Archytas clan: Difference between revisions
Wikispaces>genewardsmith **Imported revision 326138330 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 326144662 - 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>2012-04-27 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-27 15:15:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>326144662</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: 25, 27 | EDOs: 25, 27 | ||
Badness: 0.1085 | Badness: 0.1085 | ||
==11-limit== | |||
Commas: 56/55, 64/63, 1350/1331 | |||
POTE generator: ~7/5 = 577.850 | |||
Map: [<1 4 -2 -2 3|, <0 -5 9 10 1|] | |||
EDOs: 25e, 27e | |||
Badness: 0.0521 | |||
==13-limit== | |||
Commas: 56/55, 64/63, 78/77, 507/500 | |||
POTE generator: ~7/5 = 578.060 | |||
Map: [<1 4 -2 -2 3 -4|, <0 -5 9 10 1 16|] | |||
EDOs: 27e | |||
Badness: 0.0397 | |||
=Quasisuper= | =Quasisuper= | ||
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Badness: 0.0262</pre></div> | Badness: 0.0262</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:60:&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:60 --><!-- ws:start:WikiTextTocRule:61: --><a href="#Mother">Mother</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Blacksmith">Blacksmith</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Beatles">Beatles</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Schism">Schism</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Passion">Passion</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Fervor">Fervor</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> | <a href="#Quasisuper">Quasisuper</a><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Progress">Progress</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:91 --><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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<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Blacksmith-Blackwood"></a><!-- ws:end:WikiTextHeadingRule:12 -->Blackwood</h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Blacksmith-Blackwood"></a><!-- ws:end:WikiTextHeadingRule:12 -->Blackwood</h2> | ||
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Badness: 0.1085<br /> | Badness: 0.1085<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Fervor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->11-limit</h2> | ||
Commas: 56/55, 64/63, 1350/1331<br /> | |||
<br /> | |||
POTE generator: ~7/5 = 577.850<br /> | |||
<br /> | |||
Map: [&lt;1 4 -2 -2 3|, &lt;0 -5 9 10 1|]<br /> | |||
EDOs: 25e, 27e<br /> | |||
Badness: 0.0521<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Fervor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2> | |||
Commas: 56/55, 64/63, 78/77, 507/500<br /> | |||
<br /> | |||
POTE generator: ~7/5 = 578.060<br /> | |||
<br /> | |||
Map: [&lt;1 4 -2 -2 3 -4|, &lt;0 -5 9 10 1 16|]<br /> | |||
EDOs: 27e<br /> | |||
Badness: 0.0397<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:48 -->Quasisuper</h1> | |||
Commas: 64/63, 2430/2401<br /> | Commas: 64/63, 2430/2401<br /> | ||
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Badness: 0.0638<br /> | Badness: 0.0638<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Quasisuper-Quasisupra"></a><!-- ws:end:WikiTextHeadingRule:50 -->Quasisupra</h2> | ||
Commas: 64/63, 99/98, 121/120<br /> | Commas: 64/63, 99/98, 121/120<br /> | ||
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Badness: 0.0322<br /> | Badness: 0.0322<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Quasisuper-Quasisoup"></a><!-- ws:end:WikiTextHeadingRule:52 -->Quasisoup</h2> | ||
Commas: 55/54, 64/63, 2430/2401<br /> | Commas: 55/54, 64/63, 2430/2401<br /> | ||
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Badness: 0.0835<br /> | Badness: 0.0835<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Progress"></a><!-- ws:end:WikiTextHeadingRule:54 -->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:56:&lt;h2&gt; --><h2 id="toc28"><a name="Progress-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2> | ||
Commas: 56/55, 64/63, 77/75<br /> | Commas: 56/55, 64/63, 77/75<br /> | ||
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Badness: 0.0310<br /> | Badness: 0.0310<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Progress-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2> | ||
Commas: 56/55, 64/63, 66/65, 77/75<br /> | Commas: 56/55, 64/63, 66/65, 77/75<br /> | ||
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