Magic family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 325715712 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 325801172 - 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>2012-04-26 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-26 20:27:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>325801172</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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Map: [<2 0 4 5 5 3|, <0 5 1 1 3 7|] | Map: [<2 0 4 5 5 3|, <0 5 1 1 3 7|] | ||
EDOs: 16, 22f, 38 | EDOs: 16, 22f, 38 | ||
Badness: 0.0353</pre></div> | Badness: 0.0353 | ||
=Spell= | |||
Commas: 49/48, 3125/3072 | |||
POTE generator: ~28/25 = 189.927 | |||
Map: [<1 0 2 2|, <0 10 2 5|] | |||
Wedgie: <<10 2 5 -20 -20 6|| | |||
EDOs: 6, 19, 82d | |||
Badness: 0.0810 | |||
==11-limit== | |||
Commas: 49/48, 56/55, 125/121 | |||
POTE generator: ~11/10 = 190.285 | |||
Map: [<1 0 2 2 3|, <0 10 2 5 3|] | |||
EDOs: 6, 19, 44de, 63de, 82de | |||
Badness: 0.0598 | |||
==13-limit== | |||
Commas: 49/48, 56/55, 78/77, 125/121 | |||
POTE generator: ~11/10 = 189.928 | |||
Map: [<1 0 2 2 3 4|, <0 10 2 5 3 -2|] | |||
EDOs: 6, 19, 82def | |||
Badness: 0.0456 | |||
==Cantrip== | |||
Commas: 49/48, 56/55, 91/90, 125/121 | |||
POTE generator: ~11/10 = 190.360 | |||
Map: [<1 0 2 2 3 1|, <0 10 2 5 3 17|] | |||
EDOs: 19, 44de, 63de, 82de | |||
Badness: 0.0416 | |||
</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>Magic family</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>Magic family</title></head><body><!-- ws:start:WikiTextTocRule:52:&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:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 1em;"><a href="#Five limit magic">Five limit magic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 2em;"><a href="#Five limit magic-Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 1em;"><a href="#Magic">Magic</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 2em;"><a href="#Magic-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 2em;"><a href="#Magic-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 3em;"><a href="#Magic-13-limit-Sorcery">Sorcery</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 3em;"><a href="#Magic-13-limit-Necromancy">Necromancy</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 2em;"><a href="#Magic-Telepathy">Telepathy</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><div style="margin-left: 3em;"><a href="#Magic-Telepathy-13-limit telepathy">13-limit telepathy</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><div style="margin-left: 2em;"><a href="#Magic-Charisma">Charisma</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><div style="margin-left: 1em;"><a href="#Hocus">Hocus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><div style="margin-left: 2em;"><a href="#Hocus-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><div style="margin-left: 1em;"><a href="#Divination">Divination</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><div style="margin-left: 2em;"><a href="#Divination-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><div style="margin-left: 1em;"><a href="#Soothsaying">Soothsaying</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><div style="margin-left: 1em;"><a href="#Witchcraft">Witchcraft</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><div style="margin-left: 2em;"><a href="#Witchcraft-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><div style="margin-left: 1em;"><a href="#Muggles">Muggles</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><div style="margin-left: 1em;"><a href="#Astrology">Astrology</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><div style="margin-left: 2em;"><a href="#Astrology-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><div style="margin-left: 2em;"><a href="#Astrology-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><div style="margin-left: 2em;"><a href="#Astrology-Horoscope">Horoscope</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><div style="margin-left: 1em;"><a href="#Spell">Spell</a></div> | ||
< | <!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><div style="margin-left: 2em;"><a href="#Spell-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 2em;"><a href="#Spell-13-limit">13-limit</a></div> | |||
<!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><div style="margin-left: 2em;"><a href="#Spell-Cantrip">Cantrip</a></div> | |||
<!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --></div> | |||
<!-- ws:end:WikiTextTocRule:79 --><br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit magic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit magic</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Five limit magic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Five limit magic</h1> | ||
The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&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 <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> | The 5-limit parent comma for the magic family is 3125/3072, the small diesis or magic comma. Its monzo is |-10 -1 5&gt;, and flipping that yields &lt;&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 <a class="wiki_link" href="/19edo">19edo</a> or <a class="wiki_link" href="/22edo">22edo</a> is always possible.<br /> | ||
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Map: [&lt;2 0 4 5 5 3|, &lt;0 5 1 1 3 7|]<br /> | Map: [&lt;2 0 4 5 5 3|, &lt;0 5 1 1 3 7|]<br /> | ||
EDOs: 16, 22f, 38<br /> | EDOs: 16, 22f, 38<br /> | ||
Badness: 0.0353</body></html></pre></div> | Badness: 0.0353<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="Spell"></a><!-- ws:end:WikiTextHeadingRule:44 -->Spell</h1> | |||
Commas: 49/48, 3125/3072<br /> | |||
<br /> | |||
POTE generator: ~28/25 = 189.927<br /> | |||
<br /> | |||
Map: [&lt;1 0 2 2|, &lt;0 10 2 5|]<br /> | |||
Wedgie: &lt;&lt;10 2 5 -20 -20 6||<br /> | |||
EDOs: 6, 19, 82d<br /> | |||
Badness: 0.0810<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Spell-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->11-limit</h2> | |||
Commas: 49/48, 56/55, 125/121<br /> | |||
<br /> | |||
POTE generator: ~11/10 = 190.285<br /> | |||
<br /> | |||
Map: [&lt;1 0 2 2 3|, &lt;0 10 2 5 3|]<br /> | |||
EDOs: 6, 19, 44de, 63de, 82de<br /> | |||
Badness: 0.0598<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Spell-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> | |||
Commas: 49/48, 56/55, 78/77, 125/121<br /> | |||
<br /> | |||
POTE generator: ~11/10 = 189.928<br /> | |||
<br /> | |||
Map: [&lt;1 0 2 2 3 4|, &lt;0 10 2 5 3 -2|]<br /> | |||
EDOs: 6, 19, 82def<br /> | |||
Badness: 0.0456<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Spell-Cantrip"></a><!-- ws:end:WikiTextHeadingRule:50 -->Cantrip</h2> | |||
Commas: 49/48, 56/55, 91/90, 125/121<br /> | |||
<br /> | |||
POTE generator: ~11/10 = 190.360<br /> | |||
<br /> | |||
Map: [&lt;1 0 2 2 3 1|, &lt;0 10 2 5 3 17|]<br /> | |||
EDOs: 19, 44de, 63de, 82de<br /> | |||
Badness: 0.0416</body></html></pre></div> | |||