30edo: Difference between revisions
Wikispaces>jdfreivald **Imported revision 233352330 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 238636367 - Original comment: ** |
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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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-06-24 18:12:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>238636367</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> | ||
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||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= || | ||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= || | ||
||= 4000/3993 ||< | 5 -1 3 0 -3 > ||> 3.03 ||= Wizardharry ||= ||= || | ||= 4000/3993 ||< | 5 -1 3 0 -3 > ||> 3.03 ||= Wizardharry ||= ||= || | ||
||= 3025/3024 ||< | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||= ||= ||</pre></div> | ||= 3025/3024 ||< | -4 -3 2 -1 2 > ||> 0.57 ||= Lehmerisma ||= ||= || | ||
==30-EDO Intervals:== | |||
|| **Step** || **Size in Cents** || | |||
|| 0 || 0 || | |||
|| 1 || 40 || | |||
|| 2 || 80 || | |||
|| 3 || 120 || | |||
|| 4 || 160 || | |||
|| 5 || 200 || | |||
|| 6 || 240 || | |||
|| 7 || 280 || | |||
|| 8 || 320 || | |||
|| 9 || 360 || | |||
|| 10 || 400 || | |||
|| 11 || 440 || | |||
|| 12 || 480 || | |||
|| 13 || 520 || | |||
|| 14 || 560 || | |||
|| 15 || 600 || | |||
|| 16 || 640 || | |||
|| 17 || 680 || | |||
|| 18 || 720 || | |||
|| 19 || 760 || | |||
|| 20 || 800 || | |||
|| 21 || 840 || | |||
|| 22 || 880 || | |||
|| 23 || 920 || | |||
|| 24 || 960 || | |||
|| 25 || 1000 || | |||
|| 26 || 1040 || | |||
|| 27 || 1080 || | |||
|| 28 || 1120 || | |||
|| 29 || 1160 ||</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>30edo</title></head><body>The <em>30 equal division</em> divides the octave into 30 equal steps of precisely 40 cents each. Its <a class="wiki_link" href="/patent%20val">patent val</a> is a doubled version of the patent val for <a class="wiki_link" href="/15edo">15edo</a> through the 11-limit, so 30 can be viewed as a <a class="wiki_link" href="/contorted">contorted</a> version of 15. However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30.<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>30edo</title></head><body>The <em>30 equal division</em> divides the octave into 30 equal steps of precisely 40 cents each. Its <a class="wiki_link" href="/patent%20val">patent val</a> is a doubled version of the patent val for <a class="wiki_link" href="/15edo">15edo</a> through the 11-limit, so 30 can be viewed as a <a class="wiki_link" href="/contorted">contorted</a> version of 15. However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30.<br /> | ||
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Below is a plot of the Z function around 30:<br /> | Below is a plot of the Z function around 30:<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:516:&lt;img src=&quot;/file/view/plot30.png/220060356/plot30.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/plot30.png/220060356/plot30.png" alt="plot30.png" title="plot30.png" /><!-- ws:end:WikiTextLocalImageRule:516 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:0 -->Commas</h1> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Commas-30-EDO Intervals:"></a><!-- ws:end:WikiTextHeadingRule:2 -->30-EDO Intervals:</h2> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td><strong>Step</strong><br /> | |||
</td> | |||
<td><strong>Size in Cents</strong><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>0<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>40<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>80<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>120<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>160<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>200<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>240<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>280<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>320<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>360<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>400<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>440<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>480<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>520<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>560<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>600<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>640<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>680<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>720<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>760<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>800<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21<br /> | |||
</td> | |||
<td>840<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22<br /> | |||
</td> | |||
<td>880<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>920<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24<br /> | |||
</td> | |||
<td>960<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25<br /> | |||
</td> | |||
<td>1000<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26<br /> | |||
</td> | |||
<td>1040<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>27<br /> | |||
</td> | |||
<td>1080<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>28<br /> | |||
</td> | |||
<td>1120<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29<br /> | |||
</td> | |||
<td>1160<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||