26edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 574935867 - Original comment: Reverted to Feb 16, 2016 9:10 am: I checked it again, the error measure *is* cents -- sorry for this back and forth** |
Wikispaces>xenwolf **Imported revision 574939523 - 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:xenwolf|xenwolf]] and made on <tt>2016-02-16 | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-16 04:45:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>574939523</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
| Line 76: | Line 76: | ||
*based on treating 26-EDO as a 13-limit temperament; other approaches are possible. | *based on treating 26-EDO as a 13-limit temperament; other approaches are possible. | ||
== | ==Selected just intervals by error== | ||
|| Interval || Error (in [[cent|cents]] || | The following table contains some just intervals (and its octave-complement) intervals ordered by ascending absolute error. | ||
|| 13/12 || | || Interval, complement || Error (absolute, in [[cent|cents]] || | ||
|| 8/7 || | || 13/12, 24/13 || 0.111 || | ||
|| 14/11 || | || 7/4, 8/7 || 0.405 || | ||
|| 10/9 || 2.212 || | || 11/7, 14/11 || 2.123 || | ||
|| 11/8 || 2.528 || | || 9/5, 10/9 || 2.212 || | ||
|| 13/10 || 7.325 || | || 11/8, 16/11 || 2.528 || | ||
|| 6/5 || 7.436 || | || 13/10, 20/13 || 7.325 || | ||
|| 18/13 || | || 5/3, 6/5 || 7.436 || | ||
|| 4/3 || 9.647 || | || 13/9, 18/13 || 9.536 || | ||
|| 16/13 || 9.758 || | || 3/2, 4/3 || 9.647 || | ||
|| 7/6 || 10.052 || | || 13/8, 16/13 || 9.758 || | ||
|| 14/13 || 10.163 || | || 7/6, 12/7 || 10.052 || | ||
|| 12/11 || | || 13/7, 14/13 || 10.163 || | ||
|| 13/11 || | || 11/6, 12/11 || 12.176 || | ||
|| 15/13 || | || 13/11, 22/13 || 12.287 || | ||
|| 5/4 || | || 15/11, 22/15 || 16.895 || | ||
|| 7/5 || 17.488 || | || 15/13, 26/15 || 16.972 || | ||
|| | || 5/4, 8/5 || 17.083 || | ||
|| | || 7/5, 10/7 || 17.488 || | ||
|| | || 15/14, 28/15 || 19.019 || | ||
|| 11/ | || 9/8, 16/9 || 19.295 || | ||
|| 16/15, 15/8 || 19.424 || | |||
|| | || 11/10, 20/11 || 19.611 || | ||
|| | || 9/7, 14/9 || 19.699 || | ||
|| 11/9, 18/11 || 21.823 || | |||
=Rank two temperaments= | =Rank two temperaments= | ||
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<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>26edo</title></head><body><!-- ws:start:WikiTextTocRule:21:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><div style="margin-left: 1em;"><a href="#Structure">Structure</a></div> | <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>26edo</title></head><body><!-- ws:start:WikiTextTocRule:21:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><div style="margin-left: 1em;"><a href="#Structure">Structure</a></div> | ||
<!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div> | <!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div> | ||
<!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 2em;"><a href="#Intervals- | <!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 2em;"><a href="#Intervals-Selected just intervals by error">Selected just intervals by error</a></div> | ||
<!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 1em;"><a href="#Rank two temperaments">Rank two temperaments</a></div> | <!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 1em;"><a href="#Rank two temperaments">Rank two temperaments</a></div> | ||
<!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 2em;"><a href="#Rank two temperaments-Hendec in 26et">Hendec in 26et</a></div> | <!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 2em;"><a href="#Rank two temperaments-Hendec in 26et">Hendec in 26et</a></div> | ||
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*based on treating 26-EDO as a 13-limit temperament; other approaches are possible.<br /> | *based on treating 26-EDO as a 13-limit temperament; other approaches are possible.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals- | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:5 -->Selected just intervals by error</h2> | ||
The following table contains some just intervals (and its octave-complement) intervals ordered by ascending absolute error.<br /> | |||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>Interval<br /> | <td>Interval, complement<br /> | ||
</td> | </td> | ||
<td>Error (in <a class="wiki_link" href="/cent">cents</a><br /> | <td>Error (absolute, in <a class="wiki_link" href="/cent">cents</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13/12<br /> | <td>13/12, 24/13<br /> | ||
</td> | </td> | ||
<td> | <td>0.111<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>8/7<br /> | <td>7/4, 8/7<br /> | ||
</td> | </td> | ||
<td> | <td>0.405<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14/11<br /> | <td>11/7, 14/11<br /> | ||
</td> | </td> | ||
<td> | <td>2.123<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>10/9<br /> | <td>9/5, 10/9<br /> | ||
</td> | </td> | ||
<td>2.212<br /> | <td>2.212<br /> | ||
| Line 580: | Line 582: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11/8<br /> | <td>11/8, 16/11<br /> | ||
</td> | </td> | ||
<td>2.528<br /> | <td>2.528<br /> | ||
| Line 586: | Line 588: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13/10<br /> | <td>13/10, 20/13<br /> | ||
</td> | </td> | ||
<td>7.325<br /> | <td>7.325<br /> | ||
| Line 592: | Line 594: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6/5<br /> | <td>5/3, 6/5<br /> | ||
</td> | </td> | ||
<td>7.436<br /> | <td>7.436<br /> | ||
| Line 598: | Line 600: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>18/13<br /> | <td>13/9, 18/13<br /> | ||
</td> | </td> | ||
<td> | <td>9.536<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4/3<br /> | <td>3/2, 4/3<br /> | ||
</td> | </td> | ||
<td>9.647<br /> | <td>9.647<br /> | ||
| Line 610: | Line 612: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>16/13<br /> | <td>13/8, 16/13<br /> | ||
</td> | </td> | ||
<td>9.758<br /> | <td>9.758<br /> | ||
| Line 616: | Line 618: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7/6<br /> | <td>7/6, 12/7<br /> | ||
</td> | </td> | ||
<td>10.052<br /> | <td>10.052<br /> | ||
| Line 622: | Line 624: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14/13<br /> | <td>13/7, 14/13<br /> | ||
</td> | </td> | ||
<td>10.163<br /> | <td>10.163<br /> | ||
| Line 628: | Line 630: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>12/11<br /> | <td>11/6, 12/11<br /> | ||
</td> | </td> | ||
<td> | <td>12.176<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13/11<br /> | <td>13/11, 22/13<br /> | ||
</td> | </td> | ||
<td> | <td>12.287<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15/ | <td>15/11, 22/15<br /> | ||
</td> | </td> | ||
<td> | <td>16.895<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>15/13, 26/15<br /> | ||
</td> | </td> | ||
<td> | <td>16.972<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>5/4, 8/5<br /> | ||
</td> | </td> | ||
<td>17. | <td>17.083<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>7/5, 10/7<br /> | ||
</td> | </td> | ||
<td> | <td>17.488<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>15/14, 28/15<br /> | ||
</td> | </td> | ||
<td>19. | <td>19.019<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9/ | <td>9/8, 16/9<br /> | ||
</td> | </td> | ||
<td> | <td>19.295<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>16/15, 15/8<br /> | ||
</td> | </td> | ||
<td> | <td>19.424<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>11/10, 20/11<br /> | ||
</td> | </td> | ||
<td> | <td>19.611<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>9/7, 14/9<br /> | ||
</td> | </td> | ||
<td> | <td>19.699<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>11/9, 18/11<br /> | ||
</td> | </td> | ||
<td> | <td>21.823<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||