Starling family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 165435135 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 165446689 - Original comment: links added** |
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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: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-26 09:13:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>165446689</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>links added</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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===Vital statistics=== | ===Vital statistics=== | ||
Comma c = 126/125 | [[Comma]] c = 126/125 | ||
7- and 9-limit minimax: 3 and 7 just, 5 1/3c sharp | 7- and 9-limit minimax: 3 and 7 just, 5 1/3c sharp | ||
Minkowski lattice basis: 6/5 length 1.068, 5/4 length 1.206 | Minkowski lattice basis: 6/5 length 1.068, 5/4 length 1.206 | ||
Angle(6/5, 5/4) = 100.364 degrees | Angle(6/5, 5/4) = 100.364 degrees | ||
Map to lattice: [<0 1 0 -2|, <0 1 1 1|] | Map to lattice: [<0 1 0 -2|, <0 1 1 1|] | ||
EDOs 77, 108, 185 | [[edo|EDOs]]: [[77edo|77]], [[108edo|108]], [[185edo|185]] | ||
==11 limit children== | ==11 limit children== | ||
===Thrush=== | ===Thrush=== | ||
Commas: 126/125, 176/175 | [[Comma|Commas]]: 126/125, 176/175 | ||
7 and 9 limit minimax | 7 and 9 limit minimax | ||
[|1 0 0 0 0>, |0 1 0 0 0>, |1/3 2/3 0 1/3 0>, | [|1 0 0 0 0>, |0 1 0 0 0>, |1/3 2/3 0 1/3 0>, | ||
|0 0 0 1 0>, |-10/3 4/3 0 5/3 0>] | |0 0 0 1 0>, |-10/3 4/3 0 5/3 0>] | ||
Eigenmonzos: 2, 7/6, 4/3 | [[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3 | ||
Lattice basis 5/4 length 0.8576 6/5 length 0.9314 | Lattice basis 5/4 length 0.8576 6/5 length 0.9314 | ||
| Line 35: | Line 35: | ||
Map: [<1 0 0 -1 -5|, <0 1 0 -2 -2|, <0 0 1 3 5|] | Map: [<1 0 0 -1 -5|, <0 1 0 -2 -2|, <0 0 1 3 5|] | ||
Generators: 2, 3, 5 | [[Generator|Generators]]: 2, 3, 5 | ||
[[edo|EDOs]]: [[31edo|31]], [[46edo|46]], [[58edo|58]], [[89edo|89]] | |||
===Thrasher=== | ===Thrasher=== | ||
Commas: 126/125, 100/99 | [[Comma|Commas]]: 126/125, 100/99 | ||
11-limit minimax | 11-limit minimax | ||
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|1 1/2 0 1/2 -1/4>, |0 0 0 1 0>, | |1 1/2 0 1/2 -1/4>, |0 0 0 1 0>, | ||
|2 -1/2 0 1/2 1/4>] | |2 -1/2 0 1/2 1/4>] | ||
Eigenmonzos: 2, 8/7, 11/9 | [[Eigenmonzo|Eigenmonzos]]: 2, 8/7, 11/9 | ||
Lattice basis: 6/5 length 0.9089 5/4 length 1.2007 | Lattice basis: 6/5 length 0.9089 5/4 length 1.2007 | ||
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Map: [<1 0 0 -1 2|, <0 1 0 -2 -2|, <0 0 1 3 2|] | Map: [<1 0 0 -1 2|, <0 1 0 -2 -2|, <0 0 1 3 2|] | ||
Generators: 2, 3, 5 | [[Generator|Generators]]: 2, 3, 5 | ||
[[edo|EDOs]]: [[12edo|12]], [[15edo|15]], [[19edo|19]], [[34edo|34]]</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 marvel 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>. <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 marvel 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>. <br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Vital statistics"></a><!-- ws:end:WikiTextHeadingRule:0 -->Vital statistics</h3> | ||
Comma c = 126/125<br /> | <a class="wiki_link" href="/Comma">Comma</a> c = 126/125<br /> | ||
7- and 9-limit minimax: 3 and 7 just, 5 1/3c sharp<br /> | 7- and 9-limit minimax: 3 and 7 just, 5 1/3c sharp<br /> | ||
Minkowski lattice basis: 6/5 length 1.068, 5/4 length 1.206<br /> | Minkowski lattice basis: 6/5 length 1.068, 5/4 length 1.206<br /> | ||
Angle(6/5, 5/4) = 100.364 degrees<br /> | Angle(6/5, 5/4) = 100.364 degrees<br /> | ||
Map to lattice: [&lt;0 1 0 -2|, &lt;0 1 1 1|]<br /> | Map to lattice: [&lt;0 1 0 -2|, &lt;0 1 1 1|]<br /> | ||
EDOs 77, 108, 185<br /> | <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/77edo">77</a>, <a class="wiki_link" href="/108edo">108</a>, <a class="wiki_link" href="/185edo">185</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-11 limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->11 limit children</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-11 limit children"></a><!-- ws:end:WikiTextHeadingRule:2 -->11 limit children</h2> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-11 limit children-Thrush"></a><!-- ws:end:WikiTextHeadingRule:4 -->Thrush</h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-11 limit children-Thrush"></a><!-- ws:end:WikiTextHeadingRule:4 -->Thrush</h3> | ||
Commas: 126/125, 176/175<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 126/125, 176/175<br /> | ||
<br /> | <br /> | ||
7 and 9 limit minimax<br /> | 7 and 9 limit minimax<br /> | ||
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1/3 2/3 0 1/3 0&gt;, <br /> | [|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |1/3 2/3 0 1/3 0&gt;, <br /> | ||
|0 0 0 1 0&gt;, |-10/3 4/3 0 5/3 0&gt;]<br /> | |0 0 0 1 0&gt;, |-10/3 4/3 0 5/3 0&gt;]<br /> | ||
Eigenmonzos: 2, 7/6, 4/3<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6, 4/3<br /> | ||
<br /> | <br /> | ||
Lattice basis 5/4 length 0.8576 6/5 length 0.9314<br /> | Lattice basis 5/4 length 0.8576 6/5 length 0.9314<br /> | ||
| Line 84: | Line 84: | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -1 -5|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 5|]<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 /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> | ||
<a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/89edo">89</a><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-11 limit children-Thrasher"></a><!-- ws:end:WikiTextHeadingRule:6 -->Thrasher</h3> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-11 limit children-Thrasher"></a><!-- ws:end:WikiTextHeadingRule:6 -->Thrasher</h3> | ||
Commas: 126/125, 100/99<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 126/125, 100/99<br /> | ||
<br /> | <br /> | ||
11-limit minimax<br /> | 11-limit minimax<br /> | ||
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|1 1/2 0 1/2 -1/4&gt;, |0 0 0 1 0&gt;, <br /> | |1 1/2 0 1/2 -1/4&gt;, |0 0 0 1 0&gt;, <br /> | ||
|2 -1/2 0 1/2 1/4&gt;]<br /> | |2 -1/2 0 1/2 1/4&gt;]<br /> | ||
Eigenmonzos: 2, 8/7, 11/9<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 8/7, 11/9<br /> | ||
<br /> | <br /> | ||
Lattice basis: 6/5 length 0.9089 5/4 length 1.2007<br /> | Lattice basis: 6/5 length 0.9089 5/4 length 1.2007<br /> | ||
| Line 101: | Line 101: | ||
<br /> | <br /> | ||
Map: [&lt;1 0 0 -1 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 2|]<br /> | Map: [&lt;1 0 0 -1 2|, &lt;0 1 0 -2 -2|, &lt;0 0 1 3 2|]<br /> | ||
Generators: 2, 3, 5<br /> | <a class="wiki_link" href="/Generator">Generators</a>: 2, 3, 5<br /> | ||
<a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a></body></html></pre></div> | |||