9edo: Difference between revisions

Revision as of 17:38, 31 May 2011

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This revision was by author jdfreivald and made on 2011-05-31 17:38:56 UTC.

The original revision id was 233288672.

The revision comment was: Added comma table.

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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

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 1-7/6-49/36-12/7 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]].

=Compositions= 

Nocturne in 9tet by [[Daniel Wolf]] (ref?)
[[http://www.h-pi.com/mp3/Prelude9ET.mp3|Prelude in 9ET]] by [[Aaron Andrew Hunt]]

==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 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 -2 1 > || 17.58 || Mothwellsma ||   ||   ||
|| 121/120 || | -3 -1 -1 2 > || 14.37 || Biyatisma ||   ||   ||
|| 176/175 || | 4 -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 1 > || 19.13 || Superleap ||   ||   ||
|| 676/675 || | 2 -3 -2 2 > || 2.56 || Parizeksma ||   ||   ||

Original HTML content:

<html><head><title>9edo</title></head><body>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 &quot;Pelog Nawanada: Sunda&quot;. Chords such as 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 &quot;mavila&quot; or &quot;antidiatonic&quot;). 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 />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Compositions</h1>
 <br />
Nocturne in 9tet by <a class="wiki_link" href="/Daniel%20Wolf">Daniel Wolf</a> (ref?)<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Prelude9ET.mp3" rel="nofollow">Prelude in 9ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Compositions-Commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas</h2>
 9 EDO tempers out the following commas. (Note: This assumes val &lt; 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>135/128<br />
</td>
        <td>| -7 3 1 &gt;<br />
</td>
        <td>92.18<br />
</td>
        <td>Major Chroma<br />
</td>
        <td>Major Limma<br />
</td>
        <td>Pelogic Comma<br />
</td>
    </tr>
    <tr>
        <td>16875/16384<br />
</td>
        <td>| -14 3 4 &gt;<br />
</td>
        <td>51.12<br />
</td>
        <td>Negri Comma<br />
</td>
        <td>Double Augmentation Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>128/125<br />
</td>
        <td>| 7 0 -3 &gt;<br />
</td>
        <td>41.06<br />
</td>
        <td>Diesis<br />
</td>
        <td>Augmented Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2109375/2097152<br />
</td>
        <td>| -21 3 7 &gt;<br />
</td>
        <td>10.06<br />
</td>
        <td>Semicomma<br />
</td>
        <td>Fokker Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>36/35<br />
</td>
        <td>| 2 2 -1 -1 &gt;<br />
</td>
        <td>48.77<br />
</td>
        <td>Septimal Quarter Tone<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>525/512<br />
</td>
        <td>| -9 1 2 1 &gt;<br />
</td>
        <td>43.41<br />
</td>
        <td>Avicennma<br />
</td>
        <td>Avicenna's Enharmonic Diesis<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>49/48<br />
</td>
        <td>| -4 -1 2 &gt;<br />
</td>
        <td>35.70<br />
</td>
        <td>Slendro Diesis<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>686/675<br />
</td>
        <td>| 1 -3 -2 3 &gt;<br />
</td>
        <td>27.99<br />
</td>
        <td>Senga<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2430/2401<br />
</td>
        <td>| 1 5 1 -4 &gt;<br />
</td>
        <td>20.79<br />
</td>
        <td>Nuwell<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1728/1715<br />
</td>
        <td>| 6 3 -1 -3 &gt;<br />
</td>
        <td>13.07<br />
</td>
        <td>Orwellisma<br />
</td>
        <td>Orwell Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>225/224<br />
</td>
        <td>| -5 2 2 -1 &gt;<br />
</td>
        <td>7.71<br />
</td>
        <td>Septimal Kleisma<br />
</td>
        <td>Marvel Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6144/6125<br />
</td>
        <td>| 11 1 -3 -2 &gt;<br />
</td>
        <td>5.36<br />
</td>
        <td>Porwell<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>65625/65536<br />
</td>
        <td>| -16 1 5 1 &gt;<br />
</td>
        <td>2.35<br />
</td>
        <td>Horwell<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>99/98<br />
</td>
        <td>| -1 2 -2 1 &gt;<br />
</td>
        <td>17.58<br />
</td>
        <td>Mothwellsma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>121/120<br />
</td>
        <td>| -3 -1 -1 2 &gt;<br />
</td>
        <td>14.37<br />
</td>
        <td>Biyatisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>176/175<br />
</td>
        <td>| 4 -2 -1 1 &gt;<br />
</td>
        <td>9.86<br />
</td>
        <td>Valinorsma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>385/384<br />
</td>
        <td>| -7 -1 1 1 1 &gt;<br />
</td>
        <td>4.50<br />
</td>
        <td>Keenanisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>540/539<br />
</td>
        <td>| 2 3 1 -2 -1 &gt;<br />
</td>
        <td>3.21<br />
</td>
        <td>Swetisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>91/90<br />
</td>
        <td>| -1 -2 -1 1 1 &gt;<br />
</td>
        <td>19.13<br />
</td>
        <td>Superleap<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>676/675<br />
</td>
        <td>| 2 -3 -2 2 &gt;<br />
</td>
        <td>2.56<br />
</td>
        <td>Parizeksma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

9edo: Difference between revisions

Revision as of 17:38, 31 May 2011

IMPORTED REVISION FROM WIKISPACES

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