Magic family: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 337655130 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 337663318 - 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>2012-05-20 19:03:39 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-20 19:39:58 UTC</tt>.<br>
: The original revision id was <tt>337655130</tt>.<br>
: The original revision id was <tt>337663318</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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EDOs: 19, 60e
EDOs: 19, 60e
Badness: 0.0393
Badness: 0.0393
=Hocus=
Commas: 225/224, 243/242, 245/242
POTE generator: ~14/11 = 409.910
Map: [&lt;1 5 3 11 12|, &lt;0 -10 -2 -24 -25|]
EDOs: 38d, 41, 120cd, 161cd, 202cd
Badness: 0.0385
==13-limit==
Commas: 105/104, 196/195, 243/242, 245/242
POTE generator: ~14/11 = 410.004
Map: [&lt;1 5 3 11 12 16|, &lt;0 -10 -2 -24 -25 -36|]
EDOs: 41, 79d, 120cd
Badness: 0.0303


=Divination=
=Divination=
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EDOs: 19, 44de, 63de, 82de
EDOs: 19, 44de, 63de, 82de
Badness: 0.0416
Badness: 0.0416
=Hocum=
Commas: 3125/3072, 4000/3969
POTE generator: ~63/50 = 400.108
Map: [&lt;1 5 3 -3|, &lt;0 -10 -2 17|]
Wedgie: &lt;&lt;10 2 -17 -20 -55 -45||
EDOs: 38, 41, 161c, 202c, 243c, 284c
Badness: 0.1071
=Hocus=
Commas: 225/224, 243/242, 245/242
POTE generator: ~14/11 = 409.910
Map: [&lt;1 5 3 11 12|, &lt;0 -10 -2 -24 -25|]
EDOs: 38d, 41, 120cd, 161cd, 202cd
Badness: 0.0385
==13-limit==
Commas: 105/104, 196/195, 243/242, 245/242
POTE generator: ~14/11 = 410.004
Map: [&lt;1 5 3 11 12 16|, &lt;0 -10 -2 -24 -25 -36|]
EDOs: 41, 79d, 120cd
Badness: 0.0303


=Trismegistus=
=Trismegistus=
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EDOs: 41, 117c, 158cd, 199cdef
EDOs: 41, 117c, 158cd, 199cdef
Badness: 0.0440
Badness: 0.0440


</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Magic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:64:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Five limit magic"&gt;Five limit magic&lt;/a&gt;&lt;/div&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Magic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:66:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Five limit magic"&gt;Five limit magic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Five limit magic-Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Five limit magic-Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Magic"&gt;Magic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Magic"&gt;Magic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Magic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Magic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Magic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Magic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Magic-13-limit-Sorcery"&gt;Sorcery&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Magic-13-limit-Sorcery"&gt;Sorcery&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Magic-13-limit-Necromancy"&gt;Necromancy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Magic-13-limit-Necromancy"&gt;Necromancy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Magic-Telepathy"&gt;Telepathy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Magic-Telepathy"&gt;Telepathy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Magic-Telepathy-13-limit telepathy"&gt;13-limit telepathy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Magic-Telepathy-13-limit telepathy"&gt;13-limit telepathy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Magic-Horcrux"&gt;Horcrux&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Magic-Horcrux"&gt;Horcrux&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hocus"&gt;Hocus&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hocus-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Divination"&gt;Divination&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Divination"&gt;Divination&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Divination-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Divination-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Spell-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Spell-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Spell-Cantrip"&gt;Cantrip&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Spell-Cantrip"&gt;Cantrip&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Trismegistus"&gt;Trismegistus&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hocum"&gt;Hocum&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Trismegistus-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hocus"&gt;Hocus&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Trismegistus-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hocus-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quadrimage"&gt;Quadrimage&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Trismegistus"&gt;Trismegistus&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quadrimage-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Trismegistus-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quadrimage-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Trismegistus-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quadrimage"&gt;Quadrimage&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quadrimage-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quadrimage-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Five limit magic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Five limit magic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Five limit magic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Five limit magic&lt;/h1&gt;
The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&amp;gt;, and flipping that yields &amp;lt;&amp;lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of sense sense and using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; or &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; is always possible.&lt;br /&gt;
The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&amp;gt;, and flipping that yields &amp;lt;&amp;lt;5 1 -10|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require five of these. In fact, (5/4)^5 = 3 * 3125/3072. 13/41 is a highly recommendable generator, though 19\60, the optimal patent val generator, also makes a lot of sense sense and using &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; or &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; is always possible.&lt;br /&gt;
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Badness: 0.0393&lt;br /&gt;
Badness: 0.0393&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Hocus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Hocus&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Divination"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Divination&lt;/h1&gt;
Commas: 225/224, 243/242, 245/242&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~14/11 = 409.910&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 3 11 12|, &amp;lt;0 -10 -2 -24 -25|]&lt;br /&gt;
EDOs: 38d, 41, 120cd, 161cd, 202cd&lt;br /&gt;
Badness: 0.0385&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Hocus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 196/195, 243/242, 245/242&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~14/11 = 410.004&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 3 11 12 16|, &amp;lt;0 -10 -2 -24 -25 -36|]&lt;br /&gt;
EDOs: 41, 79d, 120cd&lt;br /&gt;
Badness: 0.0303&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Divination"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Divination&lt;/h1&gt;
Commas: 121/120, 225/224, 245/243&lt;br /&gt;
Commas: 121/120, 225/224, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0359&lt;br /&gt;
Badness: 0.0359&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Divination-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Divination-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 121/120, 196/195, 245/243&lt;br /&gt;
Commas: 105/104, 121/120, 196/195, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0346&lt;br /&gt;
Badness: 0.0346&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Soothsaying"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Soothsaying&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Soothsaying"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Soothsaying&lt;/h1&gt;
Commas: 100/99, 225/224, 245/243, 1352/1331&lt;br /&gt;
Commas: 100/99, 225/224, 245/243, 1352/1331&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0554&lt;br /&gt;
Badness: 0.0554&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Witchcraft"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Witchcraft&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Witchcraft"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Witchcraft&lt;/h1&gt;
Commas: 225/224, 245/243, 441/440&lt;br /&gt;
Commas: 225/224, 245/243, 441/440&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 509: Line 501:
Badness: 0.0307&lt;br /&gt;
Badness: 0.0307&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Witchcraft-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Witchcraft-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 196/195, 245/243, 275/273&lt;br /&gt;
Commas: 105/104, 196/195, 245/243, 275/273&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 518: Line 510:
Badness: 0.0235&lt;br /&gt;
Badness: 0.0235&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Muggles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Muggles&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Muggles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Muggles&lt;/h1&gt;
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &amp;lt;&amp;lt;5 1 -7 -10 -25 -19||.&lt;br /&gt;
Aside from 3125/3072 and 525/512 muggles also tempers out 126/125 and 1323/1280. A good muggles tuning is &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, in which tuning it's the same thing as magic. Muggles works better for small scales than magic in the sense that 7 or 10 note MOS are reasonable choices. The muggles wedgie is &amp;lt;&amp;lt;5 1 -7 -10 -25 -19||.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 529: Line 521:
EDOs: 19, 73bcd, 92bcd&lt;br /&gt;
EDOs: 19, 73bcd, 92bcd&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Astrology"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Astrology&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Astrology"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Astrology&lt;/h1&gt;
Commas: 50/49, 3125/3072&lt;br /&gt;
Commas: 50/49, 3125/3072&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 539: Line 531:
Badness: 0.0827&lt;br /&gt;
Badness: 0.0827&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Astrology-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Astrology-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h2&gt;
Commas: 50/49, 121/120, 176/175&lt;br /&gt;
Commas: 50/49, 121/120, 176/175&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 548: Line 540:
Badness: 0.0392&lt;br /&gt;
Badness: 0.0392&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Astrology-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Astrology-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;13-limit&lt;/h2&gt;
Commas: 50/49, 65/64, 78/77, 121/120&lt;br /&gt;
Commas: 50/49, 65/64, 78/77, 121/120&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 557: Line 549:
Badness: 0.0344&lt;br /&gt;
Badness: 0.0344&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Astrology-Horoscope"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Horoscope&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Astrology-Horoscope"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Horoscope&lt;/h2&gt;
Commas: 50/49, 66/65, 105/104, 121/120&lt;br /&gt;
Commas: 50/49, 66/65, 105/104, 121/120&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 566: Line 558:
Badness: 0.0353&lt;br /&gt;
Badness: 0.0353&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Spell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Spell&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Spell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Spell&lt;/h1&gt;
Commas: 49/48, 3125/3072&lt;br /&gt;
Commas: 49/48, 3125/3072&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 576: Line 568:
Badness: 0.0810&lt;br /&gt;
Badness: 0.0810&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Spell-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Spell-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
Commas: 49/48, 56/55, 125/121&lt;br /&gt;
Commas: 49/48, 56/55, 125/121&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 585: Line 577:
Badness: 0.0598&lt;br /&gt;
Badness: 0.0598&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Spell-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Spell-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
Commas: 49/48, 56/55, 78/77, 125/121&lt;br /&gt;
Commas: 49/48, 56/55, 78/77, 125/121&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 594: Line 586:
Badness: 0.0456&lt;br /&gt;
Badness: 0.0456&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Spell-Cantrip"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Cantrip&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Spell-Cantrip"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Cantrip&lt;/h2&gt;
Commas: 49/48, 56/55, 91/90, 125/121&lt;br /&gt;
Commas: 49/48, 56/55, 91/90, 125/121&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 603: Line 595:
Badness: 0.0416&lt;br /&gt;
Badness: 0.0416&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Trismegistus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Trismegistus&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Hocum"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Hocum&lt;/h1&gt;
Commas: 3125/3072, 4000/3969&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~63/50 = 400.108&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 3 -3|, &amp;lt;0 -10 -2 17|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;10 2 -17 -20 -55 -45||&lt;br /&gt;
EDOs: 38, 41, 161c, 202c, 243c, 284c&lt;br /&gt;
Badness: 0.1071&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Hocus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Hocus&lt;/h1&gt;
Commas: 225/224, 243/242, 245/242&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~14/11 = 409.910&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 3 11 12|, &amp;lt;0 -10 -2 -24 -25|]&lt;br /&gt;
EDOs: 38d, 41, 120cd, 161cd, 202cd&lt;br /&gt;
Badness: 0.0385&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Hocus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 196/195, 243/242, 245/242&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~14/11 = 410.004&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 3 11 12 16|, &amp;lt;0 -10 -2 -24 -25 -36|]&lt;br /&gt;
EDOs: 41, 79d, 120cd&lt;br /&gt;
Badness: 0.0303&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Trismegistus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Trismegistus&lt;/h1&gt;
Commas: 3125/3072, 1029/1024&lt;br /&gt;
Commas: 3125/3072, 1029/1024&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 613: Line 633:
Badness: 0.0983&lt;br /&gt;
Badness: 0.0983&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Trismegistus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Trismegistus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;11-limit&lt;/h2&gt;
Commas: 385/384, 441/440, 625/616&lt;br /&gt;
Commas: 385/384, 441/440, 625/616&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 622: Line 642:
Badness: 0.0456&lt;br /&gt;
Badness: 0.0456&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Trismegistus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Trismegistus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 144/143, 275/273, 625/616&lt;br /&gt;
Commas: 105/104, 144/143, 275/273, 625/616&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 631: Line 651:
Badness: 0.0331&lt;br /&gt;
Badness: 0.0331&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Quadrimage"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Quadrimage&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Quadrimage"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Quadrimage&lt;/h1&gt;
Commas: 2401/2400, 3125/3072&lt;br /&gt;
Commas: 2401/2400, 3125/3072&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 641: Line 661:
Badness: 0.1274&lt;br /&gt;
Badness: 0.1274&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Quadrimage-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Quadrimage-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;11-limit&lt;/h2&gt;
Commas: 245/242, 385/384, 625/616&lt;br /&gt;
Commas: 245/242, 385/384, 625/616&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 650: Line 670:
Badness: 0.0616&lt;br /&gt;
Badness: 0.0616&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Quadrimage-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Quadrimage-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 144/143, 245/242, 625/616&lt;br /&gt;
Commas: 105/104, 144/143, 245/242, 625/616&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;