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9edo: Difference between revisions

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| Prime factorization = 3<sup>2</sup>
| Prime factorization = 3<sup>2</sup>
| Step size = 133.333¢
| Step size = 133.333¢
| Fifth = 5\9 = 666.667¢
| Fifth = 5\9 (667¢)
| Major 2nd = 1\9 = 133.333¢
| Major 2nd = 1\9 (133¢)
| Consistency = 7
| Consistency = 7
| Monotonicity = 7
}}
}}
'''9 equal divisions of the octave''' ('''9edo''') is the [[tuning system]] derived by dividing the [[octave]] into 9 equal steps of 133+1/3 [[cent]]s each precisely. It is also the first odd composite edo.
'''9 equal divisions of the octave''' ('''9edo''') is the [[tuning system]] derived by dividing the [[octave]] into 9 equal steps of 133+1/3 [[cent]]s each precisely. It is also the first odd composite edo.


== Theory ==
== Theory ==
{{Harmonics in equal|9|intervals=odd}}
{{Harmonics in equal|9}}


The 9edo 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
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! [[Cent]]s
! [[Cent]]s
! [[Color name]]
! [[Color name]]
! Name(s)
! Name
|-
|-
| 5
| 5
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| 133.24
| 133.24
| Gugu
| Gugu
| Large Limma, Large Semitone, Bug Comma
| Large limma
|-
|-
| 5
| 5
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| 92.18
| 92.18
| Layobi
| Layobi
| Major Chroma, Major Limma, Pelogic Comma
| Major chroma
|-
|-
| 5
| 5
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| 51.12
| 51.12
| Laquadyo
| Laquadyo
| Negri Comma, Double Augmentation Diesis
| Negri comma
|-
|-
| 5
| 5
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| 41.06
| 41.06
| Trigu
| Trigu
| Diesis, Augmented Comma
| Diesis
|-
|-
| 5
| 5
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| 10.06
| 10.06
| Lasepyo
| Lasepyo
| [[Semicomma]], Fokker Comma
| [[Semicomma]]
|-
|-
| 7
| 7
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| 48.77
| 48.77
| Rugu
| Rugu
| Septimal Quarter Tone
| Septimal quartertone
|-
|-
| 7
| 7
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| 43.41
| 43.41
| Lazoyoyo
| Lazoyoyo
| Avicenna, Avicenna's Enharmonic Diesis
| Avicennma
|-
|-
| 7
| 7
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| 35.70
| 35.70
| Zozo
| Zozo
| Slendro Diesis
| Slendro diesis
|-
|-
| 7
| 7
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| 20.79
| 20.79
| Quadru-ayo
| Quadru-ayo
| Nuwell
| Nuwell comma
|-
|-
| 7
| 7
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| 13.07
| 13.07
| Triru-agu
| Triru-agu
| Orwellisma, Orwell Comma
| Orwellisma
|-
|-
| 7
| 7
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| 7.71
| 7.71
| Ruyoyo
| Ruyoyo
| Septimal Kleisma, Marvel Comma
| Marvel comma
|-
|-
| 7
| 7
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| 5.36
| 5.36
| Sarurutrigu
| Sarurutrigu
| Porwell
| Porwell comma
|-
|-
| 7
| 7
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| 2.35
| 2.35
| Lazoquinyo
| Lazoquinyo
| Horwell
| Horwell comma
|-
|-
| 7
| 7
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| 1.84
| 1.84
| Tritrizo
| Tritrizo
| [[Tritrizo clan|No-fives ennealimma]]
| [[Septimal ennealimma]]
|-
|-
| 11
| 11
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| 2.56
| 2.56
| Bithogu
| Bithogu
| Parizeksma
| Island comma
|}
|}
<references/>
<references/>


== Linear temperaments ==
== Linear temperaments ==
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 [[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].
 
== Scales ==
=== Pathological modes ===
2 1 1 1 1 1 1 1 [[1L 7s]] MOS


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


[[Category:9edo| ]] <!-- main article -->
[[Category:9edo| ]] <!-- main article -->
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