Schismatic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 209781414 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 210919316 - 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>2011-03- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-15 23:43:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>210919316</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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[[edo|Edos]]: [[41edo|41]], [[77edo|77]], [[118edo|118]], [[159edo|159]], [[200edo|200]] | [[edo|Edos]]: [[41edo|41]], [[77edo|77]], [[118edo|118]], [[159edo|159]], [[200edo|200]] | ||
Badness: 0.0266 | Badness: 0.0266 | ||
==13-limit== | |||
Commas: 196/195, 352/351, 385/384, 729/728 | |||
POTE generator: ~8/7 = 233.890 | |||
Map: [<1 1 7 3 -2 0|, <0 3 -24 -1 28 19|] | |||
EDOs: 41, 77, 118 | |||
Badness: 0.0284 | |||
=Pontiac= | =Pontiac= | ||
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The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. Adding |25 -14 0 -1&gt; gives garibaldi, |-44 26 0 1&gt; grackle, |6 -2 0 -1&gt; schism and |-59 39 0 -1&gt; pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2&gt; and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3&gt;, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3&gt; with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4&gt; and slices the fifth in four.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. Adding |25 -14 0 -1&gt; gives garibaldi, |-44 26 0 1&gt; grackle, |6 -2 0 -1&gt; schism and |-59 39 0 -1&gt; pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2&gt; and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3&gt;, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3&gt; with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4&gt; and slices the fifth in four.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:28:&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:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Guiron">Guiron</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Pontiac">Pontiac</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Grackle">Grackle</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Bischismic">Bischismic</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Term">Term</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Sesquiquartififths">Sesquiquartififths</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:2 -->Garibaldi</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:2 -->Garibaldi</h1> | ||
Commas: 225/224, 3125/3087<br /> | Commas: 225/224, 3125/3087<br /> | ||
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Badness: 0.0266<br /> | Badness: 0.0266<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Guiron-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h2> | ||
Commas: 196/195, 352/351, 385/384, 729/728<br /> | |||
<br /> | |||
POTE generator: ~8/7 = 233.890<br /> | |||
<br /> | |||
Map: [&lt;1 1 7 3 -2 0|, &lt;0 3 -24 -1 28 19|]<br /> | |||
EDOs: 41, 77, 118<br /> | |||
Badness: 0.0284<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Pontiac"></a><!-- ws:end:WikiTextHeadingRule:18 -->Pontiac</h1> | |||
Commas: 32805/32768, 4375/4374<br /> | Commas: 32805/32768, 4375/4374<br /> | ||
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Badness: 0.0141<br /> | Badness: 0.0141<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Grackle"></a><!-- ws:end:WikiTextHeadingRule:20 -->Grackle</h1> | ||
Commas: 126/125, 32805/32768<br /> | Commas: 126/125, 32805/32768<br /> | ||
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Badness: 0.070<br /> | Badness: 0.070<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Bischismic"></a><!-- ws:end:WikiTextHeadingRule:22 -->Bischismic</h1> | ||
Commas: 3136/3125, 32805/32768<br /> | Commas: 3136/3125, 32805/32768<br /> | ||
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Badness: 0.0547<br /> | Badness: 0.0547<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Term"></a><!-- ws:end:WikiTextHeadingRule:24 -->Term</h1> | ||
Commas: 32805/32768, 250047/250000<br /> | Commas: 32805/32768, 250047/250000<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0200<br /> | Badness: 0.0200<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Sesquiquartififths"></a><!-- ws:end:WikiTextHeadingRule:26 -->Sesquiquartififths</h1> | ||
Commas: 2401/2400, 32805/32768<br /> | Commas: 2401/2400, 32805/32768<br /> | ||
<br /> | <br /> | ||