28edo: Difference between revisions
Wikispaces>guest **Imported revision 229063642 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 233350614 - Original comment: Added comma table.** |
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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:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 22:30:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>233350614</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>Added comma table.</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> | ||
<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
=Basic properties= | =Basic properties= | ||
28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, of which 9/7 and its inversion 14/9 are also found in 14edo. | 28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, of which 9/7 and its inversion 14/9 are also found in 14edo. | ||
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|| 26 || 1114.29 || 40:21 || 1115.53 || -1.24 || | || 26 || 1114.29 || 40:21 || 1115.53 || -1.24 || | ||
|| 27 || 1157.14 || || || || | || 27 || 1157.14 || || || || | ||
|| 28 || 1200 || 2:1 || 1200 || 0 ||</pre></div> | || 28 || 1200 || 2:1 || 1200 || 0 || | ||
==Commas== | |||
28 EDO tempers out the following commas. (Note: This assumes the val < 28 44 65 79 97 104 |.) | |||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 || | |||
|| 2187/2048 || | -11 7 > || 113.69 || Apotome || || | |||
|| 648/625 || | 3 4 -4 > || 62.57 || Major Diesis || Diminished Comma || | |||
|| 16875/16384 || | -14 3 4 > || 51.12 || Negri Comma || Double Augmentation Diesis || | |||
|| 393216/390625 || | 17 1 -8 > || 11.45 || Wuerschmidt Comma || || | |||
|| 36/35 || | 2 2 -1 -1 > || 48.77 || Septimal Quarter Tone || || | |||
|| 50/49 || | 1 0 2 -2 > || 34.98 || Tritonic Diesis || Jubilisma || | |||
|| 3125/3087 || | 0 -2 5 -3 > || 21.18 || Gariboh || || | |||
|| 126/125 || | 1 2 -3 1 > || 13.79 || Septimal Semicomma || Starling Comma || | |||
|| 65625/65536 || | -16 1 5 1 > || 2.35 || Horwell || || | |||
|| 394839/394762 || | 47 -7 -7 -7 > || 0.34 || Akjaysma || 5\7 Octave Comma || | |||
|| 176/175 || | 4 0 -2 -1 1 > || 9.86 || Valinorsma || || | |||
|| 441/440 || | -3 2 -1 2 -1 > || 3.93 || Werckisma || || | |||
|| 4000/3993 || | 5 -1 3 0 -3 > || 3.03 || Wizardharry || ||</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>28edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>28edo</title></head><body><!-- ws:start:WikiTextTocRule:8:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Basic properties">Basic properties</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | <a href="#Subgroups">Subgroups</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> | <a href="#Table of intervals">Table of intervals</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Basic properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Basic properties</h1> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Basic properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Basic properties</h1> | |||
28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, of which 9/7 and its inversion 14/9 are also found in 14edo.<br /> | 28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, of which 9/7 and its inversion 14/9 are also found in 14edo.<br /> | ||
<br /> | <br /> | ||
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</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
</td> | |||
</tr> | |||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Table of intervals-Commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->Commas</h2> | |||
28 EDO tempers out the following commas. (Note: This assumes the val &lt; 28 44 65 79 97 104 |.)<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>Comma<br /> | |||
</th> | |||
<th>Monzo<br /> | |||
</th> | |||
<th>Value (Cents)<br /> | |||
</th> | |||
<th>Name 1<br /> | |||
</th> | |||
<th>Name 2<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>2187/2048<br /> | |||
</td> | |||
<td>| -11 7 &gt;<br /> | |||
</td> | |||
<td>113.69<br /> | |||
</td> | |||
<td>Apotome<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>648/625<br /> | |||
</td> | |||
<td>| 3 4 -4 &gt;<br /> | |||
</td> | |||
<td>62.57<br /> | |||
</td> | |||
<td>Major Diesis<br /> | |||
</td> | |||
<td>Diminished Comma<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16875/16384<br /> | |||
</td> | |||
<td>| -14 3 4 &gt;<br /> | |||
</td> | |||
<td>51.12<br /> | |||
</td> | |||
<td>Negri Comma<br /> | |||
</td> | |||
<td>Double Augmentation Diesis<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>393216/390625<br /> | |||
</td> | |||
<td>| 17 1 -8 &gt;<br /> | |||
</td> | |||
<td>11.45<br /> | |||
</td> | |||
<td>Wuerschmidt Comma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>36/35<br /> | |||
</td> | |||
<td>| 2 2 -1 -1 &gt;<br /> | |||
</td> | |||
<td>48.77<br /> | |||
</td> | |||
<td>Septimal Quarter Tone<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>50/49<br /> | |||
</td> | |||
<td>| 1 0 2 -2 &gt;<br /> | |||
</td> | |||
<td>34.98<br /> | |||
</td> | |||
<td>Tritonic Diesis<br /> | |||
</td> | |||
<td>Jubilisma<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3125/3087<br /> | |||
</td> | |||
<td>| 0 -2 5 -3 &gt;<br /> | |||
</td> | |||
<td>21.18<br /> | |||
</td> | |||
<td>Gariboh<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>126/125<br /> | |||
</td> | |||
<td>| 1 2 -3 1 &gt;<br /> | |||
</td> | |||
<td>13.79<br /> | |||
</td> | |||
<td>Septimal Semicomma<br /> | |||
</td> | |||
<td>Starling Comma<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>65625/65536<br /> | |||
</td> | |||
<td>| -16 1 5 1 &gt;<br /> | |||
</td> | |||
<td>2.35<br /> | |||
</td> | |||
<td>Horwell<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>394839/394762<br /> | |||
</td> | |||
<td>| 47 -7 -7 -7 &gt;<br /> | |||
</td> | |||
<td>0.34<br /> | |||
</td> | |||
<td>Akjaysma<br /> | |||
</td> | |||
<td>5\7 Octave Comma<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>176/175<br /> | |||
</td> | |||
<td>| 4 0 -2 -1 1 &gt;<br /> | |||
</td> | |||
<td>9.86<br /> | |||
</td> | |||
<td>Valinorsma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>441/440<br /> | |||
</td> | |||
<td>| -3 2 -1 2 -1 &gt;<br /> | |||
</td> | |||
<td>3.93<br /> | |||
</td> | |||
<td>Werckisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4000/3993<br /> | |||
</td> | |||
<td>| 5 -1 3 0 -3 &gt;<br /> | |||
</td> | |||
<td>3.03<br /> | |||
</td> | |||
<td>Wizardharry<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||