Starling family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 173058743 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 173062699 - 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>2010-10-23 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-10-23 23:30:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>173062699</tt>.<br> | ||
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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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13-limit | 13-limit | ||
Commas: 126/125, 144/143, 196/195</pre></div> | Commas: 126/125, 144/143, 196/195 | ||
===Spreo=== | |||
Starling can be extended to spreo with essentially no tuning accuracy penalty; [[135edo]] can be used for both of them. | |||
Commas: 126/125, 441/440 | |||
11-limit minimax | |||
[|1 0 0 0 0>, |0 1 0 0 0>, |1 2/5 0 0 1/5>, | |||
|2 -4/5 0 0 3/5>, |0 0 0 0 1>] | |||
Eigenmonzos: 2, 4/3, 11/8 | |||
Lattice basis: 5/4 length=0.8576 6/5 length=0.9314 | |||
Angle(5/4, 6/5) = 74.6239 | |||
Map to lattice: [<0 1 1 1 3|, <0 1 0 -2 -2|] | |||
Map: [<1 0 0 -1 -5|, <0 1 0 -2 -2|, <0 0 1 3 5|] | |||
Generators: 2, 3, 5 | |||
Edos: 12, 15, 16, 28, 31, 43, 46, 58, 73, 77, 89, | |||
<135 214 314 379 467|</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>Starling family</title></head><body>The head of the starling family is starling, which tempers out 126/125, the starling comma or septimal semicomma. Starling has a normal list basis of [2, 3, 5]; hence a 5-limit scale can be converted to starling simply by tempering it. One way to do that, and an excellent starling tuning, is given by <a class="wiki_link" href="/77edo">77edo</a>. Other possible tunings are <a class="wiki_link" href="/108edo">108edo</a> and <a class="wiki_link" href="/185edo">185edo</a>, and the nonpatent <a class="wiki_link" href="/135edo">135edo</a> val &lt;135 214 314 379|.<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>Starling family</title></head><body>The head of the starling family is starling, which tempers out 126/125, the starling comma or septimal semicomma. Starling has a normal list basis of [2, 3, 5]; hence a 5-limit scale can be converted to starling simply by tempering it. One way to do that, and an excellent starling tuning, is given by <a class="wiki_link" href="/77edo">77edo</a>. Other possible tunings are <a class="wiki_link" href="/108edo">108edo</a> and <a class="wiki_link" href="/185edo">185edo</a>, and the nonpatent <a class="wiki_link" href="/135edo">135edo</a> val &lt;135 214 314 379|.<br /> | ||
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<br /> | <br /> | ||
13-limit<br /> | 13-limit<br /> | ||
Commas: 126/125, 144/143, 196/195</body></html></pre></div> | Commas: 126/125, 144/143, 196/195<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-11 limit children-Spreo"></a><!-- ws:end:WikiTextHeadingRule:18 -->Spreo</h3> | |||
Starling can be extended to spreo with essentially no tuning accuracy penalty; <a class="wiki_link" href="/135edo">135edo</a> can be used for both of them.<br /> | |||
<br /> | |||
Commas: 126/125, 441/440<br /> | |||
<br /> | |||
11-limit minimax<br /> | |||
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1 2/5 0 0 1/5&gt;, <br /> | |||
|2 -4/5 0 0 3/5&gt;, |0 0 0 0 1&gt;]<br /> | |||
Eigenmonzos: 2, 4/3, 11/8<br /> | |||
<br /> | |||
Lattice basis: 5/4 length=0.8576 6/5 length=0.9314<br /> | |||
Angle(5/4, 6/5) = 74.6239<br /> | |||
Map to lattice: [&lt;0 1 1 1 3|, &lt;0 1 0 -2 -2|]<br /> | |||
<br /> | |||
Map: [&lt;1 0 0 -1 -5|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 5|]<br /> | |||
Generators: 2, 3, 5<br /> | |||
Edos: 12, 15, 16, 28, 31, 43, 46, 58, 73, 77, 89, <br /> | |||
&lt;135 214 314 379 467|</body></html></pre></div> | |||