9edo: Difference between revisions

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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

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".

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[[:File:9ed2-001.svg|9ed2-001.svg]]

9 EDO tempers out the following commas. (Note: This assumes val &lt; 9 14 21 25 31 33 |.)

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

[[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)

<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 Zones of Lasting Novelty] (Un12 2019) by Stephen Weigel; perf. Hans Gunter-Lock, Jacob Barton, and Stephen Weigel</li><li>[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]])

</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>

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:9edo]]