Archytas clan: Difference between revisions
Wikispaces>genewardsmith **Imported revision 313403876 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 317319106 - 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>2012-03 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-03 13:12:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>317319106</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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Commas: 64/63, 360/343 | Commas: 64/63, 360/343 | ||
[[POTE tuning|POTE generator]]: 701.556 | [[POTE tuning|POTE generator]]: ~3/2 = 701.556 | ||
Map: [<1 0 15 6|, <0 1 -8 -2|] | Map: [<1 0 15 6|, <0 1 -8 -2|] | ||
Wedgie: <<1 -8 -2 -15 -6 18|| | Wedgie: <<1 -8 -2 -15 -6 18|| | ||
EDOs: 12, | EDOs: 12, 41d, 53d | ||
Badness: 0.0566 | Badness: 0.0566 | ||
==11-limit== | |||
Commas: 45/44, 64/63, 99/98 | |||
POTE generator ~3/2 = 702.136 | |||
Map: [<1 0 15 6 13|, <0 1 -8 -2 -6|] | |||
EDOs: 12, 29de, 41de | |||
Badness: 0.0375 | |||
=Passion= | =Passion= | ||
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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:44:&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:44 --><!-- ws:start:WikiTextTocRule:45: --><a href="#Mother">Mother</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Blacksmith">Blacksmith</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- 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="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Beatles">Beatles</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Schism">Schism</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Passion">Passion</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Quasisuper">Quasisuper</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: --> | <a href="#Progress">Progress</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:67 --><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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Commas: 64/63, 360/343<br /> | Commas: 64/63, 360/343<br /> | ||
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.556<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 701.556<br /> | ||
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Map: [&lt;1 0 15 6|, &lt;0 1 -8 -2|]<br /> | Map: [&lt;1 0 15 6|, &lt;0 1 -8 -2|]<br /> | ||
Wedgie: &lt;&lt;1 -8 -2 -15 -6 18||<br /> | Wedgie: &lt;&lt;1 -8 -2 -15 -6 18||<br /> | ||
EDOs: 12, | EDOs: 12, 41d, 53d<br /> | ||
Badness: 0.0566<br /> | Badness: 0.0566<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Schism-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> | ||
Commas: 45/44, 64/63, 99/98<br /> | |||
<br /> | |||
POTE generator ~3/2 = 702.136<br /> | |||
<br /> | |||
Map: [&lt;1 0 15 6 13|, &lt;0 1 -8 -2 -6|]<br /> | |||
EDOs: 12, 29de, 41de<br /> | |||
Badness: 0.0375<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Passion"></a><!-- ws:end:WikiTextHeadingRule:32 -->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:34:&lt;h1&gt; --><h1 id="toc17"><a name="Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:34 -->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:36:&lt;h2&gt; --><h2 id="toc18"><a name="Quasisuper-Quasisupra"></a><!-- ws:end:WikiTextHeadingRule:36 -->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:38:&lt;h2&gt; --><h2 id="toc19"><a name="Quasisuper-Quasisoup"></a><!-- ws:end:WikiTextHeadingRule:38 -->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:40:&lt;h1&gt; --><h1 id="toc20"><a name="Progress"></a><!-- ws:end:WikiTextHeadingRule:40 -->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:42:&lt;h2&gt; --><h2 id="toc21"><a name="Progress-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | ||
Commas: 56/55, 64/63, 77/75<br /> | Commas: 56/55, 64/63, 77/75<br /> | ||
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