50edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 504174484 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 575219197 - 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:xenwolf|xenwolf]] and made on <tt>2016-02-18 16:45:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>575219197</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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*using the 13-limit patent val except as noted | *using the 13-limit patent val except as noted | ||
== | ==Selected just intervals by error== | ||
|| Interval || Error || | The following table shows how [[Just-24|some prominent just intervals]] are represented in 50edo (ordered by absolute error). | ||
|| 16/13 || 0.528 || | || **Interval, complement** || **Error (abs., in [[cent|cents]])** || | ||
|| 15/14 || 0.557 || | ||= [[16_13|16/13]], [[13_8|13/8]] ||= 0.528 || | ||
|| 11/8 || 0.682 || | ||= [[15_14|15/14]], [[28_15|28/15]] ||= 0.557 || | ||
|| 13/11 || | ||= [[11_8|11/8]], [[16_11|16/11]] ||= 0.682 || | ||
|| 13/10 || 1.786 || | ||= [[13_11|13/11]], [[22_13|22/13]] ||= 1.210 || | ||
|| 5/4 || | ||= [[13_10|13/10]], [[20_13|20/13]] ||= 1.786 || | ||
|| 7/6 || | ||= [[5_4|5/4]], [[8_5|8/5]] ||= 2.314 || | ||
|| 11/10 || 2.996 || | ||= [[7_6|7/6]], [[12_7|12/7]] ||= 2.871 || | ||
|| 9/7 || | ||= [[11_10|11/10]], [[20_11|20/11]] ||= 2.996 || | ||
|| 6/5 || | ||= [[9_7|9/7]], [[14_9|14/9]] ||= 3.084 || | ||
|| 13/12 || 5.427 || | ||= [[6_5|6/5]], [[5_3|5/3]] ||= 3.641 || | ||
|| 4/3 || 5.955 || | ||= [[13_12|13/12]], [[24_13|24/13]] ||= 5.427 || | ||
|| 7/5 || | ||= [[4_3|4/3]], [[3_2|3/2]] ||= 5.955 || | ||
|| 12/11 || | ||= [[7_5|7/5]], [[10_7|10/7]] ||= 6.512 || | ||
|| 15/13 || | ||= [[12_11|12/11]], [[11_6|11/6]] ||= 6.637 || | ||
|| 16/15 || 8.269 || | ||= [[15_13|15/13]], [[26_15|26/15]] ||= 7.741 || | ||
|| 14/13 || | ||= [[16_15|16/15]], [[15_8|15/8]] ||= 8.269 || | ||
|| 8/7 || 8.826 || | ||= [[14_13|14/13]], [[13_7|13/7]] ||= 8.298 || | ||
|| 15/11 || | ||= [[8_7|8/7]], [[7_4|7/4]] ||= 8.826 || | ||
|| 14/11 || | ||= [[15_11|15/11]], [[22_15|22/15]] ||= 8.951 || | ||
|| 10/9 || 9.596 || | ||= [[14_11|14/11]], [[11_7|11/7]] ||= 9.508 || | ||
|| 18/13 || | ||= [[10_9|10/9]], [[9_5|9/5]] ||= 9.596 || | ||
|| 9/ | ||= [[18_13|18/13]], [[13_9|13/9]] ||= 11.382 || | ||
|| | ||= [[11_9|11/9]], [[18_11|18/11]] ||= 11.408 || | ||
||= [[9_8|9/8]], [[16_9|16/9]] ||= 11.910 || | |||
=Commas= | =Commas= | ||
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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>50edo</title></head><body><!-- ws:start:WikiTextTocRule:12:&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:12 --><!-- ws:start:WikiTextTocRule:13: --><div style="margin-left: 1em;"><a href="#Relations">Relations</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>50edo</title></head><body><!-- ws:start:WikiTextTocRule:12:&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:12 --><!-- ws:start:WikiTextTocRule:13: --><div style="margin-left: 1em;"><a href="#Relations">Relations</a></div> | ||
<!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div> | <!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div> | ||
<!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 2em;"><a href="#Intervals- | <!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 2em;"><a href="#Intervals-Selected just intervals by error">Selected just intervals by error</a></div> | ||
<!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 1em;"><a href="#Commas">Commas</a></div> | <!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 1em;"><a href="#Commas">Commas</a></div> | ||
<!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 1em;"><a href="#Music">Music</a></div> | <!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 1em;"><a href="#Music">Music</a></div> | ||
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*using the 13-limit patent val except as noted<br /> | *using the 13-limit patent val except as noted<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals- | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:4 -->Selected just intervals by error</h2> | ||
The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 50edo (ordered by absolute error).<br /> | |||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>Interval<br /> | <td><strong>Interval, complement</strong><br /> | ||
</td> | </td> | ||
<td>Error<br /> | <td><strong>Error (abs., in <a class="wiki_link" href="/cent">cents</a>)</strong><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>16/13<br /> | <td style="text-align: center;"><a class="wiki_link" href="/16_13">16/13</a>, <a class="wiki_link" href="/13_8">13/8</a><br /> | ||
</td> | </td> | ||
<td>0.528<br /> | <td style="text-align: center;">0.528<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15/14<br /> | <td style="text-align: center;"><a class="wiki_link" href="/15_14">15/14</a>, <a class="wiki_link" href="/28_15">28/15</a><br /> | ||
</td> | </td> | ||
<td>0.557<br /> | <td style="text-align: center;">0.557<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11/8<br /> | <td style="text-align: center;"><a class="wiki_link" href="/11_8">11/8</a>, <a class="wiki_link" href="/16_11">16/11</a><br /> | ||
</td> | </td> | ||
<td>0.682<br /> | <td style="text-align: center;">0.682<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13/11<br /> | <td style="text-align: center;"><a class="wiki_link" href="/13_11">13/11</a>, <a class="wiki_link" href="/22_13">22/13</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">1.210<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13/10<br /> | <td style="text-align: center;"><a class="wiki_link" href="/13_10">13/10</a>, <a class="wiki_link" href="/20_13">20/13</a><br /> | ||
</td> | </td> | ||
<td>1.786<br /> | <td style="text-align: center;">1.786<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>5/4<br /> | <td style="text-align: center;"><a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/8_5">8/5</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">2.314<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7/6<br /> | <td style="text-align: center;"><a class="wiki_link" href="/7_6">7/6</a>, <a class="wiki_link" href="/12_7">12/7</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">2.871<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11/10<br /> | <td style="text-align: center;"><a class="wiki_link" href="/11_10">11/10</a>, <a class="wiki_link" href="/20_11">20/11</a><br /> | ||
</td> | </td> | ||
<td>2.996<br /> | <td style="text-align: center;">2.996<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9/7<br /> | <td style="text-align: center;"><a class="wiki_link" href="/9_7">9/7</a>, <a class="wiki_link" href="/14_9">14/9</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">3.084<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6/5<br /> | <td style="text-align: center;"><a class="wiki_link" href="/6_5">6/5</a>, <a class="wiki_link" href="/5_3">5/3</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">3.641<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13/12<br /> | <td style="text-align: center;"><a class="wiki_link" href="/13_12">13/12</a>, <a class="wiki_link" href="/24_13">24/13</a><br /> | ||
</td> | </td> | ||
<td>5.427<br /> | <td style="text-align: center;">5.427<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4/3<br /> | <td style="text-align: center;"><a class="wiki_link" href="/4_3">4/3</a>, <a class="wiki_link" href="/3_2">3/2</a><br /> | ||
</td> | </td> | ||
<td>5.955<br /> | <td style="text-align: center;">5.955<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7/5<br /> | <td style="text-align: center;"><a class="wiki_link" href="/7_5">7/5</a>, <a class="wiki_link" href="/10_7">10/7</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">6.512<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>12/11<br /> | <td style="text-align: center;"><a class="wiki_link" href="/12_11">12/11</a>, <a class="wiki_link" href="/11_6">11/6</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">6.637<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15/13<br /> | <td style="text-align: center;"><a class="wiki_link" href="/15_13">15/13</a>, <a class="wiki_link" href="/26_15">26/15</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">7.741<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>16/15<br /> | <td style="text-align: center;"><a class="wiki_link" href="/16_15">16/15</a>, <a class="wiki_link" href="/15_8">15/8</a><br /> | ||
</td> | </td> | ||
<td>8.269<br /> | <td style="text-align: center;">8.269<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14/13<br /> | <td style="text-align: center;"><a class="wiki_link" href="/14_13">14/13</a>, <a class="wiki_link" href="/13_7">13/7</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">8.298<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>8/7<br /> | <td style="text-align: center;"><a class="wiki_link" href="/8_7">8/7</a>, <a class="wiki_link" href="/7_4">7/4</a><br /> | ||
</td> | </td> | ||
<td>8.826<br /> | <td style="text-align: center;">8.826<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15/11<br /> | <td style="text-align: center;"><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/22_15">22/15</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">8.951<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14/11<br /> | <td style="text-align: center;"><a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/11_7">11/7</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">9.508<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>10/9<br /> | <td style="text-align: center;"><a class="wiki_link" href="/10_9">10/9</a>, <a class="wiki_link" href="/9_5">9/5</a><br /> | ||
</td> | </td> | ||
<td>9.596<br /> | <td style="text-align: center;">9.596<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>18/13<br /> | <td style="text-align: center;"><a class="wiki_link" href="/18_13">18/13</a>, <a class="wiki_link" href="/13_9">13/9</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">11.382<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9/ | <td style="text-align: center;"><a class="wiki_link" href="/11_9">11/9</a>, <a class="wiki_link" href="/18_11">18/11</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">11.408<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td style="text-align: center;"><a class="wiki_link" href="/9_8">9/8</a>, <a class="wiki_link" href="/16_9">16/9</a><br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">11.910<br /> | ||
</td> | </td> | ||
</tr> | </tr> |