10edo: Difference between revisions
Wikispaces>jdfreivald **Imported revision 233289894 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 233336834 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 21:25:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>233336834</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 20: | Line 20: | ||
|| 8 || 960 || | || 8 || 960 || | ||
|| 9 || 1080 || | || 9 || 1080 || | ||
==Commas== | ==Commas== | ||
| Line 39: | Line 30: | ||
||= 2048/2025 || | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= || || | ||= 2048/2025 || | 11 -4 -2 > ||> 19.55 ||= Diaschisma ||= || || | ||
||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis || || | ||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis || || | ||
||= 49/48 || | -4 -1 2 > ||> 35.70 ||= Slendro Diesis ||= || || | ||= 49/48 || | -4 -1 0 2 > ||> 35.70 ||= Slendro Diesis ||= || || | ||
||= 50/49 || | 1 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma || || | ||= 50/49 || | 1 0 2 -2 > ||> 34.98 ||= Tritonic Diesis ||= Jubilisma || || | ||
||= 686/675 || | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= || || | ||= 686/675 || | 1 -3 -2 3 > ||> 27.99 ||= Senga ||= || || | ||
||= 64/63 || | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma || Leipziger Komma || | ||= 64/63 || | 6 -2 0 -1 > ||> 27.26 ||= Septimal Comma ||= Archytas' Comma || Leipziger Komma || | ||
| Line 46: | Line 37: | ||
||= 1029/1024 || | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= || || | ||= 1029/1024 || | -10 1 0 3 > ||> 8.43 ||= Gamelisma ||= || || | ||
||= 225/224 || | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma || || | ||= 225/224 || | -5 2 2 -1 > ||> 7.71 ||= Septimal Kleisma ||= Marvel Comma || || | ||
||= 16875/16807 || | 3 4 -5 > ||> 6.99 ||= Mirkwai ||= || || | ||= 16875/16807 || | 0 3 4 -5 > ||> 6.99 ||= Mirkwai ||= || || | ||
||= 6772805/6751042 || | 11 -10 -10 10 > ||> 5.57 ||= Linus ||= || || | ||= 6772805/6751042 || | 11 -10 -10 10 > ||> 5.57 ||= Linus ||= || || | ||
||= 2401/2400 || | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= || || | ||= 2401/2400 || | -5 -1 -2 4 > ||> 0.72 ||= Breedsma ||= || || | ||
||= 243/242 || | -1 5 -2 > ||> 7.14 ||= Rastma ||= || || | ||= 243/242 || | -1 5 0 0 -2 > ||> 7.14 ||= Rastma ||= || || | ||
||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= || || | ||= 385/384 || | -7 -1 1 1 1 > ||> 4.50 ||= Keenanisma ||= || || | ||
||= 441/440 || | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= || || | ||= 441/440 || | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= || || | ||
||= 540/539 || | 2 3 1 -2 -1 > ||> 3.21 ||= Swetisma ||= || || | ||= 540/539 || | 2 3 1 -2 -1 > ||> 3.21 ||= Swetisma ||= || || | ||
||= 3025/3024 || | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||= || || | ||= 3025/3024 || | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||= || || | ||
||= 91/90 || | -1 -2 -1 1 1 > ||> 19.13 ||= Superleap ||= || || | ||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= || || | ||
||= 676/675 || | 2 -3 -2 2 > ||> 2.56 ||= Parizeksma ||= || ||</pre></div> | ||= 676/675 || | 2 -3 -2 0 0 2 > ||> 2.56 ||= Parizeksma ||= || || | ||
===Music=== | |||
[[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Ten Fingers]] by Bill Sethares (synth guitar) | |||
[[http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html|Circle of Thirds]] by Bill Sethares (synth ens.) | |||
[[http://www.akjmusic.com/works.html|10_fantasy]] by Aaron K. Johnson (synth monody) | |||
[[http://www.ziaspace.com/ZIA/mp3s/Future.html|Future]] and [[http://www.ziaspace.com/ZIA/mp3s/Sol.html|Sol]] by ZIA (synths and voice in 10) | |||
[[http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3|Prelude]] by Rick McGowan (Rhino synthesizer) | |||
[[http://soundclick.com/share?songid=5683815|Ideas on the Waterfall of Expression]] by Iglashion Jones (synth) | |||
||~ ||~ ||~ ||~ ||~ ||~ || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || || | |||
||= || ||> ||= ||= || ||</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>10edo</title></head><body>10edo, or 10-tone equal temperament, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 10 equal parts of exactly 120 <a class="wiki_link" href="/cent">cent</a>s. It can be thought of as two circles of <a class="wiki_link" href="/5edo">5edo</a> separated by 120 cents (or 5 circles of <a class="wiki_link" href="/2edo">2edo</a>). It adds to 5edo a small neutral second and its inversion a large neutral seventh; an excellent approximation of <a class="wiki_link" href="/13_8">13/8</a> and its inversion <a class="wiki_link" href="/16_13">16/13</a>; and the droll 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic <a class="wiki_link" href="/MOSScales">moment of symmetry scale</a> of the form 1 2 1 2 1 2 1.<br /> | <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>10edo</title></head><body>10edo, or 10-tone equal temperament, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 10 equal parts of exactly 120 <a class="wiki_link" href="/cent">cent</a>s. It can be thought of as two circles of <a class="wiki_link" href="/5edo">5edo</a> separated by 120 cents (or 5 circles of <a class="wiki_link" href="/2edo">2edo</a>). It adds to 5edo a small neutral second and its inversion a large neutral seventh; an excellent approximation of <a class="wiki_link" href="/13_8">13/8</a> and its inversion <a class="wiki_link" href="/16_13">16/13</a>; and the droll 600-cent tritone that appears in every even-numbered EDO. Taking the the 360 cent large neutral third as a generator produces a heptatonic <a class="wiki_link" href="/MOSScales">moment of symmetry scale</a> of the form 1 2 1 2 1 2 1.<br /> | ||
| Line 132: | Line 155: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h2> | |||
<!-- ws:start:WikiTextHeadingRule:4 | |||
10 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)<br /> | 10 EDO tempers out the following commas. (Note: This assumes the val &lt; 10 16 23 28 35 37 |.)<br /> | ||
<br /> | <br /> | ||
| Line 234: | Line 248: | ||
<td style="text-align: center;">49/48<br /> | <td style="text-align: center;">49/48<br /> | ||
</td> | </td> | ||
<td>| -4 -1 2 &gt;<br /> | <td>| -4 -1 0 2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">35.70<br /> | <td style="text-align: right;">35.70<br /> | ||
| Line 248: | Line 262: | ||
<td style="text-align: center;">50/49<br /> | <td style="text-align: center;">50/49<br /> | ||
</td> | </td> | ||
<td>| 1 2 -2 &gt;<br /> | <td>| 1 0 2 -2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">34.98<br /> | <td style="text-align: right;">34.98<br /> | ||
| Line 332: | Line 346: | ||
<td style="text-align: center;">16875/16807<br /> | <td style="text-align: center;">16875/16807<br /> | ||
</td> | </td> | ||
<td>| 3 4 -5 &gt;<br /> | <td>| 0 3 4 -5 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">6.99<br /> | <td style="text-align: right;">6.99<br /> | ||
| Line 374: | Line 388: | ||
<td style="text-align: center;">243/242<br /> | <td style="text-align: center;">243/242<br /> | ||
</td> | </td> | ||
<td>| -1 5 -2 &gt;<br /> | <td>| -1 5 0 0 -2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">7.14<br /> | <td style="text-align: right;">7.14<br /> | ||
| Line 444: | Line 458: | ||
<td style="text-align: center;">91/90<br /> | <td style="text-align: center;">91/90<br /> | ||
</td> | </td> | ||
<td>| -1 -2 -1 1 1 &gt;<br /> | <td>| -1 -2 -1 1 0 1 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">19.13<br /> | <td style="text-align: right;">19.13<br /> | ||
| Line 458: | Line 472: | ||
<td style="text-align: center;">676/675<br /> | <td style="text-align: center;">676/675<br /> | ||
</td> | </td> | ||
<td>| 2 -3 -2 2 &gt;<br /> | <td>| 2 -3 -2 0 0 2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">2.56<br /> | <td style="text-align: right;">2.56<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Parizeksma<br /> | <td style="text-align: center;">Parizeksma<br /> | ||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Commas-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h3> | |||
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Ten Fingers</a> by Bill Sethares (synth guitar)<br /> | |||
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/xentone.html" rel="nofollow">Circle of Thirds</a> by Bill Sethares (synth ens.)<br /> | |||
<a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow">10_fantasy</a> by Aaron K. Johnson (synth monody)<br /> | |||
<a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Future.html" rel="nofollow">Future</a> and <a class="wiki_link_ext" href="http://www.ziaspace.com/ZIA/mp3s/Sol.html" rel="nofollow">Sol</a> by ZIA (synths and voice in 10)<br /> | |||
<a class="wiki_link_ext" href="http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3" rel="nofollow">Prelude</a> by Rick McGowan (Rhino synthesizer)<br /> | |||
<a class="wiki_link_ext" href="http://soundclick.com/share?songid=5683815" rel="nofollow">Ideas on the Waterfall of Expression</a> by Iglashion Jones (synth)<br /> | |||
<br /> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: right;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||