12edo: Difference between revisions
Wikispaces>keenanpepper **Imported revision 245840171 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 245874467 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-08-14 | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-08-14 12:32:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>245874467</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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In terms of the kernel, which is to say the commas it tempers out, it tempers out the Pythagorean comma, 3^12/2^19, the Didymas comma, 81/80, the diesis, 128/125, the diaschisma, 2048/2025, the Archytas comma, 64/63, the septimal quartertone, 36/35, the jubilisma, 50/49, the septimal semicomma, 126/125, and the septimal kleisma, 225/224. Each of these affects the structure of 12et in specific ways, and tuning systems which share the comma in question will be similar to 12et in precisely those ways. | In terms of the kernel, which is to say the commas it tempers out, it tempers out the Pythagorean comma, 3^12/2^19, the Didymas comma, 81/80, the diesis, 128/125, the diaschisma, 2048/2025, the Archytas comma, 64/63, the septimal quartertone, 36/35, the jubilisma, 50/49, the septimal semicomma, 126/125, and the septimal kleisma, 225/224. Each of these affects the structure of 12et in specific ways, and tuning systems which share the comma in question will be similar to 12et in precisely those ways. | ||
==Linear temperaments== | |||
||~ Periods | |||
per octave ||~ Generator ||~ Temperaments || | |||
|| 1 || 1\12 || [[Ripple]] || | |||
|| 1 || 5\12 || [[Meantone]]/[[dominant]] || | |||
|| 2 || 1\12 || [[Srutal]]/[[pajara]] || | |||
|| 3 || 1\12 || [[Augmented]] || | |||
|| 4 || 1\12 || [[Diminished]] || | |||
|| 6 || 1\12 || [[Hexe]] || | |||
==Commas== | ==Commas== | ||
12 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes val < 12 19 28 34 42 44 |.) | 12 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes val < 12 19 28 34 42 44 |.) | ||
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||= 441/440 || | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= || | ||= 441/440 || | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= || | ||
||= 9801/9800 || | -3 4 -2 -2 2 > ||> 0.18 ||= Kalisma ||= Gauss' Comma ||= || | ||= 9801/9800 || | -3 4 -2 -2 2 > ||> 0.18 ||= Kalisma ||= Gauss' Comma ||= || | ||
||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= | ||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= ||</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>12edo</title></head><body>12<a class="wiki_link" href="/EDO">EDO</a>, perhaps better known as 12et since it really is a temperament, is the predominating tuning system in the world today. It achieved that position because it is the smallest equal division which can seriously claim to represent <a class="wiki_link" href="/5-limit">5-limit</a> harmony, and because as 1/11 comma meantone, it represents <a class="wiki_link" href="/Meantone">meantone</a>.<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>12edo</title></head><body>12<a class="wiki_link" href="/EDO">EDO</a>, perhaps better known as 12et since it really is a temperament, is the predominating tuning system in the world today. It achieved that position because it is the smallest equal division which can seriously claim to represent <a class="wiki_link" href="/5-limit">5-limit</a> harmony, and because as 1/11 comma meantone, it represents <a class="wiki_link" href="/Meantone">meantone</a>.<br /> | ||
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In terms of the kernel, which is to say the commas it tempers out, it tempers out the Pythagorean comma, 3^12/2^19, the Didymas comma, 81/80, the diesis, 128/125, the diaschisma, 2048/2025, the Archytas comma, 64/63, the septimal quartertone, 36/35, the jubilisma, 50/49, the septimal semicomma, 126/125, and the septimal kleisma, 225/224. Each of these affects the structure of 12et in specific ways, and tuning systems which share the comma in question will be similar to 12et in precisely those ways.<br /> | In terms of the kernel, which is to say the commas it tempers out, it tempers out the Pythagorean comma, 3^12/2^19, the Didymas comma, 81/80, the diesis, 128/125, the diaschisma, 2048/2025, the Archytas comma, 64/63, the septimal quartertone, 36/35, the jubilisma, 50/49, the septimal semicomma, 126/125, and the septimal kleisma, 225/224. Each of these affects the structure of 12et in specific ways, and tuning systems which share the comma in question will be similar to 12et in precisely those ways.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Commas"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Linear temperaments</h2> | ||
<table class="wiki_table"> | |||
<tr> | |||
<th>Periods<br /> | |||
per octave<br /> | |||
</th> | |||
<th>Generator<br /> | |||
</th> | |||
<th>Temperaments<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>1\12<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Ripple">Ripple</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>5\12<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Meantone">Meantone</a>/<a class="wiki_link" href="/dominant">dominant</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>1\12<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Srutal">Srutal</a>/<a class="wiki_link" href="/pajara">pajara</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>1\12<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Augmented">Augmented</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>1\12<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Diminished">Diminished</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>1\12<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Hexe">Hexe</a><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas</h2> | |||
12 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes val &lt; 12 19 28 34 42 44 |.)<br /> | 12 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes val &lt; 12 19 28 34 42 44 |.)<br /> | ||
<br /> | <br /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||