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Magic family: Difference between revisions

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Wikispaces>Gedankenwelt
**Imported revision 500990560 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 519350924 - 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:Gedankenwelt|Gedankenwelt]] and made on <tt>2014-04-07 07:50:58 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-08-22 18:24:36 UTC</tt>.<br>
: The original revision id was <tt>500990560</tt>.<br>
: The original revision id was <tt>519350924</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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[&lt;1 0 0|, &lt;0 1 0|, &lt;2 1/5 0|]
[&lt;1 0 0|, &lt;0 1 0|, &lt;2 1/5 0|]
[[Eigenmonzo|Eigenmonzos]]: 2, 3
[[Eigenmonzo|Eigenmonzos]]: 2, 3
valid range: [360.000, 400.000] (10 to 3)
nice range: [378.910, 386.314]
strict range: [378.910, 386.314]
POTE generator: ~5/4 = 380.058


Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2√13)/9; approximately 380.3175 [[Cent|cents]].
Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2√13)/9; approximately 380.3175 [[Cent|cents]].
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[|1 0 0 0&gt;, |0 1 0 0&gt;, |2 1/5 0 0&gt;, |-1 12/5 0 0&gt;]
[|1 0 0 0&gt;, |0 1 0 0&gt;, |2 1/5 0 0&gt;, |-1 12/5 0 0&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 3
[[Eigenmonzo|Eigenmonzos]]: 2, 3
valid range: [378.947, 381.818] (19 to 22)
nice range: [378.910, 386.314]
strict range: [378.947, 381.818]


[[POTE tuning|POTE generator]]: 380.352
[[POTE tuning|POTE generator]]: 380.352
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Commas: 225/224, 245/243, 100/99
Commas: 225/224, 245/243, 100/99
valid range: [378.947, 381.818] (19 to 22)
nice range: [378.910, 386.314]
strict range: [378.947, 381.818]


[[POTE tuning|POTE generator]]: 380.696
[[POTE tuning|POTE generator]]: 380.696
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==13-limit==  
==13-limit==  
Commas: 100/99, 105/104, 144/143, 196/195
Commas: 100/99, 105/104, 144/143, 196/195
valid range: [378.947, 381.818] (19 to 22f)
nice range: [378.617, 386.314]
strict range: [378.947, 381.818]


POTE generator: ~5/4 = 380.427
POTE generator: ~5/4 = 380.427
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===Sorcery===  
===Sorcery===  
Commas: 65/64, 78/77, 91/90, 100/99
Commas: 65/64, 78/77, 91/90, 100/99
valid range: 378.947 (19)
nice range: [359.472, 386.314]
strict range:  378.947


POTE generator: ~5/4 = 380.477
POTE generator: ~5/4 = 380.477
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[&amp;lt;1 0 0|, &amp;lt;0 1 0|, &amp;lt;2 1/5 0|]&lt;br /&gt;
[&amp;lt;1 0 0|, &amp;lt;0 1 0|, &amp;lt;2 1/5 0|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 3&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 3&lt;br /&gt;
&lt;br /&gt;
valid range: [360.000, 400.000] (10 to 3)&lt;br /&gt;
nice range: [378.910, 386.314]&lt;br /&gt;
strict range: [378.910, 386.314]&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 380.058&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2√13)/9; approximately 380.3175 &lt;a class="wiki_link" href="/Cent"&gt;cents&lt;/a&gt;.&lt;br /&gt;
Algebraic generator: Terzbirat, the positive root of 9x^2-8x-4 = (4+2√13)/9; approximately 380.3175 &lt;a class="wiki_link" href="/Cent"&gt;cents&lt;/a&gt;.&lt;br /&gt;
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[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |2 1/5 0 0&amp;gt;, |-1 12/5 0 0&amp;gt;]&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |2 1/5 0 0&amp;gt;, |-1 12/5 0 0&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 3&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 3&lt;br /&gt;
&lt;br /&gt;
valid range: [378.947, 381.818] (19 to 22)&lt;br /&gt;
nice range: [378.910, 386.314]&lt;br /&gt;
strict range: [378.947, 381.818]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 380.352&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 380.352&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Commas: 225/224, 245/243, 100/99&lt;br /&gt;
Commas: 225/224, 245/243, 100/99&lt;br /&gt;
&lt;br /&gt;
valid range: [378.947, 381.818] (19 to 22)&lt;br /&gt;
nice range: [378.910, 386.314]&lt;br /&gt;
strict range: [378.947, 381.818]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 380.696&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 380.696&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Magic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Magic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
  Commas: 100/99, 105/104, 144/143, 196/195&lt;br /&gt;
  Commas: 100/99, 105/104, 144/143, 196/195&lt;br /&gt;
&lt;br /&gt;
valid range: [378.947, 381.818] (19 to 22f)&lt;br /&gt;
nice range: [378.617, 386.314]&lt;br /&gt;
strict range: [378.947, 381.818]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 380.427&lt;br /&gt;
POTE generator: ~5/4 = 380.427&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Magic-13-limit-Sorcery"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Sorcery&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Magic-13-limit-Sorcery"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Sorcery&lt;/h3&gt;
  Commas: 65/64, 78/77, 91/90, 100/99&lt;br /&gt;
  Commas: 65/64, 78/77, 91/90, 100/99&lt;br /&gt;
&lt;br /&gt;
valid range: 378.947 (19)&lt;br /&gt;
nice range: [359.472, 386.314]&lt;br /&gt;
strict range:  378.947&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 380.477&lt;br /&gt;
POTE generator: ~5/4 = 380.477&lt;br /&gt;
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