9edo
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<span style="display: block; text-align: right;">[[9平均律|日本語]] </span> 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 1: 27/25 133.238 large limma, BP small semitone 2: 7/6 266.871 septimal minor third 3: 63/50 400.108 quasi-equal major third 4: 49/36 533.742 Arabic lute acute fourth 5: 72/49 666.258 Arabic lute grave fifth 6: 100/63 799.892 quasi-equal minor sixth 7: 12/7 933.129 septimal major sixth 8: 50/27 1066.762 grave major seventh 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. 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]]. [[media type="custom" key="24802430"]] [[file:9ed2-001.svg]] =Images= [[image:9edo wheel.png width="385" height="385"]] ==Commas== 9 EDO tempers out the following commas. (Note: This assumes val < 9 14 21 25 31 33 |.) ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || ||= 135/128 || | -7 3 1 > ||> 92.18 ||= Major Chroma ||= Major Limma || Pelogic Comma || ||= 16875/16384 || | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis || || ||= 128/125 || | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma || || ||= 2109375/2097152 || | -21 3 7 > ||> 10.06 ||= Semicomma ||= Fokker Comma || || ||= 36/35 || | 2 2 -1 -1 > ||> 48.77 ||= Septimal Quarter Tone ||= || || ||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis || || ||= 49/48 || | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= || || ||= 686/675 || | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= || || ||= 2430/2401 || | 1 5 1 -4 > ||> 20.79 ||= Nuwell ||= || || ||= 1728/1715 || | 6 3 -1 -3 > ||> 13.07 ||= Orwellisma ||= Orwell Comma || || ||= 225/224 || | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma || || ||= 6144/6125 || | 11 1 -3 -2 > ||> 5.36 ||= Porwell ||= || || ||= 65625/65536 || | -16 1 5 1 > ||> 2.35 ||= Horwell ||= || || ||= 99/98 || | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||= || || ||= 121/120 || | -3 -1 -1 0 2 > ||> 14.37 ||= Biyatisma ||= || || ||= 176/175 || | 4 0 -2 -1 1 > ||> 9.86 ||= Valinorsma ||= || || ||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= || || ||= 540/539 || | 2 3 1 -2 -1 > ||> 3.21 ||= Swetisma ||= || || ||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= || || ||= 676/675 || | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||= || || =Compositions= * Nocturne in 9tet by [[http://home.snafu.de/djwolf/WorksDescriptive.htm|Daniel Wolf]] * //[[http://www.h-pi.com/mp3/Prelude9ET.mp3|Prelude in 9ET]]// by [[Aaron Andrew Hunt]] * //[[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]][[media type="custom" key="10221463"]] * [[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/08%20-%208.%209%20octave.mp3|Comets Over Flatland 8]] by [[Randy Winchester]] * [[http://www.youtube.com/watch?v=bDFCsCoaUO4|Nine tones per Octave (9-EDO / 9-TET)]] by [[Ivor Darreg]] * [[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) * [[http://www.seraph.it/dep/det/NewWorld.mp3|New World]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/f533be803cb9ed1efc23fc9e2db10c6f-167.html|blog entry]]) ===**Instruments**=== [[image:IMG_2223-800x600.jpg width="400"]] Ukulele (MicroUke 1.2) set to 9 EDO with 40 lb. test fishing line (by cenobyte)
Original HTML content:
<html><head><title>9edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/9%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br />
</span><br />
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 <a class="wiki_link" href="/Harmonic%20Limit">7-limit</a> intervals almost exactly. A 7-limit version of 9EDO goes<br />
<br />
1: 27/25 133.238 large limma, BP small semitone<br />
2: 7/6 266.871 septimal minor third<br />
3: 63/50 400.108 quasi-equal major third<br />
4: 49/36 533.742 Arabic lute acute fourth<br />
5: 72/49 666.258 Arabic lute grave fifth<br />
6: 100/63 799.892 quasi-equal minor sixth<br />
7: 12/7 933.129 septimal major sixth<br />
8: 50/27 1066.762 grave major seventh<br />
9: 2/1 1200.000 octave<br />
<br />
Here the characterizations are taken from <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Scala_%28program%29" rel="nofollow">Scala</a>, 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 <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.27/25.7/3, which is closely related to 9EDO.<br />
<br />
9EDO contains a pentatonic <a class="wiki_link" href="/MOSScales">MOS scale</a> -- 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 <a class="wiki_link_ext" href="http://www.neuroscience-of-music.se/pelog%20historical.htm" rel="nofollow">9EDO tradition</a>.<br />
<br />
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<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc0"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:2 -->Images</h1>
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<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc1"><a name="Images-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h2>
9 EDO tempers out the following commas. (Note: This assumes val < 9 14 21 25 31 33 |.)<br />
<br />
<table class="wiki_table">
<tr>
<th>Comma<br />
</th>
<th>Monzo<br />
</th>
<th>Value (Cents)<br />
</th>
<th>Name 1<br />
</th>
<th>Name 2<br />
</th>
<th>Name 3<br />
</th>
</tr>
<tr>
<td style="text-align: center;">135/128<br />
</td>
<td>| -7 3 1 ><br />
</td>
<td style="text-align: right;">92.18<br />
</td>
<td style="text-align: center;">Major Chroma<br />
</td>
<td style="text-align: center;">Major Limma<br />
</td>
<td>Pelogic Comma<br />
</td>
</tr>
<tr>
<td style="text-align: center;">16875/16384<br />
</td>
<td>| -14 3 4 ><br />
</td>
<td style="text-align: right;">51.12<br />
</td>
<td style="text-align: center;">Negri Comma<br />
</td>
<td style="text-align: center;">Double Augmentation Diesis<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">128/125<br />
</td>
<td>| 7 0 -3 ><br />
</td>
<td style="text-align: right;">41.06<br />
</td>
<td style="text-align: center;">Diesis<br />
</td>
<td style="text-align: center;">Augmented Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">2109375/2097152<br />
</td>
<td>| -21 3 7 ><br />
</td>
<td style="text-align: right;">10.06<br />
</td>
<td style="text-align: center;">Semicomma<br />
</td>
<td style="text-align: center;">Fokker Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">36/35<br />
</td>
<td>| 2 2 -1 -1 ><br />
</td>
<td style="text-align: right;">48.77<br />
</td>
<td style="text-align: center;">Septimal Quarter Tone<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">525/512<br />
</td>
<td>| -9 1 2 1 ><br />
</td>
<td style="text-align: right;">43.41<br />
</td>
<td style="text-align: center;">Avicennma<br />
</td>
<td style="text-align: center;">Avicenna's Enharmonic Diesis<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">49/48<br />
</td>
<td>| -4 -1 0 2 ><br />
</td>
<td style="text-align: right;">35.70<br />
</td>
<td style="text-align: center;">Slendro Diesis<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">686/675<br />
</td>
<td>| 1 -3 -2 3 ><br />
</td>
<td style="text-align: right;">27.99<br />
</td>
<td style="text-align: center;">Senga<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">2430/2401<br />
</td>
<td>| 1 5 1 -4 ><br />
</td>
<td style="text-align: right;">20.79<br />
</td>
<td style="text-align: center;">Nuwell<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">1728/1715<br />
</td>
<td>| 6 3 -1 -3 ><br />
</td>
<td style="text-align: right;">13.07<br />
</td>
<td style="text-align: center;">Orwellisma<br />
</td>
<td style="text-align: center;">Orwell Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">225/224<br />
</td>
<td>| -5 2 2 -1 ><br />
</td>
<td style="text-align: right;">7.71<br />
</td>
<td style="text-align: center;">Septimal Kleisma<br />
</td>
<td style="text-align: center;">Marvel Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">6144/6125<br />
</td>
<td>| 11 1 -3 -2 ><br />
</td>
<td style="text-align: right;">5.36<br />
</td>
<td style="text-align: center;">Porwell<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">65625/65536<br />
</td>
<td>| -16 1 5 1 ><br />
</td>
<td style="text-align: right;">2.35<br />
</td>
<td style="text-align: center;">Horwell<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">99/98<br />
</td>
<td>| -1 2 0 -2 1 ><br />
</td>
<td style="text-align: right;">17.58<br />
</td>
<td style="text-align: center;">Mothwellsma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">121/120<br />
</td>
<td>| -3 -1 -1 0 2 ><br />
</td>
<td style="text-align: right;">14.37<br />
</td>
<td style="text-align: center;">Biyatisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">176/175<br />
</td>
<td>| 4 0 -2 -1 1 ><br />
</td>
<td style="text-align: right;">9.86<br />
</td>
<td style="text-align: center;">Valinorsma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">385/384<br />
</td>
<td>| -7 -1 1 1 1 ><br />
</td>
<td style="text-align: right;">4.50<br />
</td>
<td style="text-align: center;">Keenanisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">540/539<br />
</td>
<td>| 2 3 1 -2 -1 ><br />
</td>
<td style="text-align: right;">3.21<br />
</td>
<td style="text-align: center;">Swetisma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">91/90<br />
</td>
<td>| -1 -2 -1 1 0 1 ><br />
</td>
<td style="text-align: right;">19.13<br />
</td>
<td style="text-align: center;">Superleap<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">676/675<br />
</td>
<td>| 2 -3 -2 0 0 2 ><br />
</td>
<td style="text-align: right;">2.56<br />
</td>
<td style="text-align: center;">Parizeksma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc2"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:6 -->Compositions</h1>
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<ul><li>Nocturne in 9tet by <a class="wiki_link_ext" href="http://home.snafu.de/djwolf/WorksDescriptive.htm" rel="nofollow">Daniel Wolf</a></li><li><em><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Prelude9ET.mp3" rel="nofollow">Prelude in 9ET</a></em> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a></li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20110629_fts_e_guit_9et.mp3" rel="nofollow">Improvisation for Electric Guitar in 9 edo</a></em> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow">Chris Vaisvil</a><!-- ws:start:WikiTextMediaRule:1:<img src="http://www.wikispaces.com/site/embedthumbnail/custom/10221463?h=0&w=0" class="WikiMedia WikiMediaCustom" id="wikitext@@media@@type=&quot;custom&quot; key=&quot;10221463&quot;" title="Custom Media"/> --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js">
</script><!-- ws:end:WikiTextMediaRule:1 --></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/08%20-%208.%209%20octave.mp3" rel="nofollow">Comets Over Flatland 8</a> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a></li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=bDFCsCoaUO4" rel="nofollow">Nine tones per Octave (9-EDO / 9-TET)</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3" rel="nofollow">Gerbils at the Wheel of Government</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1402" rel="nofollow" target="_blank">Chris Vaisvil</a> (in 9 and 18 edo simultaneously)</li><li><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/NewWorld.mp3" rel="nofollow">New World</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/f533be803cb9ed1efc23fc9e2db10c6f-167.html" rel="nofollow">blog entry</a>)</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc3"><a name="Compositions--Instruments"></a><!-- ws:end:WikiTextHeadingRule:8 --><strong>Instruments</strong></h3>
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Ukulele (MicroUke 1.2) set to 9 EDO with 40 lb. test fishing line (by cenobyte)</body></html>