Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 191261592 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 191286006 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-01-05 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-05 21:17:21 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>191286006</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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Map: [<1 1 0 3|, <0 3 12 -1|] | Map: [<1 1 0 3|, <0 3 12 -1|] | ||
Generators: 2, 8/7 | Generators: 2, 8/7 | ||
Wedgie: <<3 12 -1 12 -10 -36|| | |||
EDOs: 5, 26, 31 | |||
Badness: 0.0371 | |||
===Squares=== | ===Squares=== | ||
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Generators: 2, 9/7 | Generators: 2, 9/7 | ||
EDOs: 14, 31, 262, 293 | EDOs: 14, 31, 262, 293 | ||
Badness: 0.0460 | |||
Music: | Music: | ||
By Chris Vaisvil | By Chris Vaisvil | ||
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http://tinyurl.com/24cbxse | http://tinyurl.com/24cbxse | ||
11-limit | ===11-limit=== | ||
Commas: 81/80, 385/384, 1375/1372 | Commas: 81/80, 385/384, 1375/1372 | ||
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Map: [<1 3 8 6 -4|, <0 -4 -16 -9 21|] | Map: [<1 3 8 6 -4|, <0 -4 -16 -9 21|] | ||
EDOs: 14, 31, 200 | EDOs: 14, 31, 200 | ||
Badness: 0.0568 | |||
===Liese=== | ===Liese=== | ||
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Map: [<1 0 -4 -3|, <0 3 12 11|] | Map: [<1 0 -4 -3|, <0 3 12 11|] | ||
Generators: 2, 10/7</pre></div> | Generators: 2, 10/7 | ||
EDOs: [[17edo|17]], [[19edo|19]], [[55edo|55]], [[74edo|74]] | |||
Badness: 0.0467</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>Meantone family</title></head><body>The 5-limit parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymos or <a class="wiki_link" href="/Didymos%20comma">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<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>Meantone family</title></head><body>The 5-limit parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymos or <a class="wiki_link" href="/Didymos%20comma">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<br /> | ||
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Map: [&lt;1 1 0 3|, &lt;0 3 12 -1|]<br /> | Map: [&lt;1 1 0 3|, &lt;0 3 12 -1|]<br /> | ||
Generators: 2, 8/7<br /> | Generators: 2, 8/7<br /> | ||
Wedgie: &lt;&lt;3 12 -1 12 -10 -36||<br /> | |||
EDOs: 5, 26, 31<br /> | |||
Badness: 0.0371<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="x-Mothra-Squares"></a><!-- ws:end:WikiTextHeadingRule:24 -->Squares</h3> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="x-Mothra-Squares"></a><!-- ws:end:WikiTextHeadingRule:24 -->Squares</h3> | ||
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Generators: 2, 9/7<br /> | Generators: 2, 9/7<br /> | ||
EDOs: 14, 31, 262, 293<br /> | EDOs: 14, 31, 262, 293<br /> | ||
Badness: 0.0460<br /> | |||
<br /> | |||
Music:<br /> | Music:<br /> | ||
By Chris Vaisvil<br /> | By Chris Vaisvil<br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:307:http://tinyurl.com/25kv7cq --><a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow">http://tinyurl.com/25kv7cq</a><!-- ws:end:WikiTextUrlRule:307 --><br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:308:http://tinyurl.com/24cbxse --><a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow">http://tinyurl.com/24cbxse</a><!-- ws:end:WikiTextUrlRule:308 --><br /> | ||
<br /> | <br /> | ||
11-limit< | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="x-Mothra-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h3> | ||
Commas: 81/80, 385/384, 1375/1372<br /> | Commas: 81/80, 385/384, 1375/1372<br /> | ||
<br /> | <br /> | ||
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Map: [&lt;1 3 8 6 -4|, &lt;0 -4 -16 -9 21|]<br /> | Map: [&lt;1 3 8 6 -4|, &lt;0 -4 -16 -9 21|]<br /> | ||
EDOs: 14, 31, 200<br /> | EDOs: 14, 31, 200<br /> | ||
Badness: 0.0568<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="x-Mothra-Liese"></a><!-- ws:end:WikiTextHeadingRule:28 -->Liese</h3> | ||
Commas: 81/80, 686/675<br /> | Commas: 81/80, 686/675<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
Map: [&lt;1 0 -4 -3|, &lt;0 3 12 11|]<br /> | Map: [&lt;1 0 -4 -3|, &lt;0 3 12 11|]<br /> | ||
Generators: 2, 10/7</body></html></pre></div> | Generators: 2, 10/7<br /> | ||
EDOs: <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/55edo">55</a>, <a class="wiki_link" href="/74edo">74</a><br /> | |||
Badness: 0.0467</body></html></pre></div> | |||