8edo: Difference between revisions

Revision as of 17:30, 31 May 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author jdfreivald and made on 2011-05-31 17:30:28 UTC.

The original revision id was 233286326.

The revision comment was: Added comma table.

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=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 -1 > || 17.40 |||| Ptolemisma ||   ||
|| 121/120 || | -3 -1 -1 2 > || 14.37 |||| Biyatisma ||   ||
|| 176/175 || | 4 -2 -1 1 > || 9.86 |||| Valinorsma ||   ||
|| 65536/65219 || | 16 -2 -3 > || 8.39 |||| Orgonisma ||   ||
|| 385/384 || | -7 -1 1 1 1 > || 4.50 |||| Keenanisma ||   ||
|| 4000/3993 || | 5 -1 3 -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>648/625<br />
</td>
        <td>| 3 4 -4 &gt;<br />
</td>
        <td>62.57<br />
</td>
        <td>Major Diesis<br />
</td>
        <td>Diminished Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>250/243<br />
</td>
        <td>| 1 -5 3 &gt;<br />
</td>
        <td>49.17<br />
</td>
        <td>Maximal Diesis<br />
</td>
        <td>Porcupine Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>78732/78125<br />
</td>
        <td>| 2 9 -7 &gt;<br />
</td>
        <td>13.40<br />
</td>
        <td>Medium Semicomma<br />
</td>
        <td>Sensipent Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>64/63<br />
</td>
        <td>| 6 -2 0 -1 &gt;<br />
</td>
        <td>27.26<br />
</td>
        <td>Septimal Comma<br />
</td>
        <td>Archytas' Comma<br />
</td>
        <td>Leipziger Komma<br />
</td>
    </tr>
    <tr>
        <td>875/864<br />
</td>
        <td>| -5 -3 3 1 &gt;<br />
</td>
        <td>21.90<br />
</td>
        <td colspan="2">Keema<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>321489/320000<br />
</td>
        <td>| -9 8 -4 2 &gt;<br />
</td>
        <td>8.04<br />
</td>
        <td colspan="2">Varunisma<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 colspan="2">Porwell<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>100/99<br />
</td>
        <td>| 2 -2 2 -1 &gt;<br />
</td>
        <td>17.40<br />
</td>
        <td colspan="2">Ptolemisma<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 colspan="2">Biyatisma<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 colspan="2">Valinorsma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>65536/65219<br />
</td>
        <td>| 16 -2 -3 &gt;<br />
</td>
        <td>8.39<br />
</td>
        <td colspan="2">Orgonisma<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 colspan="2">Keenanisma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4000/3993<br />
</td>
        <td>| 5 -1 3 -3 &gt;<br />
</td>
        <td>3.03<br />
</td>
        <td colspan="2">Wizardharry<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:xenwolf|xenwolf]] and made on <tt>2011-03-05 16:17:53 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 17:30:28 UTC</tt>.<br>
-: The original revision id was <tt>207629400</tt>.<br>
+: The original revision id was <tt>233286326</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>Added comma table.</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 29: / Line 29: @@
 [[@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</pre></div>
+*[[Octatonic scale]] - a scale based on alternating whole and half steps
+==Commas==
+EDO tempers out the following commas. (Note: This assumes val &lt; 8 13 19 22 28 30 |).
+||~ Comma ||~ Monzo ||~ Cents ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
+|| 648/625 || | 3 4 -4 &gt; || 62.57 || Major Diesis || Diminished Comma ||   ||
+|| 250/243 || | 1 -5 3 &gt; || 49.17 || Maximal Diesis || Porcupine Comma ||   ||
+|| 78732/78125 || | 2 9 -7 &gt; || 13.40 || Medium Semicomma || Sensipent Comma ||   ||
+|| 64/63 || | 6 -2 0 -1 &gt; || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma ||
+|| 875/864 || | -5 -3 3 1 &gt; || 21.90 |||| Keema ||   ||
+|| 321489/320000 || | -9 8 -4 2 &gt; || 8.04 |||| Varunisma ||   ||
+|| 6144/6125 || | 11 1 -3 -2 &gt; || 5.36 |||| Porwell ||   ||
+|| 100/99 || | 2 -2 2 -1 &gt; || 17.40 |||| Ptolemisma ||   ||
+|| 121/120 || | -3 -1 -1 2 &gt; || 14.37 |||| Biyatisma ||   ||
+|| 176/175 || | 4 -2 -1 1 &gt; || 9.86 |||| Valinorsma ||   ||
+|| 65536/65219 || | 16 -2 -3 &gt; || 8.39 |||| Orgonisma ||   ||
+|| 385/384 || | -7 -1 1 1 1 &gt; || 4.50 |||| Keenanisma ||   ||
+|| 4000/3993 || | 5 -1 3 -3 &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 56: / Line 74: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x8 - Equal Divisions of the Octave-See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;See also&lt;/h2&gt;
-*&lt;a class="wiki_link" href="/Octatonic%20scale"&gt;Octatonic scale&lt;/a&gt; - a scale based on alternating whole and half steps&lt;/body&gt;&lt;/html&gt;</pre></div>
+ *&lt;a class="wiki_link" href="/Octatonic%20scale"&gt;Octatonic scale&lt;/a&gt; - a scale based on alternating whole and half steps&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x8 - Equal Divisions of the Octave-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Commas&lt;/h2&gt;
+EDO tempers out the following commas. (Note: This assumes val &amp;lt; 8 13 19 22 28 30 |).&lt;br /&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;Comma&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Monzo&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Cents&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 1&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 2&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Name 3&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;648/625&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 3 4 -4 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;62.57&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Major Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Diminished Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;250/243&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 1 -5 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;49.17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Maximal Diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Porcupine Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;78732/78125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 9 -7 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13.40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Medium Semicomma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Sensipent Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;64/63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27.26&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Septimal Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Archytas' Comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Leipziger Komma&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;875/864&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -5 -3 3 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21.90&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Keema&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;321489/320000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -9 8 -4 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.04&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Varunisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;6144/6125&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 11 1 -3 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.36&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Porwell&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;100/99&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 -2 2 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17.40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Ptolemisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;121/120&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 -1 -1 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14.37&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Biyatisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;176/175&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 4 -2 -1 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9.86&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Valinorsma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;65536/65219&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 16 -2 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.39&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Orgonisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;385/384&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.50&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Keenanisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4000/3993&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -1 3 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.03&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2"&gt;Wizardharry&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;/body&gt;&lt;/html&gt;</pre></div>

8edo: Difference between revisions

Revision as of 17:30, 31 May 2011

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