Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 224328536 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 224331716 - 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>2011-04-30 15: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-30 15:30:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>224331716</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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Wedgie: <<4 16 9 16 3 -24|| | Wedgie: <<4 16 9 16 3 -24|| | ||
EDOs: 5, 8, 11, 14, 17, 31 | EDOs: 5, 8, 11, 14, 17, 31 | ||
Badness: 0.0460</pre></div> | Badness: 0.0460 | ||
==11-limit== | |||
Commas: 81/80, 99/98, 121/120 | |||
POTE generator: ~9/7 = 425.957 | |||
Map: [<1 3 8 6 7|, <0 -4 -16 -9 -10|] | |||
EDOs: 5, 8, 11, 14, 17, 31 | |||
Badness: 0.0216 | |||
==13-limit== | |||
Commas: 81/80, 99/98, 121/120, 66/65 | |||
POTE generator: ~9/7 = 425.550 | |||
Map: [<1 3 8 6 7 3|, <0 -4 -16 -9 -10 2|] | |||
EDOs: 5, 8, 11, 14, 17, 31 | |||
Badness: 0.0255</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><!-- 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>Meantone family</title></head><body><!-- ws:start:WikiTextTocRule:44:&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:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Septimal meantone">Septimal meantone</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Flattone">Flattone</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Dominant">Dominant</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Sharptone">Sharptone</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Injera">Injera</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Godzilla">Godzilla</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Mohajira">Mohajira</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Mothra">Mothra</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --> | <a href="#Liese">Liese</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Squares">Squares</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:67 --><br /> | ||
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 Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">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 /> | 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 Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">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 /> | ||
<br /> | <br /> | ||
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Music:<br /> | Music:<br /> | ||
By <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | By <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
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<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:520:http://tinyurl.com/24cbxse --><a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow">http://tinyurl.com/24cbxse</a><!-- ws:end:WikiTextUrlRule:520 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Mothra-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Mothra-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | ||
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Wedgie: &lt;&lt;4 16 9 16 3 -24||<br /> | Wedgie: &lt;&lt;4 16 9 16 3 -24||<br /> | ||
EDOs: 5, 8, 11, 14, 17, 31<br /> | EDOs: 5, 8, 11, 14, 17, 31<br /> | ||
Badness: 0.0460</body></html></pre></div> | Badness: 0.0460<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Squares-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> | |||
Commas: 81/80, 99/98, 121/120<br /> | |||
<br /> | |||
POTE generator: ~9/7 = 425.957<br /> | |||
<br /> | |||
Map: [&lt;1 3 8 6 7|, &lt;0 -4 -16 -9 -10|]<br /> | |||
EDOs: 5, 8, 11, 14, 17, 31<br /> | |||
Badness: 0.0216<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Squares-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h2> | |||
Commas: 81/80, 99/98, 121/120, 66/65<br /> | |||
<br /> | |||
POTE generator: ~9/7 = 425.550<br /> | |||
<br /> | |||
Map: [&lt;1 3 8 6 7 3|, &lt;0 -4 -16 -9 -10 2|]<br /> | |||
EDOs: 5, 8, 11, 14, 17, 31<br /> | |||
Badness: 0.0255</body></html></pre></div> | |||