8edo: Difference between revisions

Revision as of 21:27, 31 May 2011

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This revision was by author jdfreivald and made on 2011-05-31 21:27:27 UTC.

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=8 - Equal Divisions of the Octave= 

==Theory== 

8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[Just intonation subgroups|just intonation subgroup]] 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6.

0. 1/1 C
1. 150.000 cents C#
2. 300.000 cents D#
3. 450.000 cents E
4. 600.000 cents F#
5. 750.000 cents G
6. 900.000 cents A
7. 1050.000 cents A#
8. 2/1 C

==Compositions== 

[[http://www.h-pi.com/mp3/Fantasia8ET.mp3|Fantasia in 8ET]] by Aaron Andrew Hunt
[[http://www.h-pi.com/mp3/Fugue8ET.mp3|Fugue in 8ET]] by Aaron Andrew Hunt
[[http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html|Špendlíky]] by Milan Guštar
[[@http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3|Acoustic Improvisation in 8-edo]] by Ron Sword

==See also== 
*[[Octatonic scale]] - a scale based on alternating whole and half steps

==Commas== 
8 EDO tempers out the following commas. (Note: This assumes val < 8 13 19 22 28 30 |).

||~ Comma ||~ Monzo ||~ Cents ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= 648/625 || | 3 4 -4 > ||> 62.57 ||= Major Diesis ||= Diminished Comma ||   ||
||= 250/243 || | 1 -5 3 > ||> 49.17 ||= Maximal Diesis ||= Porcupine Comma ||   ||
||= 78732/78125 || | 2 9 -7 > ||> 13.40 ||= Medium Semicomma ||= Sensipent Comma ||   ||
||= 64/63 || | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma || Leipziger Komma ||
||= 875/864 || | -5 -3 3 1 > ||> 21.90 ||= Keema ||   ||   ||
||= 321489/320000 || | -9 8 -4 2 > ||> 8.04 ||= Varunisma ||   ||   ||
||= 6144/6125 || | 11 1 -3 -2 > ||> 5.36 ||= Porwell ||   ||   ||
||= 100/99 || | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma ||   ||   ||
||= 121/120 || | -3 -1 -1 0 2 > ||> 14.37 ||= Biyatisma ||   ||   ||
||= 176/175 || | 4 0 -2 -1 1 > ||> 9.86 ||= Valinorsma ||   ||   ||
||= 65536/65219 || | 16 0 0 -2 -3 > ||> 8.39 ||= Orgonisma ||   ||   ||
||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||   ||   ||
||= 4000/3993 || | 5 -1 3 0 -3 > ||> 3.03 ||= Wizardharry ||   ||   ||

Original HTML content:

<html><head><title>8edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x8 - Equal Divisions of the Octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->8 - Equal Divisions of the Octave</h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x8 - Equal Divisions of the Octave-Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h2>
 <br />
8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a &quot;barbaric&quot; harmonic system; even so, it does a good job representing the <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6.<br />
<br />
0. 1/1 C<br />
1. 150.000 cents C#<br />
2. 300.000 cents D#<br />
3. 450.000 cents E<br />
4. 600.000 cents F#<br />
5. 750.000 cents G<br />
6. 900.000 cents A<br />
7. 1050.000 cents A#<br />
8. 2/1 C<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x8 - Equal Divisions of the Octave-Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 -->Compositions</h2>
 <br />
<a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Fantasia8ET.mp3" rel="nofollow">Fantasia in 8ET</a> by Aaron Andrew Hunt<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Fugue8ET.mp3" rel="nofollow">Fugue in 8ET</a> by Aaron Andrew Hunt<br />
<a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html" rel="nofollow">Špendlíky</a> by Milan Guštar<br />
<a class="wiki_link_ext" href="http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3" rel="nofollow" target="_blank">Acoustic Improvisation in 8-edo</a> by Ron Sword<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x8 - Equal Divisions of the Octave-See also"></a><!-- ws:end:WikiTextHeadingRule:6 -->See also</h2>
 *<a class="wiki_link" href="/Octatonic%20scale">Octatonic scale</a> - a scale based on alternating whole and half steps<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x8 - Equal Divisions of the Octave-Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h2>
 8 EDO tempers out the following commas. (Note: This assumes val &lt; 8 13 19 22 28 30 |).<br />
<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Monzo<br />
</th>
        <th>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;">648/625<br />
</td>
        <td>| 3 4 -4 &gt;<br />
</td>
        <td style="text-align: right;">62.57<br />
</td>
        <td style="text-align: center;">Major Diesis<br />
</td>
        <td style="text-align: center;">Diminished Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">250/243<br />
</td>
        <td>| 1 -5 3 &gt;<br />
</td>
        <td style="text-align: right;">49.17<br />
</td>
        <td style="text-align: center;">Maximal Diesis<br />
</td>
        <td style="text-align: center;">Porcupine Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">78732/78125<br />
</td>
        <td>| 2 9 -7 &gt;<br />
</td>
        <td style="text-align: right;">13.40<br />
</td>
        <td style="text-align: center;">Medium Semicomma<br />
</td>
        <td style="text-align: center;">Sensipent Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">64/63<br />
</td>
        <td>| 6 -2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">27.26<br />
</td>
        <td style="text-align: center;">Septimal Comma<br />
</td>
        <td style="text-align: center;">Archytas' Comma<br />
</td>
        <td>Leipziger Komma<br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">875/864<br />
</td>
        <td>| -5 -3 3 1 &gt;<br />
</td>
        <td style="text-align: right;">21.90<br />
</td>
        <td style="text-align: center;">Keema<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">321489/320000<br />
</td>
        <td>| -9 8 -4 2 &gt;<br />
</td>
        <td style="text-align: right;">8.04<br />
</td>
        <td style="text-align: center;">Varunisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6144/6125<br />
</td>
        <td>| 11 1 -3 -2 &gt;<br />
</td>
        <td style="text-align: right;">5.36<br />
</td>
        <td style="text-align: center;">Porwell<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">100/99<br />
</td>
        <td>| 2 -2 2 0 -1 &gt;<br />
</td>
        <td style="text-align: right;">17.40<br />
</td>
        <td style="text-align: center;">Ptolemisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">121/120<br />
</td>
        <td>| -3 -1 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">14.37<br />
</td>
        <td style="text-align: center;">Biyatisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">176/175<br />
</td>
        <td>| 4 0 -2 -1 1 &gt;<br />
</td>
        <td style="text-align: right;">9.86<br />
</td>
        <td style="text-align: center;">Valinorsma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">65536/65219<br />
</td>
        <td>| 16 0 0 -2 -3 &gt;<br />
</td>
        <td style="text-align: right;">8.39<br />
</td>
        <td style="text-align: center;">Orgonisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td>| -7 -1 1 1 1 &gt;<br />
</td>
        <td style="text-align: right;">4.50<br />
</td>
        <td style="text-align: center;">Keenanisma<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4000/3993<br />
</td>
        <td>| 5 -1 3 0 -3 &gt;<br />
</td>
        <td style="text-align: right;">3.03<br />
</td>
        <td style="text-align: center;">Wizardharry<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 17:33:15 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 21:27:27 UTC</tt>.<br>
-: The original revision id was <tt>233287140</tt>.<br>
+: The original revision id was <tt>233337420</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 43: / Line 43: @@
 ||= 321489/320000 || | -9 8 -4 2 &gt; ||&gt; 8.04 ||= Varunisma ||   ||   ||
 ||= 6144/6125 || | 11 1 -3 -2 &gt; ||&gt; 5.36 ||= Porwell ||   ||   ||
-||= 100/99 || | 2 -2 2 -1 &gt; ||&gt; 17.40 ||= Ptolemisma ||   ||   ||
+||= 100/99 || | 2 -2 2 0 -1 &gt; ||&gt; 17.40 ||= Ptolemisma ||   ||   ||
-||= 121/120 || | -3 -1 -1 2 &gt; ||&gt; 14.37 ||= Biyatisma ||   ||   ||
+||= 121/120 || | -3 -1 -1 0 2 &gt; ||&gt; 14.37 ||= Biyatisma ||   ||   ||
-||= 176/175 || | 4 -2 -1 1 &gt; ||&gt; 9.86 ||= Valinorsma ||   ||   ||
+||= 176/175 || | 4 0 -2 -1 1 &gt; ||&gt; 9.86 ||= Valinorsma ||   ||   ||
-||= 65536/65219 || | 16 -2 -3 &gt; ||&gt; 8.39 ||= Orgonisma ||   ||   ||
+||= 65536/65219 || | 16 0 0 -2 -3 &gt; ||&gt; 8.39 ||= Orgonisma ||   ||   ||
 ||= 385/384 || | -7 -1 1 1 1 &gt; ||&gt; 4.50 ||= Keenanisma ||   ||   ||
-||= 4000/3993 || | 5 -1 3 -3 &gt; ||&gt; 3.03 ||= Wizardharry ||   ||   ||</pre></div>
+||= 4000/3993 || | 5 -1 3 0 -3 &gt; ||&gt; 3.03 ||= Wizardharry ||   ||   ||</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;8edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x8 - Equal Divisions of the Octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;8 - Equal Divisions of the Octave&lt;/h1&gt;
@@ Line 197: / Line 197: @@
          &lt;td style="text-align: center;"&gt;100/99&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| 2 -2 2 -1 &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 2 -2 2 0 -1 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;17.40&lt;br /&gt;
@@ Line 211: / Line 211: @@
          &lt;td style="text-align: center;"&gt;121/120&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| -3 -1 -1 2 &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| -3 -1 -1 0 2 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;14.37&lt;br /&gt;
@@ Line 225: / Line 225: @@
          &lt;td style="text-align: center;"&gt;176/175&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| 4 -2 -1 1 &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 4 0 -2 -1 1 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;9.86&lt;br /&gt;
@@ Line 239: / Line 239: @@
          &lt;td style="text-align: center;"&gt;65536/65219&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| 16 -2 -3 &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 16 0 0 -2 -3 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;8.39&lt;br /&gt;
@@ Line 267: / Line 267: @@
          &lt;td style="text-align: center;"&gt;4000/3993&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| 5 -1 3 -3 &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 5 -1 3 0 -3 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;3.03&lt;br /&gt;

8edo: Difference between revisions

Revision as of 21:27, 31 May 2011

IMPORTED REVISION FROM WIKISPACES

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