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Starling family: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 188547407 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 188551369 - 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>2010-12-15 20:42:19 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-15 21:03:47 UTC</tt>.<br>
: The original revision id was <tt>188547407</tt>.<br>
: The original revision id was <tt>188551369</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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====Mockingbird====
====Mockingbird====
Commas: 126/125, 100/99, 40/39
Commas: 126/125, 100/99, 40/39
EDOs: 15


====Catbird====
====Catbird====
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===Aplonis===
===Aplonis===
Commas: 126/125, 540/539
Commas: 126/125, 540/539
EDOs: 19, 31, 58, 89


13-limit
13-limit
Commas: 126/125, 144/143, 196/195
Commas: 126/125, 144/143, 196/195


===Spreo===
EDOs: 19, 31, 50, 58
Starling can be extended to spreo with essentially no tuning accuracy penalty; [[135edo]] can be used for both of them.
</pre></div>
 
Commas: 126/125, 441/440
 
11-limit minimax
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1 2/5 0 0 1/5&gt;,
|2 -4/5 0 0 3/5&gt;, |0 0 0 0 1&gt;]
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: [&lt;0 1 1 1 3|, &lt;0 1 0 -2 -2|]
 
Map: [&lt;1 0 0 -1 -5|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 5|]
Generators: 2, 3, 5
Edos: 12, 15, 16, 28, 31, 43, 46, 58, 73, 77, 89,
&lt;135 214 314 379 467|
 
Scales: [[starling11]], [[starling12]], [[starling15]], [[starling16]], [[starling17]], [[starling19]]</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Starling family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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 &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt;.  Other possible tunings are &lt;a class="wiki_link" href="/108edo"&gt;108edo&lt;/a&gt; and &lt;a class="wiki_link" href="/185edo"&gt;185edo&lt;/a&gt;, and the nonpatent &lt;a class="wiki_link" href="/135edo"&gt;135edo&lt;/a&gt; val &amp;lt;135 214 314 379|.&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Starling family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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 &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt;.  Other possible tunings are &lt;a class="wiki_link" href="/108edo"&gt;108edo&lt;/a&gt; and &lt;a class="wiki_link" href="/185edo"&gt;185edo&lt;/a&gt;, and the nonpatent &lt;a class="wiki_link" href="/135edo"&gt;135edo&lt;/a&gt; val &amp;lt;135 214 314 379|.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc7"&gt;&lt;a name="x-11 limit children-Thrasher-Mockingbird"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Mockingbird&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc7"&gt;&lt;a name="x-11 limit children-Thrasher-Mockingbird"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Mockingbird&lt;/h4&gt;
Commas: 126/125, 100/99, 40/39&lt;br /&gt;
Commas: 126/125, 100/99, 40/39&lt;br /&gt;
&lt;br /&gt;
EDOs: 15&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc8"&gt;&lt;a name="x-11 limit children-Thrasher-Catbird"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Catbird&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc8"&gt;&lt;a name="x-11 limit children-Thrasher-Catbird"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Catbird&lt;/h4&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-11 limit children-Aplonis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Aplonis&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-11 limit children-Aplonis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Aplonis&lt;/h3&gt;
Commas: 126/125, 540/539&lt;br /&gt;
Commas: 126/125, 540/539&lt;br /&gt;
&lt;br /&gt;
EDOs: 19, 31, 58, 89&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
13-limit&lt;br /&gt;
13-limit&lt;br /&gt;
Commas: 126/125, 144/143, 196/195&lt;br /&gt;
Commas: 126/125, 144/143, 196/195&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="x-11 limit children-Spreo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Spreo&lt;/h3&gt;
EDOs: 19, 31, 50, 58&lt;/body&gt;&lt;/html&gt;</pre></div>
Starling can be extended to spreo with essentially no tuning accuracy penalty; &lt;a class="wiki_link" href="/135edo"&gt;135edo&lt;/a&gt; can be used for both of them.&lt;br /&gt;
&lt;br /&gt;
Commas: 126/125, 441/440&lt;br /&gt;
&lt;br /&gt;
11-limit minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |0 1 0 0 0&amp;gt;, |1 2/5 0 0 1/5&amp;gt;, &lt;br /&gt;
|2 -4/5 0 0 3/5&amp;gt;, |0 0 0 0 1&amp;gt;]&lt;br /&gt;
Eigenmonzos: 2, 4/3, 11/8&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 5/4 length=0.8576 6/5 length=0.9314&lt;br /&gt;
Angle(5/4, 6/5) = 74.6239&lt;br /&gt;
Map to lattice: [&amp;lt;0 1 1 1 3|, &amp;lt;0 1 0 -2 -2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -1 -5|, &amp;lt;0 1 0 -2 -2|, &amp;lt;0 0 1 3 5|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
Edos: 12, 15, 16, 28, 31, 43, 46, 58, 73, 77, 89, &lt;br /&gt;
&amp;lt;135 214 314 379 467|&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/starling11"&gt;starling11&lt;/a&gt;, &lt;a class="wiki_link" href="/starling12"&gt;starling12&lt;/a&gt;, &lt;a class="wiki_link" href="/starling15"&gt;starling15&lt;/a&gt;, &lt;a class="wiki_link" href="/starling16"&gt;starling16&lt;/a&gt;, &lt;a class="wiki_link" href="/starling17"&gt;starling17&lt;/a&gt;, &lt;a class="wiki_link" href="/starling19"&gt;starling19&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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