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| Fifth = 5\9 = 666.667¢
| Fifth = 5\9 = 666.667¢
| Major 2nd = 1\9 = 133¢
| Major 2nd = 1\9 = 133¢
| Minor 2nd = 2\9 = 267¢
| Augmented 1sn = -1\9 = -133¢
}}
}}
'''9 EDO''' divides the octave into nine equal parts each of 133+1/3 [[cent]]s precisely. It is also the first odd composite edo.
'''9 EDO''' divides the octave into nine equal parts each of 133+1/3 [[cent]]s precisely. It is also the first odd composite EDO.


== Theory ==
== Theory ==
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| -23
| -23
|-
|-
! colspan="2" | [[nearest edomapping]]
! colspan="2" | [[Patent val|nearest EDO-mapping]]
| 9
| 9
| 5
| 5
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| +4
| +4
|}
|}
The 9-EDO scale has the peculiar property of representing certain [[7-limit]] intervals almost exactly. A 7-limit version of 9EDO goes
The 9EDO scale has the peculiar property of representing certain [[7-limit]] intervals almost exactly. A 7-limit version of 9EDO goes


1: 27/25 133.238 large limma, BP small semitone
1: 27/25 133.238 large limma, BP small semitone
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Here the characterizations are taken from [http://en.wikipedia.org/wiki/Scala_%28program%29 Scala], which also describes the scale itself as "Pelog Nawanada: Sunda". Chords such as 1/1 - 7/6 - 49/36 - 12/7 are therefore natural ones for 9EDO. The above scale generates the [[Just_intonation_subgroups|just intonation subgroup]] 2.27/25.7/3, which is closely related to 9EDO.
Here the characterizations are taken from [http://en.wikipedia.org/wiki/Scala_%28program%29 Scala], which also describes the scale itself as "Pelog Nawanada: Sunda". Chords such as 1/1 - 7/6 - 49/36 - 12/7 are therefore natural ones for 9EDO. The above scale generates the [[Just_intonation_subgroups|just intonation subgroup]] 2.27/25.7/3, which is closely related to 9EDO.


=== Differences between distributionally-even scales and smaller edos ===
=== Differences between distributionally-even scales and smaller EDOs ===
{| class="wikitable"
{| class="wikitable"
|+
|+
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!s-Nedo
!s-Nedo
|-
|-
|2
| 2
|66.666¢
| 66.666¢
| -66.666¢
| -66.666¢
|-
|-
|4
| 4
|100¢
| 100¢
| -33.333¢
| -33.333¢
|-
|-
|5
| 5
|26.667¢
| 26.667¢
| -106.667¢
| -106.667¢
|-
|-
|6
| 6
|66.666¢
| 66.666¢
| -66.666¢
| -66.666¢
|-
|-
|7
| 7
|95.238¢
| 95.238¢
| -38.095¢
| -38.095¢
|-
|-
|8
| 8
|116.667¢
| 116.667¢
| -16.667¢
| -16.667¢
|}
|}


== Notation ==
== Notation ==
9EDO can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> 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.


9edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> 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.
The second approach preserves the <u>harmonic</u> meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12EDO music can be directly translated to 9EDO "on the fly".
 
The second approach preserves the <u>harmonic</u> meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 9edo "on the fly".


{| class="wikitable center-all right-1 right-2"
{| class="wikitable center-all right-1 right-2"
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== Commas ==
== Commas ==
 
9EDO [[tempers out]] the following [[comma]]s. (Note: This assumes [[val]] {{val| 9 14 21 25 31 33 }}.)
9 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes [[val]] {{val| 9 14 21 25 31 33 }}.)


{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
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9EDO contains a pentatonic [[MOSScales|MOS scale]] -- 2L 3s (1 3 1 3 1) -- with a heptatonic extension -- 2L 5s (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic"). Indonesian pelog scales sometimes use five-tone subsets of a seven-tone superset in a similar way, and it has been suggested that Indonesian gamelan music stems from a [http://www.neuroscience-of-music.se/pelog%20historical.htm 9EDO tradition].
9EDO contains a pentatonic [[MOSScales|MOS scale]] -- 2L 3s (1 3 1 3 1) -- with a heptatonic extension -- 2L 5s (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic"). Indonesian pelog scales sometimes use five-tone subsets of a seven-tone superset in a similar way, and it has been suggested that Indonesian gamelan music stems from a [http://www.neuroscience-of-music.se/pelog%20historical.htm 9EDO tradition].


==Pathological Modes==
== Pathological Modes==
2 1 1 1 1 1 1 1 [[1L 7s]] MOS
2 1 1 1 1 1 1 1 [[1L 7s]] MOS
== Selected Just Intervals ==
== Selected Just Intervals ==
[[File:9ed2-001.svg|alt=alt : Your browser has no SVG support.]]
[[File:9ed2-001.svg|alt=alt : Your browser has no SVG support.]]


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== Images ==
== Images ==
[[File:9edo_wheel.png|alt=9edo wheel.png|385x385px|9edo wheel.png]]
[[File:9edo_wheel.png|alt=9edo wheel.png|385x385px|9edo wheel.png]]


== Instruments ==
== Instruments ==
[[File:IMG_2223-800x600.jpg|alt=IMG_2223-800x600.jpg|400px|IMG_2223-800x600.jpg]]
[[File:IMG_2223-800x600.jpg|alt=IMG_2223-800x600.jpg|400px|IMG_2223-800x600.jpg]]


Ukulele (MicroUke 1.2) set to 9 EDO with 40 lb. test fishing line (by cenobyte)
Ukulele (MicroUke 1.2) set to 9EDO with 40 lb. test fishing line (by cenobyte)


== Music ==
== Music ==
 
* [https://soundcloud.com/overtoneshock/tencaious-chorale-9-edo-studio-version Tenacious Chorale (only movement I is in 9EDO)] by [[Stephen Weigel]]
* [https://soundcloud.com/overtoneshock/tencaious-chorale-9-edo-studio-version Tenacious Chorale (only movement I is in 9-EDO)] by [[Stephen Weigel]]
* [https://soundcloud.com/overtoneshock/in-our-own-little-worlds-9-edo Zones of Lasting Novelty] (Un12 2019) by [[Stephen Weigel]]; perf. [[Hans Gunter-Lock]], [[Jacob Barton]], and Stephen Weigel
* [https://soundcloud.com/overtoneshock/in-our-own-little-worlds-9-edo Zones of Lasting Novelty] (Un12 2019) by [[Stephen Weigel]]; perf. [[Hans Gunter-Lock]], [[Jacob Barton]], and Stephen Weigel
* [https://soundcloud.com/overtoneshock/gamelan-genesis-and-birth-9-edo Gamelan, Origin, Creation] by Stephen Weigel ([http://www.beostringquartet.com/ Beo String Quartet], dedicated to [[wikipedia:Lou_Harrison|Lou Harrison]])
* [https://soundcloud.com/overtoneshock/gamelan-genesis-and-birth-9-edo Gamelan, Origin, Creation] by Stephen Weigel ([http://www.beostringquartet.com/ Beo String Quartet], dedicated to [[wikipedia:Lou_Harrison|Lou Harrison]])
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* [https://tabytha.bandcamp.com/track/69-pentangled 69 Pentangled] by [https://tabytha.bandcamp.com/album/bad-musick Tabytha]
* [https://tabytha.bandcamp.com/track/69-pentangled 69 Pentangled] by [https://tabytha.bandcamp.com/album/bad-musick Tabytha]


* Nocturne in 9tet by [http://home.snafu.de/djwolf/WorksDescriptive.htm Daniel Wolf]
* Nocturne in 9EDO by [http://home.snafu.de/djwolf/WorksDescriptive.htm Daniel Wolf]
* ''[http://www.h-pi.com/mp3/Prelude9ET.mp3 Prelude in 9ET]'' by [[Aaron Andrew Hunt]]
* ''[http://www.h-pi.com/mp3/Prelude9ET.mp3 Prelude in 9ET]'' by [[Aaron Andrew Hunt]]
* ''[http://micro.soonlabel.com/9-edo/daily20110629_fts_e_guit_9et.mp3 Improvisation for Electric Guitar in 9 edo]'' by [[Chris Vaisvil]]
* ''[http://micro.soonlabel.com/9-edo/daily20110629_fts_e_guit_9et.mp3 Improvisation for Electric Guitar in 9EDO]'' by [[Chris Vaisvil]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/08%20-%208.%209%20octave.mp3 Comets Over Flatland 8] by [[Randy Winchester]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/08%20-%208.%209%20octave.mp3 Comets Over Flatland 8] by [[Randy Winchester]]
* [http://www.youtube.com/watch?v=bDFCsCoaUO4 Nine tones per Octave (9-EDO / 9-TET)] by [[Ivor Darreg]]
* [http://www.youtube.com/watch?v=bDFCsCoaUO4 Nine tones per Octave (9-EDO / 9-TET)] by [[Ivor Darreg]]
* [http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3 Gerbils at the Wheel of Government] by [[Chris Vaisvil]] (in 9 and 18 edo simultaneously)
* [http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3 Gerbils at the Wheel of Government] by [[Chris Vaisvil]] (in 9 and 18 EDOsimultaneously)
* [http://www.seraph.it/dep/det/NewWorld.mp3 New World] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/f533be803cb9ed1efc23fc9e2db10c6f-167.html blog entry])
* [http://www.seraph.it/dep/det/NewWorld.mp3 New World] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/f533be803cb9ed1efc23fc9e2db10c6f-167.html blog entry])
* [https://soundcloud.com/santiagocosentino/interdimensional-train-ride Interdimensional Train Ride by Santiago Cosentino]
* [https://soundcloud.com/santiagocosentino/interdimensional-train-ride Interdimensional Train Ride by Santiago Cosentino]


== Ear Training ==
== Ear Training ==
 
9EDO ear-training exercises by Alex Ness available [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list here].
9 EDO ear-training exercises by Alex Ness available [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list here].


[[Category:9-tone]]
[[Category:9-tone]]
[[Category:9edo]]
[[Category:9edo| ]]
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Macrotonal]]
[[Category:Macrotonal]]
[[Category:Todo:unify precision]]
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