9edo: Difference between revisions

'''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.

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The 9EDO scale has the peculiar property of representing certain [[7-limit]] intervals almost exactly. A 7-limit version of 9EDO goes

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.

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".

9EDO [[tempers out]] the following [[comma]]s. (Note: This assumes [[val]] {{val| 9 14 21 25 31 33 }}.)

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].

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

* ''[http://www.h-pi.com/mp3/Prelude9ET.mp3 Prelude in 9ET]'' by [[Aaron Andrew Hunt]]

* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/08%20-%208.%209%20octave.mp3 Comets Over Flatland 8] by [[Randy Winchester]]

9EDO 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:9edo| ]]