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