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'''5-edo''' divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of two.  
'''5-edo''' divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of two.  


== 5 Equal Divisions of the Octave: Theory ==
== Theory ==


5-edo is the 3rd [[prime numbers|prime]] edo, after [[2edo]] and [[3edo]]. Most importantly, 5-edo is the smallest [[EDO|edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.)
5-edo is the 3rd [[prime numbers|prime]] edo, after [[2edo]] and [[3edo]]. Most importantly, 5-edo is the smallest [[EDO|edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.)
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* Cycle of sevenths: 0-4-3-2-1-0
* Cycle of sevenths: 0-4-3-2-1-0


== 5-edo in Musicmaking ==
== Commas Tempered ==
 
=== Compositions, Improvisations ===
* [http://www.io.com/%7Ehmiller/ Herman Miller]: ''[http://micro.soonlabel.com/herman_miller/Daybreak.mp3 Daybreak on Slendro Mountain]'' (2000)
* Aaron K. Johnson: ''[http://www.akjmusic.com/audio/5tet_funk.mp3 5tet funk]'' (2004)
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=1519939 Andrew Heathwaite: //Pinta Penta// (2004)] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3 play] (rendered in 6 alternative pentatonics as well)
* [[Hans_Straub|Hans Straub]]: [http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia Asîmchômsaia] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3 play]
* [[Brian_Wong|Brian Wong]]: [http://bwong.ca/template1.php?sub=3 Slendronica#1b] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg play]
* Brian McLaren: various and sundry<li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>X.J.Scott: ''Sleeping Through It All'' (2004)
* Bill Sethares: ''5-tet funk'' (2004), ''Pentacle'' (2004)
* "Cenobyte" Ukulele http://www.youtube.com/watch?v=UKUCRnEJKKU
* "[http://www.jamendo.com/en/list/a104474/true-island-5-equal-divisions-of-the-octave-ukulele True Island]" (album) by Small Scale Revolution (2011)
* Ralph Jarzombek: [http://webzoom.freewebs.com/ralphjarzombek/micro12.mp3 Micro12]
 
There is a lot of 5edo world music, search for "gyil" or "amadinda" or "slendro".
 
=== Ear Training ===
5edo ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web here].
 
=== Notation ===
* via Reinhard's cents notation
* naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C
* a four-line hybrid treble/bass staff.
 
=== Harmony ===
5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather "dirty" but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.
 
In contrast to other EDOs, all of the notes can be used at once in order to get a functioning scale. (As in Blackwood in [[10edo|10-EDO]]).
 
Important chords:
* 0+1+3
* 0+2+3
* 0+1+3+4
* 0+2+3+4
 
=== Melody ===
Smallest EDO that can be used for melodies in a "standard" way. The relatively large step of 240 cents can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character.
 
=== Chord or scale? ===
Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.
 
=== Commas Tempered ===
5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)
5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)


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== 5-edo in Musicmaking ==
=== Compositions, Improvisations ===
* [http://www.io.com/%7Ehmiller/ Herman Miller]: ''[http://micro.soonlabel.com/herman_miller/Daybreak.mp3 Daybreak on Slendro Mountain]'' (2000)
* Aaron K. Johnson: ''[http://www.akjmusic.com/audio/5tet_funk.mp3 5tet funk]'' (2004)
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=1519939 Andrew Heathwaite: //Pinta Penta// (2004)] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+pintapentain5tet.mp3 play] (rendered in 6 alternative pentatonics as well)
* [[Hans_Straub|Hans Straub]]: [http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia Asîmchômsaia] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Straub/asimchomsaia.mp3 play]
* [[Brian_Wong|Brian Wong]]: [http://bwong.ca/template1.php?sub=3 Slendronica#1b] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Wong/Slendronica1b.ogg play]
* Brian McLaren: various and sundry<li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>X.J.Scott: ''Sleeping Through It All'' (2004)
* Bill Sethares: ''5-tet funk'' (2004), ''Pentacle'' (2004)
* "Cenobyte" Ukulele http://www.youtube.com/watch?v=UKUCRnEJKKU
* "[http://www.jamendo.com/en/list/a104474/true-island-5-equal-divisions-of-the-octave-ukulele True Island]" (album) by Small Scale Revolution (2011)
* Ralph Jarzombek: [http://webzoom.freewebs.com/ralphjarzombek/micro12.mp3 Micro12]
There is a lot of 5edo world music, search for "gyil" or "amadinda" or "slendro".
=== Ear Training ===
5edo ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web here].
=== Notation ===
* via Reinhard's cents notation
* naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C
* a four-line hybrid treble/bass staff.
=== Harmony ===
5edo does not have any strong consonance nor dissonance. The 240 cent interval can serve as either a major second or minor third, and the 960 cent interval as either a major sixth or minor seventh. The fourth is about 18 cents flat of a just fourth, making it rather "dirty" but recognizable. The fifth is likewise about 18 cents sharp of a just fifth, dissonant but still easily recognizable.
In contrast to other EDOs, all of the notes can be used at once in order to get a functioning scale. (As in Blackwood in [[10edo|10-EDO]]).
Important chords:
* 0+1+3
* 0+2+3
* 0+1+3+4
* 0+2+3+4
=== Melody ===
Smallest EDO that can be used for melodies in a "standard" way. The relatively large step of 240 cents can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character.
=== Chord or scale? ===
Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.


[[Category:5-tone]]
[[Category:5-tone]]
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