Starling family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 302810008 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 361691190 - 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>2012- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-09-03 13:16:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>361691190</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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31: 81/80, 1990656/1953125 | 31: 81/80, 1990656/1953125 | ||
34: 15625/15552, 2048/2025 | 34: 15625/15552, 2048/2025 | ||
==11-limit== | |||
Commas: 126/125, 385/384 | |||
Map: [<1 0 0 -1 8|, <0 1 0 -2 3|, <0 0 1 3 -4]] | |||
Generators: 2, 3, 5 | |||
EDOs: 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de, 300de | |||
Badness: .000677 | |||
=Thrush= | =Thrush= | ||
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Map: [<1 0 0 -1 -3 2|, <0 1 0 -2 7 4|, <0 0 1 3 -2 -2|] | Map: [<1 0 0 -1 -3 2|, <0 1 0 -2 7 4|, <0 0 1 3 -2 -2|] | ||
EDOs: 34, 46, 172cd, 218cdf, 264bcdf, 310bcdf | EDOs: 34, 46, 172cd, 218cdf, 264bcdf, 310bcdf | ||
Badness: 0.001588 | Badness: 0.001588</pre></div> | ||
</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><!-- 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>Starling family</title></head><body><!-- ws:start:WikiTextTocRule:36:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 1em;"><a href="#x7-limit starling">7-limit starling</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#x7-limit starling-Minkowski blocks">Minkowski blocks</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#x7-limit starling-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 1em;"><a href="#Thrush">Thrush</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 2em;"><a href="#Thrush-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 2em;"><a href="#Thrush-Bluebird">Bluebird</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 2em;"><a href="#Thrush-Nightingale">Nightingale</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Thrush-Veery">Veery</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 1em;"><a href="#Thrasher">Thrasher</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 2em;"><a href="#Thrasher-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 2em;"><a href="#Thrasher-Mockingbird">Mockingbird</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 2em;"><a href="#Thrasher-Catbird">Catbird</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 1em;"><a href="#Aplonis">Aplonis</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Aplonis-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 1em;"><a href="#Oxpecker">Oxpecker</a></div> | ||
<!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 2em;"><a href="#Oxpecker-Woodpecker">Woodpecker</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 1em;"><a href="#Treecreeper">Treecreeper</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 2em;"><a href="#Treecreeper-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --></div> | ||
<!-- ws:end:WikiTextTocRule:55 --><br /> | |||
The head of the starling <a class="wiki_link" href="/family">family</a> is starling, which tempers out <a class="wiki_link" href="/126_125">126/125</a>, the <a class="wiki_link" href="/starling%20comma">starling comma</a> or <a class="wiki_link" href="/septimal%20semicomma">septimal semicomma</a>. 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 /> | The head of the starling <a class="wiki_link" href="/family">family</a> is starling, which tempers out <a class="wiki_link" href="/126_125">126/125</a>, the <a class="wiki_link" href="/starling%20comma">starling comma</a> or <a class="wiki_link" href="/septimal%20semicomma">septimal semicomma</a>. 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 /> | ||
<br /> | <br /> | ||
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34: 15625/15552, 2048/2025<br /> | 34: 15625/15552, 2048/2025<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x7-limit starling-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | ||
Commas: 126/125, 385/384<br /> | |||
<br /> | |||
Map: [&lt;1 0 0 -1 8|, &lt;0 1 0 -2 3|, &lt;0 0 1 3 -4]]<br /> | |||
Generators: 2, 3, 5<br /> | |||
EDOs: 15, 19, 27, 31, 46, 77, 96d, 127d, 173d, 204de, 300de<br /> | |||
Badness: .000677<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Thrush"></a><!-- ws:end:WikiTextHeadingRule:6 -->Thrush</h1> | |||
<a class="wiki_link" href="/Comma">Commas</a>: 126/125, 176/175<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 126/125, 176/175<br /> | ||
Associated linear temperament: <a class="wiki_link" href="/Starling%20temperaments">myna</a><br /> | Associated linear temperament: <a class="wiki_link" href="/Starling%20temperaments">myna</a><br /> | ||
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Scales: <a class="wiki_link" href="/thrush12">thrush12</a><br /> | Scales: <a class="wiki_link" href="/thrush12">thrush12</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Thrush-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> | ||
Commas: 126/125, 176/175, 196/195<br /> | Commas: 126/125, 176/175, 196/195<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000677<br /> | Badness: 0.000677<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Thrush-Bluebird"></a><!-- ws:end:WikiTextHeadingRule:10 -->Bluebird</h2> | ||
Commas 126/125, 176/175, 144/143<br /> | Commas 126/125, 176/175, 144/143<br /> | ||
<br /> | <br /> | ||
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Projection pairs: 7 125/18 11 3125/288 13 41472/3125<br /> | Projection pairs: 7 125/18 11 3125/288 13 41472/3125<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Thrush-Nightingale"></a><!-- ws:end:WikiTextHeadingRule:12 -->Nightingale</h2> | ||
Commas: 126/125, 176/175, 66/65<br /> | Commas: 126/125, 176/175, 66/65<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000837<br /> | Badness: 0.000837<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Thrush-Veery"></a><!-- ws:end:WikiTextHeadingRule:14 -->Veery</h2> | ||
Commas: 91/90, 126/125, 176/175<br /> | Commas: 91/90, 126/125, 176/175<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000991<br /> | Badness: 0.000991<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Thrasher"></a><!-- ws:end:WikiTextHeadingRule:16 -->Thrasher</h1> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 56/55, 100/99<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 56/55, 100/99<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000480<br /> | Badness: 0.000480<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Thrasher-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2> | ||
Commas: 126/125, 100/99, 91/90<br /> | Commas: 126/125, 100/99, 91/90<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000876<br /> | Badness: 0.000876<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Thrasher-Mockingbird"></a><!-- ws:end:WikiTextHeadingRule:20 -->Mockingbird</h2> | ||
Commas: 126/125, 100/99, 40/39<br /> | Commas: 126/125, 100/99, 40/39<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000859<br /> | Badness: 0.000859<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Thrasher-Catbird"></a><!-- ws:end:WikiTextHeadingRule:22 -->Catbird</h2> | ||
Commas: 126/125, 100/99, 78/77<br /> | Commas: 126/125, 100/99, 78/77<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000905<br /> | Badness: 0.000905<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Aplonis"></a><!-- ws:end:WikiTextHeadingRule:24 -->Aplonis</h1> | ||
Commas: 126/125, 540/539<br /> | Commas: 126/125, 540/539<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000648<br /> | Badness: 0.000648<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Aplonis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2> | ||
Commas: 126/125, 144/143, 196/195<br /> | Commas: 126/125, 144/143, 196/195<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000821<br /> | Badness: 0.000821<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Oxpecker"></a><!-- ws:end:WikiTextHeadingRule:28 -->Oxpecker</h1> | ||
Commas: 121/120, 126/125<br /> | Commas: 121/120, 126/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.000699<br /> | Badness: 0.000699<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Oxpecker-Woodpecker"></a><!-- ws:end:WikiTextHeadingRule:30 -->Woodpecker</h2> | ||
Commas: 66/65, 121/120, 126/125<br /> | Commas: 66/65, 121/120, 126/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.001093<br /> | Badness: 0.001093<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Treecreeper"></a><!-- ws:end:WikiTextHeadingRule:32 -->Treecreeper</h1> | ||
Commas: 126/125, 1232/1215<br /> | Commas: 126/125, 1232/1215<br /> | ||
<br /> | <br /> | ||
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Badness: 0.001585<br /> | Badness: 0.001585<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Treecreeper-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | ||
Commas: 91/90, 126/125, 352/351<br /> | Commas: 91/90, 126/125, 352/351<br /> | ||
<br /> | <br /> | ||