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| {{ED intro}} | | {{ED intro}} |
| == Theory == | | == Theory == |
| {{Harmonics in equal|11|intervals=odd}}
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| Compared to 12edo, the intervals of 11edo are stretched: | | Compared to 12edo, the intervals of 11edo are stretched: |
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| * The "major third" at 436.36 cents, is quite sharp, and closer to the [[supermajor]] third of frequency ratio [[9/7]] than the simpler third of 5/4. | | * The "major third" at 436.36 cents, is quite sharp, and closer to the [[supermajor]] third of frequency ratio [[9/7]] than the simpler third of 5/4. |
| * The "perfect fourth" at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the [[11/8]] superfourth than the simpler perfect fourth of 4/3. | | * The "perfect fourth" at 545.45 cents, does not sound like a perfect fourth at all, and passes more easily as the [[11/8]] superfourth than the simpler perfect fourth of 4/3. |
| | {{Harmonics in equal|11}} |
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| 11edo does not approximate many small prime harmonics well, only providing good approximations to 7/4 and 11/8. However, 11edo can be treated as a subset of 22edo, and take 22edo's [[6/5]], [[9/7]], and [[16/15]] via direct approximation. | | 11edo does not approximate many small prime harmonics well, only providing good approximations to 7/4 and 11/8. However, 11edo can be treated as a subset of 22edo, and take 22edo's [[6/5]], [[9/7]], and [[16/15]] via direct approximation. |
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| Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving [[Orgone]][7] on the whites. The superfluous Ab can be made a note of [[22edo]], a tuning known as "[[elevenplus]]". | | Being less than twelve, 11edo maps easily to the standard keyboard. The suggested mapping disregards the Ab/G# key, leaving [[Orgone]][7] on the whites. The superfluous Ab can be made a note of [[22edo]], a tuning known as "[[elevenplus]]". |
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| [[File:0-8-16-20 chord.wav|thumb|A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]] | | [[File:0-8-16-20 chord.wav|thumb|A 0–8–16–20 chord in 11edo illustrating harmony generated from stacking 9/7 intervals.]] |
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| == Notation == | | == Intervals and Notation == |
| === Ups and downs notation === | | === Ups and downs notation === |
| 11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the ''melodic'' meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5. | | 11edo can be notated using ups and downs. Conventional notation, including the staff, note names, relative notation, etc. can be used in two ways. The first preserves the ''melodic'' meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5. |
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| | Layobi | | | Layobi |
| | Major chroma | | | Major chroma |
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| | | 5 |
| | | [[144/125]] |
| | | {{Monzo| 4 2 -3 }} |
| | | 244.97 |
| | | Trigu |
| | | University comma |
| |- | | |- |
| | 5 | | | 5 |
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| [[File:11edo_approx_2-7-9-11-15-17_2ndsave.png|alt=11edo_approx_2-7-9-11-15-17_2ndsave.png|11edo_approx_2-7-9-11-15-17_2ndsave.png]] | | [[File:11edo_approx_2-7-9-11-15-17_2ndsave.png|alt=11edo_approx_2-7-9-11-15-17_2ndsave.png|11edo_approx_2-7-9-11-15-17_2ndsave.png]] |
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| | == Octave stretch or compression == |
| | 11edo has about equally bad sharp and flat mappings of [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. Examples of slightly compressed versions of 11edo include (least to most compressed) [[ed6|28ed6]], [[ed12|39ed12]], [[zpi|30zpi]], [[equal tuning|35ed9]] and [[ed7|31ed7]]. |
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| | To use its primes 3 or 5, extreme octave shrinking can be used, at the cost of making the octaves sound significantly weaker. [[equal tuning|37ed10]] is a very compressed version of 11edo. |
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| == Scales == | | == Scales == |
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| [[File:11-edo-ukulele.JPG|alt=11-edo-ukulele.JPG|404x304px|11-edo-ukulele.JPG]] | | [[File:11-edo-ukulele.JPG|alt=11-edo-ukulele.JPG|404x304px|11-edo-ukulele.JPG]] |
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| '''Ensembles''' | | '''Ensembles''' |
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| In February 2011, [http://oddmusicuc.wordpress.com/ Oddmusic U-C], as part of its Microtonal Design Seminar, generated a 7-piece ensemble for playing music in 11edo. Instrumentation: autotuner, cümbüş, electronic keyboard, kalimba, retrofretted guitar, tuned bottles, udderbot. Recordings forthcoming. | | In February 2011, [http://oddmusicuc.wordpress.com/ Oddmusic U-C], as part of its Microtonal Design Seminar, generated a 7-piece ensemble for playing music in 11edo. Instrumentation: autotuner, cümbüş, electronic keyboard, kalimba, retrofretted guitar, tuned bottles, udderbot. Recordings forthcoming. |
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| '''Lumatone''' | | '''Lumatone''' |
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| There is a [[Lumatone mapping for 11edo]].
| | [[Lumatone mapping for 11edo|Lumatone mappings for 11edo]] are available. |
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| == Introductory Materials == | | == Introductory Materials == |
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| == Music == | | == Music == |
| {{Catrel|11edo tracks}} | | {{Catrel|11edo tracks}} |
| === Strict 11edo ===
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| ==== Modern renderings ====
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| ; {{W|Arthur Schutt}}
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| * [https://www.youtube.com/watch?v=GEzxtHILDr8 ''Bluin' The Black Keys''] (1926) – rendered by Francium (2024)
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| ==== 20th century ====
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| ; [[George Secor]]
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| * [http://xenharmony.wikispaces.com/space/showimage/11edo-improv.mp3 First Piece Ever]{{dead link}} (1970) — apparently the first piece ever written for 11edo.
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| ; [[Bill Sethares]]
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| * [https://sethares.engr.wisc.edu/mp3s/dabo_girl.html "The Turquoise Dabo Girl"], from [https://sethares.engr.wisc.edu/xentone.html ''Xentonality''] (1997)
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| ==== 21st century ====
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| ; [[Abnormality]]
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| * [https://www.youtube.com/watch?v=G1rUu9qmXkE ''Scatter Brain''] (2024)
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| ; [[Christopher Bailey]]
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| * [https://www.youtube.com/playlist?list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3 ''The Stuffed Ones''] (2004) – 4-piece suite ([http://christopherbaileymusic.com/composition-list/ details])
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| ** [https://www.youtube.com/watch?v=NU0VvGRelUQ&list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3&index=1 "Goopy"] · [https://www.youtube.com/watch?v=4D9wDl_oxHE&list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3&index=2 "Ellie"] · [https://www.youtube.com/watch?v=53IiHdXfJwI&list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3&index=3 "Ziggy"] · [https://www.youtube.com/watch?v=4sZqpRcB-lk&list=PLby8OiGBluOXODbJpiRhzNftxy5-DV-I3&index=4 "Towelbear"]
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| ; [[Jacob Barton]]
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| * ''Hyperimprovisations Nuggetwarp'' (2009)
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| ** [https://soundclick.com/share.cfm?id=10267904 "Piece I"] · [https://soundclick.com/share.cfm?id=10267905 "Piece II"] · [https://soundclick.com/share.cfm?id=10267906 "Piece III"]
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| ; [[City of the Asleep]]
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| * [https://cityoftheasleep.bandcamp.com/track/she-is-my-lilac-hued-obsession "She is My Lilac-Hued Obsession"], from [https://cityoftheasleep.bandcamp.com/album/map-of-an-internal-landscape-reissue ''Map of an Internal Landscape''] (2007)
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| ; [[Jason Conklin]]
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| * ''The City Sleeps, A Madrigal'' (2011) – [http://web.archive.org/web/20201127013549/http://micro.soonlabel.com/gene_ward_smith/Others/Conklin/Conklin-The_City_Sleeps_A_Madrigal.mp3 play] | [https://soundcloud.com/ninly/the-city-sleeps SoundCloud]
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| ; [[E8 Heterotic]]
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| * [https://youtu.be/9tJHJEZnvFs?si=9n6I3VnejVon_iot ''Olive Flamenco''] (2019)
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| ; [[Francium]]
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| * "Tostadosto" from ''The Decatonic Album'' (2024) – [https://open.spotify.com/track/27hl1xKswTuaQG0vIjMHhk Spotify] | [https://francium223.bandcamp.com/track/tostadosto Bandcamp] | [https://www.youtube.com/watch?v=28SOTJvT6sw YouTube]
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| * "Sleep Slope" from ''XenRhythms'' (2024) – [https://open.spotify.com/track/2GnUioPrMlJmMaacE6DK7i Spotify] | [https://francium223.bandcamp.com/track/sleep-slope Bandcamp] | [https://www.youtube.com/watch?v=hM0BAC_YZnQ YouTube]
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| ; [[David Hamill]]
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| * [http://www.focalchords.com/audio/Cool_My_Head_11EDO.mp3 ''Cool My Head''] (2010)
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| ; [[Andrew Heathwaite]]
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| * ''Orange Clips on Sausages'' (2004) – [http://web.archive.org/web/20201127012301/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+orangeclipsonsausagesin11tet.mp3 play] | [https://www.soundclick.com/music/songInfo.cfm?songID=933772 SoundClick]
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| * ''Blue Gel'' (2004) – [http://web.archive.org/web/20201127012646/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+improvisationin11tet.mp3 play] | [https://www.soundclick.com/music/songInfo.cfm?songID=834492 SoundClick]
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| * ''conversation is'' (2010) – [http://web.archive.org/web/20201127012932/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+conversationis.mp3 play] | [https://www.soundclick.com/music/songInfo.cfm?songid=8839070 SoundClick]
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| ; [[Hideya]]
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| * [https://www.youtube.com/watch?v=PcY3HrwQRRY ''Like Parker 3''] (2019)
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| * [https://www.youtube.com/watch?v=YawFcH4cXfs ''Like 40s music''] (2022)
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| ; [[Aaron Andrew Hunt]]
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| * From [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal-Tempered Keyboard''] (1999–2022)
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| ** [https://aaronandrewhunt.bandcamp.com/track/prelude-in-11et "Prelude in 11ET"]
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| ** "Adagio in 11ET" – [https://aaronandrewhunt.bandcamp.com/track/adagio-in-11et Bandcamp] | [https://soundcloud.com/uz1kt3k/adagio-in-11et?in=uz1kt3k/sets/adagio-invention-in-11et SoundCloud]{{dead link}}
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| ** "Invention in 11ET" – [https://aaronandrewhunt.bandcamp.com/track/invention-in-11et Bandcamp] | [https://soundcloud.com/uz1kt3k/invention-in-11et?in=uz1kt3k/sets/adagio-invention-in-11et SoundCloud]{{dead link}}
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| ; [[User:Ayceman|Alexandru Ianu]]
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| * ''Divertimento in 11 tone Orgone'' (2021) – [[:File:Divertimento in 11 tone Orgone.pdf|sheet music]] | [https://youtu.be/8x1f5WFkF4k YouTube] – orgone in 11edo tuning
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| * ''Sylvian Moon Dance'' (2021) – [[:File:SylvianMoonDance.ogg|audio]] | [[:File:Sylvian_Moon_Dance.pdf|sheet music]] | [https://youtu.be/81uZbsmbet8 YouTube] – orgone in 11edo tuning
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| * ''Ocean of the Necrophages'' (2021) – orgone in 11edo tuning
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| ** Piano: [[:File:Ocean of the Necrophages (4U UP).ogg|audio]] | [[:File:Ocean of the Necrophages.pdf|sheet music]] | [https://youtu.be/CWU09fXXy1s YouTube]
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| ** Strings: [[:File:Ocean of the Necrophages (strings).ogg|audio]] | [[:File:Ocean of the Necrophages (strings).pdf|sheet music]]
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| ; [[Aaron Krister Johnson]]
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| * [http://www.akjmusic.com/audio/black_ritual_dirge.mp3 ''Black Ritual Dirge'']{{dead link}}
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| ; [[User:ks26|groundfault]]
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| * [https://www.youtube.com/watch?v=AEnEYk3X1as ''Ghost Bridge''] (2020)
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| ; [[Claudi Meneghin]]
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| * [https://www.youtube.com/watch?v=bqIDxbc21O8 ''Micropiece in 11edo''] (2020)
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| * [https://www.youtube.com/watch?v=fwyM3quEzu4 ''Prelude & Fugue in 11edo, in Four Parts, for Recorder, Organ, Cello''] (2022)
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| * [https://www.youtube.com/watch?v=qNqDuAq6O5k ''George Secor · 11EDO improvisation (1971)''] (2022)
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| ; [[Mundoworld]]
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| * [https://www.youtube.com/watch?v=69TiqslCgeg ''Fire Memes'' (with Anthony "Pomp" Pompliano)] – Machine[6] in 11edo tuning
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| * [https://www.youtube.com/watch?v=MfNLxcbVzs8 ''Theory of Creation''] – Machine[6] in 11edo tuning
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| * "Search Party" from ''No Fun House'' (2025) – [https://open.spotify.com/track/7CMiwDuuRuFpB0skfwT2Ap Spotify] | [https://mundoworld.bandcamp.com/track/search-party Bandcamp] | [https://www.youtube.com/watch?v=hLs6MjuousI YouTube]
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| ; [[User:GlitchyDarkness|No Clue Music]]
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| * [https://www.youtube.com/watch?v=lPKc1B6YBn4 ''Cursed Star''] (2024)
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| ; [[NullPointerException Music]]
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| * [https://www.youtube.com/watch?v=AbWxZ6yh69s "Overcoming"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
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| ; [[User:Phanomium|Phanomium]]
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| * [https://www.youtube.com/watch?v=y939ciE9MQY ''33322''] (2024)
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| ; [[X. J. Scott]]
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| * [https://soundclick.com/share.cfm?id=955383 ''Angkor Wat, September 1066''] (2004)
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| ; [[Sevish]]
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| * "[[Longwayaway People]]", from ''[[Rhythm and Xen]]'' (2015)
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| * "[[Make a Dream]]", from ''[[Rhythm and Xen]]'' (2015)
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| ; [[Jon Lyle Smith]]
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| * [https://archive.org/details/jls_ArchiveVol2/Jaunt_reMix2012.wav ''Jaunt''] (2012) – [http://web.archive.org/web/20201127014902/http://micro.soonlabel.com/jon-lyle-smith/Jaunt.mp3 play] | [https://www.youtube.com/watch?v=HKULte3WhuE YouTube]
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| * [http://archive.org/download/CounterpointIn11edo/CounterpointIn11edo.mp3 ''Counterpoint in 11EDO'']{{dead link}}
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| ; [[Chris Vaisvil]]
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| * [https://web.archive.org/web/20201127012602/http://micro.soonlabel.com/11-ET/daily201110-gpo-jeffery-dahmer-cooks.mp3 ''Jeffrey Dahmer Cooks at 11EDO''] (2011)
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| * [https://web.archive.org/web/20201127015348/http://micro.soonlabel.com/11-ET/20110902_prepared_seagull_metamorphis.mp3 ''The Metamorphosis of Gregor''] (2011)
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| * ''Eleven Birds'' (2012) – [https://www.chrisvaisvil.com/eleven-birds/ blog] | [http://micro.soonlabel.com/11-ET/20120928-piano-11edo-eleven-birds.mp3 play]
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| * [https://soundcloud.com/vaisvil/the-execution-of-12-equal ''The Execution of 12 Equal'']{{dead link}}
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| ; [[Randy Winchester]]
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| * [https://archive.org/details/jamendo-005173/10.mp3 "10. 11 / octave"], from ''[[Comets Over Flatland]]'' (2007)
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| ; [[Ozan Yarman]]
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| * [http://www.ozanyarman.com/files/music/Icicle_Caverns.mp3 ''Icicle Caverns''] (2010) ([http://www.ozanyarman.com/files/music/icicle_caverns_score.pdf score])
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| ; [[Yeah Gore]]
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| * [https://www.youtube.com/watch?v=FL72Z4H1IF8 ''11 TET Hernya''] (2020)
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| * [https://www.youtube.com/watch?v=dwel2K1Bgds ''YG_A''] (2022)
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| === Unequal Derivatives of 11edo ===
| | See [[11edo/Music]]. |
| ; [[Bryan Deister]]
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| * [https://www.youtube.com/watch?v=z0lWcguNsNs ''11 Tone March''] (2024)
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| == Videos == | | == Videos == |
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| * [https://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike Battaglia FAQ|Mike Battaglia]] - youtube | | * [https://www.youtube.com/watch?v=AhPjsCoMy-Q 11-equal Improvisation]'', [[Mike Battaglia FAQ|Mike Battaglia]] - youtube |
| | * [https://www.youtube.com/watch?v=4WlTPfRDPCY untitled1], computer |
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| == See also == | | == See also == |