Archytas clan: Difference between revisions
Wikispaces>genewardsmith **Imported revision 491645692 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 491648586 - 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>2014-02-24 14: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-24 14:28:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>491648586</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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Badness: 0.0322 | Badness: 0.0322 | ||
==Quasisoup | ==13-limit== | ||
Commas: 64/63, 78/77, 91/90, 121/120 | |||
POTE generator: ~3/2 = 708.004 | |||
Map: [<1 0 23 6 13 18|, <0 1 -13 -2 -6 -9|] | |||
EDOs: 17c, 22, 39d, 61df, 100bcdf | |||
Badness: 0.0302 | |||
=Quasisoup= | |||
Commas: 55/54, 64/63, 2430/2401 | Commas: 55/54, 64/63, 2430/2401 | ||
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Badness: 0.0327</pre></div> | Badness: 0.0327</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:72:&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:72 --><!-- ws:start:WikiTextTocRule:73: --><div style="margin-left: 1em;"><a href="#Mother">Mother</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><div style="margin-left: 1em;"><a href="#Blacksmith">Blacksmith</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><div style="margin-left: 2em;"><a href="#Blacksmith-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><div style="margin-left: 2em;"><a href="#Blacksmith-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 2em;"><a href="#Blacksmith-Farrier">Farrier</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><div style="margin-left: 2em;"><a href="#Blacksmith-Ferrum">Ferrum</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><div style="margin-left: 2em;"><a href="#Blacksmith-Blackwood">Blackwood</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><div style="margin-left: 1em;"><a href="#Superpyth">Superpyth</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><div style="margin-left: 2em;"><a href="#Superpyth-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><div style="margin-left: 2em;"><a href="#Superpyth-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 2em;"><a href="#Superpyth-Suprapyth">Suprapyth</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 3em;"><a href="#Superpyth-Suprapyth-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 1em;"><a href="#Beatles">Beatles</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 2em;"><a href="#Beatles-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#Beatles-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 2em;"><a href="#Beatles-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 2em;"><a href="#Beatles-Ringo">Ringo</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 3em;"><a href="#Beatles-Ringo-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 1em;"><a href="#Schism">Schism</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 2em;"><a href="#Schism-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 1em;"><a href="#Passion">Passion</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#Passion-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 2em;"><a href="#Passion-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 1em;"><a href="#Fervor">Fervor</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 2em;"><a href="#Fervor-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 2em;"><a href="#Fervor-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Fervor-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 1em;"><a href="#Quasisuper">Quasisuper</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 2em;"><a href="#Quasisuper-Quasisupra">Quasisupra</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Quasisuper-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 1em;"><a href="#Quasisoup">Quasisoup</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 1em;"><a href="#Progress">Progress</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Progress-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 2em;"><a href="#Progress-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 2em;"><a href="#Progress-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Progress-Progressive">Progressive</a></div> | ||
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<!-- ws:end:WikiTextTocRule:109 --><br /> | |||
The <em>archytas clan</em> tempers out the <a class="wiki_link" href="/64_63">Archytas comma</a>, 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to <a class="wiki_link" href="/81_80">81/80</a> in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) 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" href="/64_63">Archytas comma</a>, 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to <a class="wiki_link" href="/81_80">81/80</a> in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) 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: 0.0322<br /> | Badness: 0.0322<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Quasisuper-Quasisoup"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Quasisuper-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2> | ||
Commas: 64/63, 78/77, 91/90, 121/120<br /> | |||
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POTE generator: ~3/2 = 708.004<br /> | |||
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Map: [&lt;1 0 23 6 13 18|, &lt;0 1 -13 -2 -6 -9|]<br /> | |||
EDOs: 17c, 22, 39d, 61df, 100bcdf<br /> | |||
Badness: 0.0302<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Quasisoup"></a><!-- ws:end:WikiTextHeadingRule:60 -->Quasisoup</h1> | |||
Commas: 55/54, 64/63, 2430/2401<br /> | |||
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POTE generator: ~3/2 = 709.021<br /> | POTE generator: ~3/2 = 709.021<br /> | ||
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Badness: 0.0835<br /> | Badness: 0.0835<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Progress"></a><!-- ws:end:WikiTextHeadingRule:62 -->Progress</h1> | ||
Comma: 32768/30375<br /> | Comma: 32768/30375<br /> | ||
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Badness: 0.2461<br /> | Badness: 0.2461<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Progress-7-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->7-limit</h2> | ||
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:66:&lt;h2&gt; --><h2 id="toc33"><a name="Progress-11-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->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:68:&lt;h2&gt; --><h2 id="toc34"><a name="Progress-13-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->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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Badness: 0.0262<br /> | Badness: 0.0262<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Progress-Progressive"></a><!-- ws:end:WikiTextHeadingRule:70 -->Progressive</h2> | ||
Commas: 26/25, 56/55, 64/63, 77/75<br /> | Commas: 26/25, 56/55, 64/63, 77/75<br /> | ||
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