/~~h2>~~

{{interwiki

~~This~~ is an ~~imported revision from Wikispaces~~. The ~~revision metadata~~ is ~~included below for reference:<br>~~

| de = 1-EDO

~~: This revision was by author~~ [[~~User:xenwolf|xenwolf~~]] and ~~made on <tt>2010~~-05-~~22 06~~:~~06:53 UTC<~~/~~tt>~~.~~<br>~~

| en = 1edo

: ~~The original revision id was <tt>143894535<~~/~~tt>~~.~~<br>~~

| es = 1-EDO

: ~~The revision comment was: <tt><~~/~~tt><br>~~

| ja =

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~

| ro = 1DEO

~~<h4>Original Wikitext content:</h4>~~

}}

~~<div style=~~"~~width~~:~~100%; max~~-~~height~~:~~400pt; overflow:auto; background~~-~~color:#f8f9fa~~; ~~border~~: ~~1px solid #eaecf0; padding~~:~~0em"><pre style~~=~~"margin:0px~~;~~border~~:~~none;background~~:~~none;word~~-~~wrap:break~~-~~word;white~~-~~space~~: ~~pre-wrap ! important" class="old-revision-html">~~

[[~~György Ligeti~~]]~~, Musica Ricercata, piece 1, is in 1edo, expluding the very last tone<~~/~~pre><~~/~~div>~~

'''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.

~~<h4>Original HTML content~~:</~~h4>~~

~~<div style="width~~:~~100%; max~~-~~height~~:~~400pt~~; ~~overflow~~:~~auto; background-color~~:~~#f8f9fa~~; ~~border: 1px solid #eaecf0; padding:0em~~"~~><pre style=~~"~~margin~~:~~0px;border:none;background:none;word~~-~~wrap:break~~-~~word;width:200%;white~~-~~space~~: ~~pre~~-~~wrap ! important" class="old~~-~~revision~~-~~html"><html><head><title>1edo<~~/~~title><~~/~~head><body><br~~ /~~&gt~~;

== Theory ==

~~<a class="wiki_link" href="~~/~~Gy%C3%B6rgy%20Ligeti">György Ligeti<~~/~~a>, Musica Ricercata~~, ~~piece 1, is~~ in 1edo~~, expluding the very last tone</body></html></pre></div>~~

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.

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)

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

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

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

; [[Mandrake]]

* ''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]]

* [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]]

* "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 ==

* [[Unison]]

* [[Octave]]

[[Category:Trivial temperaments]]

[[Category:2-limit]]

[[Category:1-odd-limit]]

[[Category:Just intonation scales]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{interwiki
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| de = 1-EDO
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-05-22 06:06:53 UTC</tt>.<br>
+| en = 1edo
-: The original revision id was <tt>143894535</tt>.<br>
+| es = 1-EDO
-: The revision comment was: <tt></tt><br>
+| ja =
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+| ro = 1DEO
-<h4>Original Wikitext content:</h4>
+}}
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">
+{{Infobox ET}}
-[[György Ligeti]], Musica Ricercata, piece 1, is in 1edo, expluding the very last tone</pre></div>
+'''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.
-<h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;1edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
+== Theory ==
-&lt;a class="wiki_link" href="/Gy%C3%B6rgy%20Ligeti"&gt;György Ligeti&lt;/a&gt;, Musica Ricercata, piece 1, is in 1edo, expluding the very last tone&lt;/body&gt;&lt;/html&gt;</pre></div>
+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.
+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 ==
+{{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)
+{{Wikipedia|Musica ricercata #I. Sostenuto – Misurato – Prestissimo}}
+; [[Wikipedia:György Ligeti|György Ligeti]]
+* [https://soundcloud.com/elizamccarthy/ligeti-musica-ricercata-i ''Musica ricercata'': I. Sostenuto – Misurato – Prestissimo] (1951–1953)
+; [[Mandrake]]
+* ''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]]
+* [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]]
+* "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 ==
+* [[Unison]]
+* [[Octave]]
+[[Category:Trivial temperaments]]
+[[Category:2-limit]]
+[[Category:1-odd-limit]]
+[[Category:Just intonation scales]]
+[[Category:Listen]]