Hemimean clan: Difference between revisions
Wikispaces>genewardsmith **Imported revision 328067106 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 328107000 - 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>2012-05-01 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-01 14:57:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>328107000</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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=Semisept= | =Semisept= | ||
Comma: 782757789696/762939453125 | |||
POTE generator: ~192/125 = 735.146 | |||
Map: [<1 12 6|, <0 -17 -6|] | |||
EDOs: 18, 31, 80, 111 | |||
Badness: 0.6306 | |||
==7-limit== | |||
Commas: 3136/3126, 1728/1715 | Commas: 3136/3126, 1728/1715 | ||
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EDOs: 43, 87, 130, 217, 347e, 564e | EDOs: 43, 87, 130, 217, 347e, 564e | ||
Badness: 0.0195 | Badness: 0.0195 | ||
</pre></div> | </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>Hemimean 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>Hemimean clan</title></head><body><!-- ws:start:WikiTextTocRule:42:&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:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 1em;"><a href="#Misty">Misty</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Misty-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 2em;"><a href="#Misty-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 1em;"><a href="#Mystic">Mystic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 2em;"><a href="#Mystic-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 2em;"><a href="#Mystic-19-limit">19-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 1em;"><a href="#Semisept">Semisept</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Semisept-7-limit">7-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 2em;"><a href="#Semisept-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 3em;"><a href="#Semisept-11-limit-Semishly">Semishly</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 2em;"><a href="#Semisept-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 2em;"><a href="#Semisept-17-limit">17-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 2em;"><a href="#Semisept-19-limit">19-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 2em;"><a href="#Semisept-23-limit">23-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 1em;"><a href="#Sengagen">Sengagen</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 1em;"><a href="#Subpental">Subpental</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 2em;"><a href="#Subpental-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 2em;"><a href="#Subpental-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><div style="margin-left: 1em;"><a href="#Arch">Arch</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><div style="margin-left: 2em;"><a href="#Arch-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><div style="margin-left: 2em;"><a href="#Arch-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --></div> | ||
<!-- ws:end:WikiTextTocRule:64 --><br /> | |||
The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwuerschmidt, parakleismic, hemithirds, clyde, hemischismic, passion, hexe and sycamore considered elsewhere.<br /> | The hemimean clan, tempering out the no-threes hemimean comma 3136/3125, contains the temperaments misty and semisept, considered below, as well as meantone, hemiwuerschmidt, parakleismic, hemithirds, clyde, hemischismic, passion, hexe and sycamore considered elsewhere.<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Semisept"></a><!-- ws:end:WikiTextHeadingRule:12 -->Semisept</h1> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Semisept"></a><!-- ws:end:WikiTextHeadingRule:12 -->Semisept</h1> | ||
Comma: 782757789696/762939453125<br /> | |||
<br /> | |||
POTE generator: ~192/125 = 735.146<br /> | |||
<br /> | |||
Map: [&lt;1 12 6|, &lt;0 -17 -6|]<br /> | |||
EDOs: 18, 31, 80, 111<br /> | |||
Badness: 0.6306<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Semisept-7-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->7-limit</h2> | |||
Commas: 3136/3126, 1728/1715<br /> | Commas: 3136/3126, 1728/1715<br /> | ||
<br /> | <br /> | ||
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EDOs: <a class="wiki_link" href="/18edo">18</a>, 31, <a class="wiki_link" href="/80edo">80</a>, 111<br /> | EDOs: <a class="wiki_link" href="/18edo">18</a>, 31, <a class="wiki_link" href="/80edo">80</a>, 111<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Semisept-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> | ||
Commas: 176/175, 540/539, 1331/1323<br /> | Commas: 176/175, 540/539, 1331/1323<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0225<br /> | Badness: 0.0225<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Semisept-11-limit-Semishly"></a><!-- ws:end:WikiTextHeadingRule:18 -->Semishly</h3> | ||
Commas: 144/143, 176/175, 196/195, 275/273<br /> | Commas: 144/143, 176/175, 196/195, 275/273<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0284<br /> | Badness: 0.0284<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Semisept-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> | ||
Commas: 176/175, 351/350, 540/539, 1375/1372<br /> | Commas: 176/175, 351/350, 540/539, 1375/1372<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0252<br /> | Badness: 0.0252<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Semisept-17-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->17-limit</h2> | ||
Commas: 176/175, 256/255, 351/350, 640/637, 715/714<br /> | Commas: 176/175, 256/255, 351/350, 640/637, 715/714<br /> | ||
<br /> | <br /> | ||
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EDOs: 31, 80, 111<br /> | EDOs: 31, 80, 111<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Semisept-19-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->19-limit</h2> | ||
Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323<br /> | Commas: 176/175, 286/285, 351/350, 476/475, 540/539, 1331/1323<br /> | ||
<br /> | <br /> | ||
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EDOs: 31, 80, 111<br /> | EDOs: 31, 80, 111<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Semisept-23-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->23-limit</h2> | ||
Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459<br /> | Commas: 176/175, 253/252, 286/285, 345/343, 351/350, 391/390, 460/459<br /> | ||
<br /> | <br /> | ||
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EDOs: 31, 80, 111, 191cdh, 302cdgh<br /> | EDOs: 31, 80, 111, 191cdh, 302cdgh<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Sengagen"></a><!-- ws:end:WikiTextHeadingRule:28 -->Sengagen</h1> | ||
Commas: 3136/3125, 420175/419904<br /> | Commas: 3136/3125, 420175/419904<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0580<br /> | Badness: 0.0580<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Subpental"></a><!-- ws:end:WikiTextHeadingRule:30 -->Subpental</h1> | ||
Commas: 3136/3125, 19683/19600<br /> | Commas: 3136/3125, 19683/19600<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0543<br /> | Badness: 0.0543<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Subpental-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | ||
Commas: 540/539, 3136/3125, 8019/8000<br /> | Commas: 540/539, 3136/3125, 8019/8000<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0453<br /> | Badness: 0.0453<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Subpental-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | ||
Commas: 351/350, 540/539, 676/675, 3136/3125<br /> | Commas: 351/350, 540/539, 676/675, 3136/3125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0239<br /> | Badness: 0.0239<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Arch"></a><!-- ws:end:WikiTextHeadingRule:36 -->Arch</h1> | ||
Commas: 3136/3125, 5250987/5242880<br /> | Commas: 3136/3125, 5250987/5242880<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0943<br /> | Badness: 0.0943<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Arch-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> | ||
Commas: 441/440, 3136/3125, 4000/3993<br /> | Commas: 441/440, 3136/3125, 4000/3993<br /> | ||
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Badness: 0.0365<br /> | Badness: 0.0365<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Arch-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->13-limit</h2> | ||
Commasa: 364/363, 441/440, 676/675, 3136/3125<br /> | Commasa: 364/363, 441/440, 676/675, 3136/3125<br /> | ||
<br /> | <br /> | ||