13edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 164990969 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 233314848 - Original comment: Added comma table.** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 19:42:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>233314848</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> | 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> | <h4>Original Wikitext content:</h4> | ||
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[[http://www.h-pi.com/midi/13ET.mid|Two-Part Invention in 13ET]] by [[Aaron Andrew Hunt]] | [[http://www.h-pi.com/midi/13ET.mid|Two-Part Invention in 13ET]] by [[Aaron Andrew Hunt]] | ||
[[http://www.h-pi.com/midi/Prelude13ET.mid|Prelude in 13ET]] by [[Aaron Andrew Hunt]] | [[http://www.h-pi.com/midi/Prelude13ET.mid|Prelude in 13ET]] by [[Aaron Andrew Hunt]] | ||
[[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=835265|Spikey Hair in 13tET]] by [[Andrew Heathwaite]]</pre></div> | [[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&songID=835265|Spikey Hair in 13tET]] by [[Andrew Heathwaite]] | ||
==Commas== | |||
13 EDO tempers out the following commas. (Note: This assumes the val < 13 21 30 36 45 48 |.) | |||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | |||
|| 2109375/2097152 || | -21 3 7 > || 10.06 || Semicomma || Fokker Comma || || | |||
|| 1029/1000 || | -3 1 -3 3 > || 49.49 || Keega || || || | |||
|| 525/512 || | -9 1 2 1 > || 43.41 || Avicennma || Avicenna's Enharmonic Diesis || || | |||
|| 64/63 || | 6 -2 0 -1 > || 27.26 || Septimal Comma || Archytas' Comma || Leipziger Komma || | |||
|| 64827/64000 || | -9 3 -3 4 > || 22.23 || Squalentine || || || | |||
|| 3125/3087 || | -2 5 -3 > || 21.18 || Gariboh || || || | |||
|| 3136/3125 || | 6 -5 2 > || 6.08 || Hemimean || || || | |||
|| 121/120 || | -3 -1 -1 2 > || 14.37 || Biyatisma || || || | |||
|| 441/440 || | -3 2 -1 2 -1 > || 3.93 || Werckisma || || ||</pre></div> | |||
<h4>Original HTML content:</h4> | <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"><html><head><title>13edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x13 tone equal temperament / 13edo"></a><!-- ws:end:WikiTextHeadingRule:0 -->13 tone equal temperament / 13edo</h1> | <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"><html><head><title>13edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x13 tone equal temperament / 13edo"></a><!-- ws:end:WikiTextHeadingRule:0 -->13 tone equal temperament / 13edo</h1> | ||
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13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo). Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | 13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo). Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two degrees of 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:146:&lt;img src=&quot;/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /><!-- ws:end:WikiTextLocalImageRule:146 --><br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:147:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/13edo%20horograms.pdf?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@13edo horograms.pdf&quot; title=&quot;File: 13edo horograms.pdf&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');"><img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="13edo horograms.pdf" /></a><div><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf" onclick="ws.common.trackFileLink('/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf');" class="filename" title="13edo horograms.pdf">13edo horograms.pdf</a><br /><ul><li><a href="/file/detail/13edo%20horograms.pdf">Details</a></li><li><a href="/file/view/13edo%20horograms.pdf/104047129/13edo%20horograms.pdf">Download</a></li><li style="color: #666">242 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:147 --><br /> | ||
~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br /> | ~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link_ext" href="http://www.h-pi.com/midi/13ET.mid" rel="nofollow">Two-Part Invention in 13ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | <a class="wiki_link_ext" href="http://www.h-pi.com/midi/13ET.mid" rel="nofollow">Two-Part Invention in 13ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | ||
<a class="wiki_link_ext" href="http://www.h-pi.com/midi/Prelude13ET.mid" rel="nofollow">Prelude in 13ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | <a class="wiki_link_ext" href="http://www.h-pi.com/midi/Prelude13ET.mid" rel="nofollow">Prelude in 13ET</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a><br /> | ||
<a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=835265" rel="nofollow">Spikey Hair in 13tET</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=122613&amp;songID=835265" rel="nofollow">Spikey Hair in 13tET</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a><br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x13 tone equal temperament / 13edo-Commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas</h2> | |||
13 EDO tempers out the following commas. (Note: This assumes the val &lt; 13 21 30 36 45 48 |.)<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>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>1029/1000<br /> | |||
</td> | |||
<td>| -3 1 -3 3 &gt;<br /> | |||
</td> | |||
<td>49.49<br /> | |||
</td> | |||
<td>Keega<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>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>64827/64000<br /> | |||
</td> | |||
<td>| -9 3 -3 4 &gt;<br /> | |||
</td> | |||
<td>22.23<br /> | |||
</td> | |||
<td>Squalentine<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3125/3087<br /> | |||
</td> | |||
<td>| -2 5 -3 &gt;<br /> | |||
</td> | |||
<td>21.18<br /> | |||
</td> | |||
<td>Gariboh<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3136/3125<br /> | |||
</td> | |||
<td>| 6 -5 2 &gt;<br /> | |||
</td> | |||
<td>6.08<br /> | |||
</td> | |||
<td>Hemimean<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>441/440<br /> | |||
</td> | |||
<td>| -3 2 -1 2 -1 &gt;<br /> | |||
</td> | |||
<td>3.93<br /> | |||
</td> | |||
<td>Werckisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||