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{{interwiki
{{interwiki
| de =  
| de = 9edo
| en = 9edo
| en = 9edo
| es =  
| es =  
| ja = 9平均律
| ja = 9平均律
}}
}}
{{Infobox ET}}
{{ED intro}}


= Theory =
== Theory ==
The 9EDO scale, which divides the octave into nine equal parts each of 133+1/3 cents precisely, has the peculiar property of representing certain [[Harmonic_Limit|7-limit]] intervals almost exactly. A 7-limit version of 9EDO goes
[[File:9edo scale.mp3|thumb|A chromatic 9edo scale on C.]]


1: 27/25 133.238 large limma, BP small semitone
9edo is the most basic tuning which supports an [[antidiatonic]] scale. Its fifth is considerably flatter than just, but still falls into the category of "fifth" despite this. 9edo is also the first edo to have distinct major and minor chords (if 5edo's tendo and arto chords are ignored).


2: 7/6 266.871 septimal minor third
9edo splits the octave into three parts, each representing the major third 5/4, similarly to 12edo, which is of moderate accuracy. A similarly crude approximation of 11/8 (a sharp fourth) is available at the perfect fourth of 4 steps, which means 9edo can be seen as a simple 2.5.11 system. Looking at the intervals in this subgroup, the submajor second 11/10 is tuned to 133 cents (extremely flat) and 25/22 is even worse (but still consistent); the supermajor sixth 55/32 is tuned very accurately at 933 cents (only slightly flat). Overall, 9edo is not a great system for approximating low-complexity JI intervals consistently. However, if we turn to inconsistent representations, we see quite a few options before us. In particular, the 9edo scale has the peculiar property of representing certain [[7-limit]] intervals almost exactly, but not the harmonic 7/4 (a subminor seventh) itself (unless [[semaphore]], which equates it with the supermajor sixth 12/7, is taken as an acceptable temperament in this tuning). A 7-limit version of 9edo goes


3: 63/50 400.108 quasi-equal major third
1: [[27/25]] 133.238 large limma, BP small semitone


4: 49/36 533.742 Arabic lute acute fourth
2: [[7/6]] 266.871 septimal minor third


5: 72/49 666.258 Arabic lute grave fifth
3: [[63/50]] 400.108 quasi-equal major third


6: 100/63 799.892 quasi-equal minor sixth
4: [[49/36]] 533.742 Arabic lute acute fourth


7: 12/7 933.129 septimal major sixth
5: [[72/49]] 666.258 Arabic lute grave fifth


8: 50/27 1066.762 grave major seventh
6: [[100/63]] 799.892 quasi-equal minor sixth


9: 2/1 1200.000 octave
7: [[12/7]] 933.129 septimal major sixth


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.
8: [[50/27]] 1066.762 grave major seventh


=Notation=
9: [[2/1]] 1200.000 octave


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.
Chords such as {{dash|1/1, 7/6, 49/36, 12/7|med}} are therefore natural ones for 9edo. The above scale generates the [[just intonation subgroup]] 2.27/25.7/3, which is closely related to 9edo.  


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".
=== Odd harmonics ===
{{Harmonics in equal|9}}


{| class="wikitable"
=== Subsets and supersets ===
! style="text-align:center;" | [[degree]]
9edo is the first odd composite edo, containing [[3edo]] as a subset.
! style="text-align:center;" | [[cent]]s
 
! style="text-align:center;" | Approximate <br>Ratios
The [[ennealimmal]] temperament contains 9edo as a subset (splitting 2/1 into 9 equal parts) and is excellent in the 7-limit. However, 9edo by itself tempers out 27/25 by [[Val|patent val]], rather than representing it as 1\9 like in ennealimmal, although the 9bccd val contains both the 27/25 and 7/6 representations above and therefore supports ennealimmal.
! colspan="2" style="text-align:center;" | Melodic notation
 
Major wider than minor
== Notation ==
! colspan="2" style="text-align:center;" | Harmonic notation
{{Mavila}}
Major narrower than minor
In this notation, the [[enharmonic unison]] is the augmented 2nd, e.g. E♭ to F♯.
 
{| class="wikitable center-all right-1 right-2"
|-
|-
| style="text-align:center;" | 0
![[degree]]
| style="text-align:center;" | 0
![[cent]]s
| style="text-align:center;" | 1/1
! Approximate<br />Ratios
| style="text-align:center;" | perfect unison
! colspan="2" | Antidiatonic<br />Major wider than minor
| style="text-align:center;" | D
! colspan="2" | Diatonic<br />Major narrower than minor
| style="text-align:center;" | perfect unison
! Audio
| style="text-align:center;" | D
|-
|-
| style="text-align:center;" | 1
| 0
| style="text-align:center;" | 133
| 0.00
| style="text-align:center;" | 14/13, 13/12, 12/11
|[[1/1]]
| style="text-align:center;" | minor 2nd
| perfect unison
| style="text-align:center;" | E
| D
| style="text-align:center;" | major 2nd
| perfect unison
| style="text-align:center;" | E
| D
|[[File:0-0 unison.mp3|frameless]]
|-
|-
| style="text-align:center;" | 2
| 1
| style="text-align:center;" | 267
| 133.33
| style="text-align:center;" | 7/6
|[[14/13]] (+5.035), [[13/12]] (−5.239),<br />[[12/11]] (−17.304)
| style="text-align:center;" | major 2nd, minor 3rd
| minor 2nd
| style="text-align:center;" | E#, Fb
| E
| style="text-align:center;" | minor 2nd, major 3rd
| major 2nd
| style="text-align:center;" | Eb, F#
| E
|[[File:0-133,33 minor second (9-EDO).mp3|frameless]]
|-
|-
| style="text-align:center;" | 3
| 2
| style="text-align:center;" | 400
| 266.67
| style="text-align:center;" | 5/4, 14/11, 9/7
|[[7/6]] (−0.204)
| style="text-align:center;" | major 3rd
| major 2nd, minor 3rd
| style="text-align:center;" | F
| E♯, F♭
| style="text-align:center;" | minor 3rd
| minor 2nd, major 3rd
| style="text-align:center;" | F
| E♭, F♯
|[[File:0-266,67 major 2nd, minor 3rd (9-EDO).mp3|frameless]]
|-
|-
| style="text-align:center;" | 4
| 3
| style="text-align:center;" | 533
| 400.00
| style="text-align:center;" | 4/3, 11/8
|[[5/4]] (+13.686), [[14/11]] (−17.508),<br />[[9/7]] (−35.084)
| style="text-align:center;" | perfect 4th
| major 3rd
| style="text-align:center;" | G
| F
| style="text-align:center;" | perfect 4th
| minor 3rd
| style="text-align:center;" | G
| F
|[[File:0-400 major third (12-EDO).mp3|frameless]]
|-
|-
| style="text-align:center;" | 5
| 4
| style="text-align:center;" | 667
| 533.33
| style="text-align:center;" | 16/11, 3/2
|[[4/3]] (+35.288), [[11/8]] (−17.985)
| style="text-align:center;" | perfect 5th
| perfect 4th
| style="text-align:center;" | A
| G
| style="text-align:center;" | perfect 5th
| perfect 4th
| style="text-align:center;" | A
| G
|[[File:0-533,33 fourth (9-EDO).mp3|frameless]]
|-
|-
| style="text-align:center;" | 6
| 5
| style="text-align:center;" | 800
| 666.67
| style="text-align:center;" | 14/9, 11/7, 8/5
|[[16/11]] (+17.985), [[3/2]] (−35.288)
| style="text-align:center;" | minor 6th
| perfect 5th
| style="text-align:center;" | B
| A
| style="text-align:center;" | major 6th
| perfect 5th
| style="text-align:center;" | B
| A
|[[File:0-666,67 fifth (9-EDO).mp3|frameless]]
|-
|-
| style="text-align:center;" | 7
| 6
| style="text-align:center;" | 933
| 800.00
| style="text-align:center;" | 12/7
|[[14/9]] (+35.084) [[11/7]] (+17.508),<br />[[8/5]] (−13.686)
| style="text-align:center;" | major 6th, minor 7th
| minor 6th
| style="text-align:center;" | B#, Cb
| B
| style="text-align:center;" | minor 6th, major 7th
| major 6th
| style="text-align:center;" | Bb, C#
| B
|[[File:0-800 minor sixth (12-EDO).mp3|frameless]]
|-
|-
| style="text-align:center;" | 8
| 7
| style="text-align:center;" | 1067
| 933.33
| style="text-align:center;" | 11/6, 13/7
|[[12/7]] (+0.204)
| style="text-align:center;" | major 7th
| major 6th, minor 7th
| style="text-align:center;" | C
| B♯, C♭
| style="text-align:center;" | minor 7th
| minor 6th, major 7th
| style="text-align:center;" | C
| B♭, C♯
|[[File:0-933,33 major 6th, minor 7th (9-EDO).mp3|frameless]]
|-
|-
| style="text-align:center;" | 9
| 8
| style="text-align:center;" | 1200
| 1066.67
| style="text-align:center;" | 2/1
|[[11/6]] (+17.304) [[13/7]] (−5.035)
| style="text-align:center;" | octave
| major 7th
| style="text-align:center;" | D
| C
| style="text-align:center;" | octave
| minor 7th
| style="text-align:center;" | D
| C
|[[File:0-1066,67 major seventh (9-EDO).mp3|frameless]]
|-
| 9
| 1200.00
|[[2/1]]
| octave
| D
| octave
| D
|[[File:0-1200 octave.mp3|frameless]]
|}
|}


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].
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[14edo#Sagittal notation|14-EDO]].


<imagemap>
File:9-EDO_Sagittal.svg
desc none
rect 80 0 296 50 [[Sagittal_notation]]
rect 296 0 456 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 296 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation |limma-fraction notation]]
default [[File:9-EDO_Sagittal.svg]]
</imagemap>
== Approximation to JI ==
=== 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.]]


[[:File:9ed2-001.svg|9ed2-001.svg]]
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -14 9 }}
| {{mapping| 9 14 }}
| +11.13
| 11.24
| 8.35
|-
| 2.3.5
| 27/25, 128/125
| {{mapping| 9 14 21 }}
| +5.36
| 12.18
| 9.10
|-
| 2.3.5.7
| 21/20, 36/35, 49/48
| {{mapping| 9 14 21 25 }}
| +7.20
| 11.02
| 8.21
|-
| 2.3.5.7.11
| 21/20, 33/32, 36/35, 45/44
| {{mapping| 9 14 21 25 31 }}
| +6.80
| 9.89
| 7.37
|}
 
=== Uniform maps ===
{{Uniform map|edo=9}}


=Commas=
=== Commas ===
9 EDO tempers out the following commas. (Note: This assumes val &lt; 9 14 21 25 31 33 |.)
9et [[tempering out|tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 9 14 21 25 31 33 }}.


{| class="wikitable"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
! [[Harmonic limit|Prime<br />limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name
|-
| 3
| [[19683/16384]]
| {{monzo| -14 9 }}
| 317.59
| Lawa 2nd
| Pythagorean augmented second
|-
|-
! | [[Ratios|Ratio]]
| 5
! | [[Monzo]]
| [[27/25]]
! | [[Cent]]s
| {{monzo| 0 3 -2 }}
![[Color notation/Temperament Names|Color Name]]
| 133.24
! | Name 1
| Gugu
! | Name 2
| Bug comma, large limma
! | Name 3
|-
|-
| style="text-align:center;" | 27/25
| 5
| |<nowiki> | 0 3 -2 </nowiki>&gt;
| [[135/128]]
| style="text-align:right;" | 133.24
| {{monzo| -7 3 1 }}
| style="text-align:center;" |Gugu
| 92.18
| style="text-align:center;" | Large Limma
| Layobi
| style="text-align:center;" | Large Semitone
| Mavila comma, major chroma
| | Bug Comma
|-
|-
| style="text-align:center;" | 135/128
| 5
| |<nowiki> | -7 3 1 </nowiki>&gt;
| [[16875/16384]]
| style="text-align:right;" | 92.18
| {{monzo| -14 3 4 }}
| style="text-align:center;" |Layobi
| 51.12
| style="text-align:center;" | Major Chroma
| Laquadyo
| style="text-align:center;" | Major Limma
| Negri comma
| | Pelogic Comma
|-
|-
| style="text-align:center;" | 16875/16384
| 5
| |<nowiki> | -14 3 4 </nowiki>&gt;
| [[128/125]]
| style="text-align:right;" | 51.12
| {{monzo| 7 0 -3 }}
| style="text-align:center;" |Laquadyo
| 41.06
| style="text-align:center;" | Negri Comma
| Trigu
| style="text-align:center;" | Double Augmentation Diesis
| Augmented comma, lesser diesis
| |
|-
|-
| style="text-align:center;" | 128/125
| 5
| |<nowiki> | 7 0 -3 </nowiki>&gt;
| [[2109375/2097152|(14 digits)]]
| style="text-align:right;" | 41.06
| {{monzo| -21 3 7 }}
| style="text-align:center;" |Trigu
| 10.06
| style="text-align:center;" | Diesis
| Lasepyo
| style="text-align:center;" | Augmented Comma
| [[Semicomma]]
| |
|-
|-
| style="text-align:center;" | 2109375/2097152
| 7
| |<nowiki> | -21 3 7 </nowiki>&gt;
| [[36/35]]
| style="text-align:right;" | 10.06
| {{monzo| 2 2 -1 -1 }}
| style="text-align:center;" |Lasepyo
| 48.77
| style="text-align:center;" | Semicomma
| Rugu
| style="text-align:center;" | Fokker Comma
| Mint comma, septimal quarter tone
| |
|-
|-
| style="text-align:center;" | 36/35
| 7
| |<nowiki> | 2 2 -1 -1 </nowiki>&gt;
| [[525/512]]
| style="text-align:right;" | 48.77
| {{monzo| -9 1 2 1 }}
| style="text-align:center;" |Rugu
| 43.41
| style="text-align:center;" | Septimal Quarter Tone
| Lazoyoyo
| style="text-align:center;" |
| Avicennma
| |
|-
|-
| style="text-align:center;" | 525/512
| 7
| |<nowiki> | -9 1 2 1 </nowiki>&gt;
| 49/48
| style="text-align:right;" | 43.41
| {{monzo| -4 -1 0 2 }}
| style="text-align:center;" |Lazoyoyo
| 35.70
| style="text-align:center;" | Avicenna
| Zozo
| style="text-align:center;" | Avicenna's Enharmonic Diesis
| Semaphoresma, slendro diesis
| |
|-
|-
| style="text-align:center;" | 49/48
| 7
| |<nowiki> | -4 -1 0 2 </nowiki>&gt;
| [[686/675]]
| style="text-align:right;" | 35.70
| {{monzo| 1 -3 -2 3 }}
| style="text-align:center;" |Zozo
| 27.99
| style="text-align:center;" | Slendro Diesis
| Trizo-agugu
| style="text-align:center;" |
| Senga
| |
|-
|-
| style="text-align:center;" | 686/675
| 7
| |<nowiki> | 1 -3 -2 3 </nowiki>&gt;
| [[2430/2401]]
| style="text-align:right;" | 27.99
| {{monzo| 1 5 1 -4 }}
| style="text-align:center;" |Trizo-agugu
| 20.79
| style="text-align:center;" | Senga
| Quadru-ayo
| style="text-align:center;" |
| Nuwell comma
| |
|-
|-
| style="text-align:center;" | 2430/2401
| 7
| |<nowiki> | 1 5 1 -4 </nowiki>&gt;
| [[1728/1715]]
| style="text-align:right;" | 20.79
| {{monzo| 6 3 -1 -3 }}
| style="text-align:center;" |Quadru-ayo
| 13.07
| style="text-align:center;" | Nuwell
| Triru-agu
| style="text-align:center;" |
| Orwellisma
| |
|-
|-
| style="text-align:center;" | 1728/1715
| 7
| |<nowiki> | 6 3 -1 -3 </nowiki>&gt;
| [[225/224]]
| style="text-align:right;" | 13.07
| {{monzo| -5 2 2 -1 }}
| style="text-align:center;" |Triru-agu
| 7.71
| style="text-align:center;" | Orwellisma
| Ruyoyo
| style="text-align:center;" | Orwell Comma
| Marvel comma
| |
|-
|-
| style="text-align:center;" | 225/224
| 7
| |<nowiki> | -5 2 2 -1 </nowiki>&gt;
| [[6144/6125]]
| style="text-align:right;" | 7.71
| {{monzo| 11 1 -3 -2 }}
| style="text-align:center;" |Ruyoyo
| 5.36
| style="text-align:center;" | Septimal Kleisma
| Sarurutrigu
| style="text-align:center;" | Marvel Comma
| Porwell comma
| |
|-
|-
| style="text-align:center;" | 6144/6125
| 7
| |<nowiki> | 11 1 -3 -2 </nowiki>&gt;
| [[65625/65536]]
| style="text-align:right;" | 5.36
| {{monzo| -16 1 5 1 }}
| style="text-align:center;" |Sarurutrigu
| 2.35
| style="text-align:center;" | Porwell
| Lazoquinyo
| style="text-align:center;" |
| Horwell comma
| |
|-
|-
| style="text-align:center;" | 65625/65536
| 7
| |<nowiki> | -16 1 5 1 </nowiki>&gt;
| <abbr title="40353607/40310784">(16 digits)</abbr>
| style="text-align:right;" | 2.35
| {{monzo| -11 -9 0 9 }}
| style="text-align:center;" |Lazoquinyo
| 1.84
| style="text-align:center;" | Horwell
| Tritrizo
| style="text-align:center;" |
| [[Septimal ennealimma]]
| |
|-
|-
| style="text-align:center;" | 99/98
| 11
| |<nowiki> | -1 2 0 -2 1 </nowiki>&gt;
| [[99/98]]
| style="text-align:right;" | 17.58
| {{monzo| -1 2 0 -2 1 }}
| style="text-align:center;" |Loruru
| 17.58
| style="text-align:center;" | Mothwellsma
| Loruru
| style="text-align:center;" |
| Mothwellsma
| |
|-
|-
| style="text-align:center;" | 121/120
| 11
| |<nowiki> | -3 -1 -1 0 2 </nowiki>&gt;
| [[121/120]]
| style="text-align:right;" | 14.37
| {{monzo| -3 -1 -1 0 2 }}
| style="text-align:center;" |Lologu
| 14.37
| style="text-align:center;" | Biyatisma
| Lologu
| style="text-align:center;" |
| Biyatisma
| |
|-
|-
| style="text-align:center;" | 176/175
| 11
| |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
| [[176/175]]
| style="text-align:right;" | 9.86
| {{monzo| 4 0 -2 -1 1 }}
| style="text-align:center;" |Lorugugu
| 9.86
| style="text-align:center;" | Valinorsma
| Lorugugu
| style="text-align:center;" |
| Valinorsma
| |
|-
|-
| style="text-align:center;" | 385/384
| 11
| |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
| [[385/384]]
| style="text-align:right;" | 4.50
| {{monzo| -7 -1 1 1 1 }}
| style="text-align:center;" |Lozoyo
| 4.50
| style="text-align:center;" | Keenanisma
| Lozoyo
| style="text-align:center;" |
| Keenanisma
| |
|-
|-
| style="text-align:center;" | 540/539
| 11
| |<nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
| [[540/539]]
| style="text-align:right;" | 3.21
| {{monzo| 2 3 1 -2 -1 }}
| style="text-align:center;" |Lururuyo
| 3.21
| style="text-align:center;" | Swetisma
| Lururuyo
| style="text-align:center;" |
| Swetisma
| |
|-
|-
| style="text-align:center;" | 91/90
| 13
| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>&gt;
| [[91/90]]
| style="text-align:right;" | 19.13
| {{monzo| -1 -2 -1 1 0 1 }}
| style="text-align:center;" |Thozogu
| 19.13
| style="text-align:center;" | Superleap
| Thozogu
| style="text-align:center;" |
| Superleap comma, biome comma
| |
|-
|-
| style="text-align:center;" | 676/675
| 13
| |<nowiki> | 2 -3 -2 0 0 2 </nowiki>&gt;
| [[676/675]]
| style="text-align:right;" | 2.56
| {{monzo| 2 -3 -2 0 0 2 }}
| style="text-align:center;" |Bithogu
| 2.56
| style="text-align:center;" | Parizeksma
| Bithogu
| style="text-align:center;" |
| Island comma
| |
|}
|}


=Images=
=== Rank-2 temperaments ===
9edo contains a pentatonic [[mos scale]] produced by stacking 4\9 of [[2L&nbsp;3s]] (1 3 1 3 1), which has a heptatonic extension, [[2L&nbsp;5s]] (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic").
 
You can also use 2\9, which generates mos scales of [[1L&nbsp;3s]] (3 2 2 2) and [[4L&nbsp;1s]] (2 2 2 2 1) and can be interpreted as either an extremely sharp [[bug]] scale or an extremely flat [[orwell]] one.


== Historical (and other) relevance ==
[[Indonesian]] pelog scales sometimes use five-tone subsets of a seven-tone superset in a similar way as the 5-tone and 7-tone mavila scale (see [[#Rank-2 temperaments|Rank-2 temperaments]]), and it has been suggested that Indonesian gamelan music stems from a [http://www.neuroscience-of-music.se/pelog%20historical.htm 9edo tradition].
As a division of the octave into 3<sup>2</sup> parts, i. e. a dominant position of the number 3, 9edo also has some suitability as base tuning for [https://en.wikipedia.org/wiki/Klingon Klingon] music (since the tradtional Klingon number system is also based on 3). See, for this:
[http://%5B%5Bhttps://www.youtube.com/watch?v=1LjcBv-OWtQ%5D%5D Levi McClain, Klingon music theory is weird]
== Octave stretch or compression ==
9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]].
Pure-octaves 9edo makes a decent 2.5.11 tuning, approximating all those three primes within 18{{c}}.
9edo with octaves stretched about 5{{c}}, as in [[zpi|22zpi]], makes a decent 2.7.11.13 tuning, approximating all those four primes within 17{{c}}.
9edo with octaves stretched about 10{{c}}, as in [[ed12|32ed12]], makes a decent 2.3.7.11.13 tuning, approximating all those five primes within 20{{c}}.
== Diagrams ==
[[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]]
* Ukulele (MicroUke 1.2) set to 9edo with 40 lb. test fishing line (by cenobyte)


[[File:IMG_2223-800x600.jpg|alt=IMG_2223-800x600.jpg|400px|IMG_2223-800x600.jpg]]
* 9edo can be played on the Lumatone, see [[Lumatone mapping for 9edo]]
== Music ==
{{Main|Music in 9edo}}


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


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


<ul><li>[https://soundcloud.com/overtoneshock/tencaious-chorale-9-edo-studio-version Tenacious Chorale (only movement I is in 9-EDO)] by Stephen Weigel</li><li>[https://soundcloud.com/overtoneshock/in-our-own-little-worlds-9-edo In Our Own Lonely Worlds] by Stephen Weigel</li><li>Nocturne in 9tet by [http://home.snafu.de/djwolf/WorksDescriptive.htm Daniel Wolf]</li><li>''[http://www.h-pi.com/mp3/Prelude9ET.mp3 Prelude in 9ET]'' by [[Aaron_Andrew_Hunt|Aaron Andrew Hunt]]</li><li>''[http://micro.soonlabel.com/9-edo/daily20110629_fts_e_guit_9et.mp3 Improvisation for Electric Guitar in 9 edo]'' by [http://www.chrisvaisvil.com Chris Vaisvil]</li><li>[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/08%20-%208.%209%20octave.mp3 Comets Over Flatland 8] by [[Randy_Winchester|Randy Winchester]]</li><li>[http://www.youtube.com/watch?v=bDFCsCoaUO4 Nine tones per Octave (9-EDO / 9-TET)] by [[Ivor_Darreg|Ivor Darreg]]</li><li>[http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3 Gerbils at the Wheel of Government] by [http://chrisvaisvil.com/?p=1402 Chris Vaisvil] (in 9 and 18 edo simultaneously)</li><li>[http://www.seraph.it/dep/det/NewWorld.mp3 New World] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/f533be803cb9ed1efc23fc9e2db10c6f-167.html blog entry])</li><li>[https://soundcloud.com/santiagocosentino/interdimensional-train-ride Interdimensional Train Ride by Santiago Cosentino]</li></ul>
=== Werntz Nocturne scale ===
{{main|Werntz Nocturne scale}}


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


[[Category:9-tone]]
[[Category:9-tone scales]]
[[Category:9edo]]
[[Category:Pelog]]
[[Category:aaron_andrew_hunt]]
[[Category:edo]]
[[Category:listen]]
[[Category:macrotonal]]
[[Category:scale]]
[[Category:todo:unify_precision]]
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