Archytas clan: Difference between revisions
Wikispaces>genewardsmith **Imported revision 288876135 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 289121799 - 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> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-02 16:35:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>289121799</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: 28/27, 49/48 | Commas: 28/27, 49/48 | ||
[[POTE tuning|POTE generator]]: 392.767 | [[POTE tuning|POTE generator]]: ~5/4 = 392.767 | ||
Map: [<5 8 0 14|, <0 0 1 0|] | Map: [<5 8 0 14|, <0 0 1 0|] | ||
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EDOs: 5, 10, 15, 25, 55 | EDOs: 5, 10, 15, 25, 55 | ||
Badness: 0.0256 | Badness: 0.0256 | ||
==11-limit== | |||
Commas: 28/27, 49/48, 55/54 | |||
POTE generator: ~5/4 = 394.948 | |||
Map: [<5 8 0 14 29|, <0 0 1 0 -1|] | |||
EDOs: 5, 10, 15, 40be, 55be, 70bde, 85bcde | |||
Badness: 0.0246 | |||
==Farrier== | |||
Commas: 28/27, 49/48, 77/75 | |||
POTE generator: ~5/4 = 398.070 | |||
Map: [<5 8 0 14 -6|, <0 0 1 0 2|] | |||
EDOs: 5e, 15 | |||
Badness: 0.0292 | |||
[[image:blacksmith10.jpg]] | [[image:blacksmith10.jpg]] | ||
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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:30:&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:30 --><!-- ws:start:WikiTextTocRule:31: --><a href="#Mother">Mother</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Blacksmith">Blacksmith</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Beatles">Beatles</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Schism">Schism</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Passion">Passion</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Quasisuper">Quasisuper</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Progress">Progress</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:46 --><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 /> | ||
<br /> | <br /> | ||
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Commas: 28/27, 49/48<br /> | Commas: 28/27, 49/48<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 392.767<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~5/4 = 392.767<br /> | ||
<br /> | <br /> | ||
Map: [&lt;5 8 0 14|, &lt;0 0 1 0|]<br /> | Map: [&lt;5 8 0 14|, &lt;0 0 1 0|]<br /> | ||
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Badness: 0.0256<br /> | Badness: 0.0256<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Blacksmith-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | ||
Commas: 28/27, 49/48, 55/54<br /> | |||
<br /> | |||
POTE generator: ~5/4 = 394.948<br /> | |||
<br /> | |||
Map: [&lt;5 8 0 14 29|, &lt;0 0 1 0 -1|]<br /> | |||
EDOs: 5, 10, 15, 40be, 55be, 70bde, 85bcde<br /> | |||
Badness: 0.0246<br /> | |||
<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Blacksmith-Farrier"></a><!-- ws:end:WikiTextHeadingRule:6 -->Farrier</h2> | |||
Commas: 28/27, 49/48, 77/75<br /> | |||
<br /> | |||
POTE generator: ~5/4 = 398.070<br /> | |||
<br /> | |||
Map: [&lt;5 8 0 14 -6|, &lt;0 0 1 0 2|]<br /> | |||
EDOs: 5e, 15<br /> | |||
Badness: 0.0292<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:47:&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:47 --><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Blacksmith-Blackwood"></a><!-- ws:end:WikiTextHeadingRule:8 -->Blackwood</h2> | ||
<em>Blackwood (5-limit)</em><br /> | <em>Blackwood (5-limit)</em><br /> | ||
<br /> | <br /> | ||
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Badness: 0.0638<br /> | Badness: 0.0638<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Superpyth"></a><!-- ws:end:WikiTextHeadingRule:10 -->Superpyth</h1> | ||
<a class="wiki_link" href="/Superpyth">Main article</a><br /> | <a class="wiki_link" href="/Superpyth">Main article</a><br /> | ||
Commas: 64/63, 245/243<br /> | Commas: 64/63, 245/243<br /> | ||
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Badness: 0.0323<br /> | Badness: 0.0323<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Superpyth-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> | ||
Commas: 64/63, 100/99, 245/243<br /> | Commas: 64/63, 100/99, 245/243<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0250<br /> | Badness: 0.0250<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Superpyth-Suprapyth"></a><!-- ws:end:WikiTextHeadingRule:14 -->Suprapyth</h2> | ||
Commas: 55/54, 64/63, 99/98<br /> | Commas: 55/54, 64/63, 99/98<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0328<br /> | Badness: 0.0328<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Beatles"></a><!-- ws:end:WikiTextHeadingRule:16 -->Beatles</h1> | ||
Commas: 64/63, 686/675<br /> | Commas: 64/63, 686/675<br /> | ||
<br /> | <br /> | ||
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Music: <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3" rel="nofollow">Beatles Improv</a> by Herman Miller<br /> | Music: <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3" rel="nofollow">Beatles Improv</a> by Herman Miller<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Schism"></a><!-- ws:end:WikiTextHeadingRule:18 -->Schism</h1> | ||
Commas: 64/63, 360/343<br /> | Commas: 64/63, 360/343<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0566<br /> | Badness: 0.0566<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Passion"></a><!-- ws:end:WikiTextHeadingRule:20 -->Passion</h1> | ||
Commas: 64/63, 3125/3087<br /> | Commas: 64/63, 3125/3087<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:22 -->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:24:&lt;h2&gt; --><h2 id="toc12"><a name="Quasisuper-Quasisupra"></a><!-- ws:end:WikiTextHeadingRule:24 -->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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Progress"></a><!-- ws:end:WikiTextHeadingRule:26 -->Progress</h1> | ||
Commas: 64/63, 392/375<br /> | Commas: 64/63, 392/375<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0664<br /> | Badness: 0.0664<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Progress-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h2> | ||
Commas: 56/55, 64/63, 77/75<br /> | Commas: 56/55, 64/63, 77/75<br /> | ||
<br /> | <br /> | ||