Archytas clan: Difference between revisions
Wikispaces>genewardsmith **Imported revision 299856932 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 303033032 - 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>2012-02- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-18 18:16:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>303033032</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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EDOs: 10, 17c, 27e | EDOs: 10, 17c, 27e | ||
Badness: 0.0329 | Badness: 0.0329 | ||
===13-limit=== | |||
Commas: 56/55, 64/63, 78/77, 91/90 | |||
POTE generator: ~11/9 = 355.456 | |||
Map: [<1 1 5 4 2 4|,<0 2 -9 -4 5 -1|] | |||
EDOs: 10, 17c, 27e | |||
Badness: 0.0226 | |||
=Schism= | =Schism= | ||
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Badness: 0.0310</pre></div> | Badness: 0.0310</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>Archytas clan</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>Archytas clan</title></head><body><!-- ws:start:WikiTextTocRule:38:&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:38 --><!-- ws:start:WikiTextTocRule:39: --><a href="#Mother">Mother</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Blacksmith">Blacksmith</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Beatles">Beatles</a><!-- 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: --> | <a href="#Schism">Schism</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Passion">Passion</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Quasisuper">Quasisuper</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Progress">Progress</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:58 --><br /> | ||
The <em>archytas clan</em> tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">Archytas comma</a>, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of <a class="wiki_link" href="/22edo">22edo</a>. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>, dominant under <a class="wiki_link" href="/meantone%20family">meantone family</a>, augene under <a class="wiki_link" href="/augmented%20family">augmented family</a> and porcupine under <a class="wiki_link" href="/porcupine%20family">porcupine family</a>. The rest are considered below.<br /> | The <em>archytas clan</em> tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">Archytas comma</a>, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of <a class="wiki_link" href="/22edo">22edo</a>. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>, dominant under <a class="wiki_link" href="/meantone%20family">meantone family</a>, augene under <a class="wiki_link" href="/augmented%20family">augmented family</a> and porcupine under <a class="wiki_link" href="/porcupine%20family">porcupine family</a>. The rest are considered below.<br /> | ||
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Badness: 0.0292<br /> | Badness: 0.0292<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:59:&lt;img src=&quot;/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg" alt="blacksmith10.jpg" title="blacksmith10.jpg" /><!-- ws:end:WikiTextLocalImageRule:59 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Blacksmith-Blackwood"></a><!-- ws:end:WikiTextHeadingRule:10 -->Blackwood</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Blacksmith-Blackwood"></a><!-- ws:end:WikiTextHeadingRule:10 -->Blackwood</h2> | ||
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Badness: 0.0329<br /> | Badness: 0.0329<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Beatles-Ringo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h3> | ||
Commas: 56/55, 64/63, 78/77, 91/90<br /> | |||
<br /> | |||
POTE generator: ~11/9 = 355.456<br /> | |||
<br /> | |||
Map: [&lt;1 1 5 4 2 4|,&lt;0 2 -9 -4 5 -1|]<br /> | |||
EDOs: 10, 17c, 27e<br /> | |||
Badness: 0.0226<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Schism"></a><!-- ws:end:WikiTextHeadingRule:26 -->Schism</h1> | |||
Commas: 64/63, 360/343<br /> | Commas: 64/63, 360/343<br /> | ||
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Badness: 0.0566<br /> | Badness: 0.0566<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Passion"></a><!-- ws:end:WikiTextHeadingRule:28 -->Passion</h1> | ||
Commas: 64/63, 3125/3087<br /> | Commas: 64/63, 3125/3087<br /> | ||
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Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:30 -->Quasisuper</h1> | ||
Commas: 64/63, 2430/2401<br /> | Commas: 64/63, 2430/2401<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0638<br /> | Badness: 0.0638<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Quasisuper-Quasisupra"></a><!-- ws:end:WikiTextHeadingRule:32 -->Quasisupra</h2> | ||
Commas: 64/63, 99/98, 121/120<br /> | Commas: 64/63, 99/98, 121/120<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0322<br /> | Badness: 0.0322<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Progress"></a><!-- ws:end:WikiTextHeadingRule:34 -->Progress</h1> | ||
Commas: 64/63, 392/375<br /> | Commas: 64/63, 392/375<br /> | ||
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Badness: 0.0664<br /> | Badness: 0.0664<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Progress-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
Commas: 56/55, 64/63, 77/75<br /> | Commas: 56/55, 64/63, 77/75<br /> | ||
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