15edo: Difference between revisions
Wikispaces>k9assassin **Imported revision 562310719 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 575175567 - 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 11:25:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>575175567</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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[[file:15ed2-001.svg]] | [[file:15ed2-001.svg]] | ||
== | ==Selected just intervals by error== | ||
|| Interval || Error || | The following table shows how [[Just-24|some prominent just intervals]] are represented in 15edo (ordered by absolute error). | ||
|| 18/13 || | || **Interval, complement** || **Error (abs., in [[cent|cents]])** || | ||
|| 6/5 || 4.359 || | ||= [[18_13|18/13]], [[13_9|13/9]] ||= 3.382 || | ||
|| 11/10 || | ||= [[6_5|6/5]], [[5_3|5/3]] ||= 4.359 || | ||
|| 15/13 || | ||= [[11_10|11/10]], [[20_11|20/11]] ||= 5.004 || | ||
|| 11/8 || 8.682 || | ||= [[15_13|15/13]], [[26_15|26/15]] ||= 7.741 || | ||
|| 8/7 || 8.826 || | ||= [[11_8|11/8]], [[16_11|16/11]] ||= 8.682 || | ||
|| 12/11 || 9.363 || | ||= [[8_7|8/7]], [[7_4|7/4]] ||= 8.826 || | ||
|| 5/4 || 13.686 || | ||= [[12_11|12/11]], [[11_6|11/6]] ||= 9.363 || | ||
|| 14/11 || | ||= [[5_4|5/4]], [[8_5|8/5]] ||= 13.686 || | ||
|| 4/3 || | ||= [[14_11|14/11]], [[11_7|11/7]] ||= 17.508 || | ||
|| 13/12 || 21.427 || | ||= [[4_3|4/3]], [[3_2|3/2]] ||= 18.045 || | ||
|| 10/9 || | ||= [[13_12|13/12]], [[24_13|24/13]] ||= 21.427 || | ||
|| 7/5 || | ||= [[10_9|10/9]], [[9_5|9/5]] ||= 22.404 || | ||
|| 15/11 || 23.049 || | ||= [[7_5|7/5]], [[10_7|10/7]] ||= 22.512 || | ||
|| 13/10 || 25.786 || | ||= [[15_11|15/11]], [[22_15|22/15]] ||= 23.049 || | ||
|| 7/6 || | ||= [[13_10|13/10]], [[20_13|20/13]] ||= 25.786 || | ||
|| 11/9 || | ||= [[7_6|7/6]], [[12_7|12/7]] ||= 26.871 || | ||
|| 13/11 || 30. | ||= [[11_9|11/9]], [[18_11|18/11]] ||= 27.408 || | ||
|| | ||= [[13_11|13/11]], [[22_13|22/13]] ||= 30.790 || | ||
|| | ||= [[14_13|14/13]], [[13_7|13/7]] ||= 31.702 || | ||
|| | ||= [[16_15|16/15]], [[15_8|15/8]] ||= 31.731 || | ||
|| | ||= [[9_7|9/7]], [[14_9|14/9]] ||= 35.084 || | ||
|| | ||= [[9_8|9/8]], [[16_9|16/9]] ||= 36.090 || | ||
|| | ||= [[15_14|15/14]], [[28_15|28/15]] ||= 39.443 || | ||
||= [[16_13|16/13]], [[13_8|13/8]] ||= 39.472 || | |||
=Notation= | =Notation= | ||
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<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 1em;"><a href="#Images">Images</a></div> | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 1em;"><a href="#Images">Images</a></div> | ||
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div> | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#Intervals">Intervals</a></div> | ||
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Intervals- | <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Intervals-Selected just intervals by error">Selected just intervals by error</a></div> | ||
<!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div> | <!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div> | ||
<!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Notation-Blackwood Notation">Blackwood Notation</a></div> | <!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Notation-Blackwood Notation">Blackwood Notation</a></div> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="Intervals- | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="Intervals-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:8 -->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 15edo (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>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;">3.382<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>4.359<br /> | <td style="text-align: center;">4.359<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> | <td style="text-align: center;">5.004<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>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>8.682<br /> | <td style="text-align: center;">8.682<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>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>9.363<br /> | <td style="text-align: center;">9.363<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>13.686<br /> | <td style="text-align: center;">13.686<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;">17.508<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> | <td style="text-align: center;">18.045<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>21.427<br /> | <td style="text-align: center;">21.427<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> | <td style="text-align: center;">22.404<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;">22.512<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>23.049<br /> | <td style="text-align: center;">23.049<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>25.786<br /> | <td style="text-align: center;">25.786<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;">26.871<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11/9<br /> | <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;">27.408<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>30. | <td style="text-align: center;">30.790<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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;">31.702<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | <td style="text-align: center;">31.731<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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;">35.084<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;">36.090<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | <td style="text-align: center;">39.443<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <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> | <td style="text-align: center;">39.472<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||