9edo: Difference between revisions

→Theory: the 7-limit mapping is a property of all ennealimmal tunings
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|9}}
{{EDO intro|9}}
9edo is  the first odd composite edo.


== Theory ==
== Theory ==
{{Harmonics in equal|9}}
[[File:9edo scale.mp3|thumb|A chromatic 9edo scale on C.]]
[[File:9edo scale.mp3|thumb|A chromatic 9edo scale on C.]]
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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9: 2/1 1200.000 octave
9: 2/1 1200.000 octave


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 [[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 subgroup]] 2.27/25.7/3, which is closely related to 9edo.  
 
The [[ennealimmal]] temperament, which contains 9et as a subset and are excellent in the 7-limit, maps the scale above consistently with regards to their respective steps. Thus 9edo can be viewed as the trivial tuning of ennealimmal.
 
=== Odd harmonics ===
{{Harmonics in equal|9}}


The [[ennealimmal]] temperament, which contains 9et as a subset and are excellent in the 7-limit, maps the scale above consistently with regards to their respective steps.
=== Divisors ===
9edo is the first odd composite edo.


== Notation ==
== Notation ==