Optimal patent val: Difference between revisions
Wikispaces>genewardsmith **Imported revision 205333798 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 205351134 - 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>2011-02- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-27 02:36:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>205351134</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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==13-limit rank two== | ==13-limit rank two== | ||
Name: Optimal patent val: Val name: 1000*badness | |||
[[Quartonic temperaments|Progression]]: [[9edo]] [<1 1 2 2 3 3|, <0 5 3 7 4 6|] 18.158 | [[Quartonic temperaments|Progression]]: [[9edo]] [<1 1 2 2 3 3|, <0 5 3 7 4 6|] 18.158 | ||
[[Marvel temperaments|Negric]]: [[9edo]] 1&9 20.205 | [[Marvel temperaments|Negric]]: [[9edo]] 1&9 20.205 | ||
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[[Ragismic microtemperaments|Hemiennealimmal]]: [[270edo]] 72&198 12.505 | [[Ragismic microtemperaments|Hemiennealimmal]]: [[270edo]] 72&198 12.505 | ||
[[Breedsmic temperaments|Decoid]]: [[940edo]] 130&270 13.475 | [[Breedsmic temperaments|Decoid]]: [[940edo]] 130&270 13.475 | ||
[[Ragismic microtemperaments|Abigail]]: [[1258edo]] 46&178 8.856</pre></div> | [[Ragismic microtemperaments|Abigail]]: [[1258edo]] 46&178 8.856 | ||
==13-limit rank three== | |||
Name: Optimal patent val: Val name: 10^5 * badness | |||
[[Marvel family|Deecee]]: [[72edo]] 9&22&41 92.048 | |||
[[Marvel family|Tripod]]: [[91edo]] 9&10&31 74.546 | |||
[[Marvel family|Marvell]]: [[166edo]] 9&31&63 86.160 | |||
</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>Optimal patent val</title></head><body>Given any collection of p-limit commas, there is a finite list of p-limit <a class="wiki_link" href="/Patent%20val">patent vals</a> tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">TE error</a>; this is the <em>optimal (TE) patent val</em> for the temperament defined by the commas. Note that other definitions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.<br /> | <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>Optimal patent val</title></head><body>Given any collection of p-limit commas, there is a finite list of p-limit <a class="wiki_link" href="/Patent%20val">patent vals</a> tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">TE error</a>; this is the <em>optimal (TE) patent val</em> for the temperament defined by the commas. Note that other definitions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-13-limit rank two"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit rank two</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-13-limit rank two"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit rank two</h2> | ||
<a class="wiki_link" href="/Quartonic%20temperaments">Progression</a>: <a class="wiki_link" href="/9edo">9edo</a> [&lt;1 1 2 2 3 3|, &lt;0 5 3 7 4 6|] 18.158<br /> | Name: Optimal patent val: Val name: 1000*badness<br /> | ||
<a class="wiki_link" href="/Quartonic%20temperaments">Progression</a>: <a class="wiki_link" href="/9edo">9edo</a> [&lt;1 1 2 2 3 3|, &lt;0 5 3 7 4 6|] 18.158<br /> | |||
<a class="wiki_link" href="/Marvel%20temperaments">Negric</a>: <a class="wiki_link" href="/9edo">9edo</a> 1&amp;9 20.205<br /> | <a class="wiki_link" href="/Marvel%20temperaments">Negric</a>: <a class="wiki_link" href="/9edo">9edo</a> 1&amp;9 20.205<br /> | ||
<a class="wiki_link" href="/Trienstonic%20clan">Opossum</a>: <a class="wiki_link" href="/15edo">15edo</a> [&lt;1 2 3 4 4 4|, &lt;0 -3 -5 -9 -4 -2|] 19.389<br /> | <a class="wiki_link" href="/Trienstonic%20clan">Opossum</a>: <a class="wiki_link" href="/15edo">15edo</a> [&lt;1 2 3 4 4 4|, &lt;0 -3 -5 -9 -4 -2|] 19.389<br /> | ||
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<a class="wiki_link" href="/Ragismic%20microtemperaments">Hemiennealimmal</a>: <a class="wiki_link" href="/270edo">270edo</a> 72&amp;198 12.505<br /> | <a class="wiki_link" href="/Ragismic%20microtemperaments">Hemiennealimmal</a>: <a class="wiki_link" href="/270edo">270edo</a> 72&amp;198 12.505<br /> | ||
<a class="wiki_link" href="/Breedsmic%20temperaments">Decoid</a>: <a class="wiki_link" href="/940edo">940edo</a> 130&amp;270 13.475<br /> | <a class="wiki_link" href="/Breedsmic%20temperaments">Decoid</a>: <a class="wiki_link" href="/940edo">940edo</a> 130&amp;270 13.475<br /> | ||
<a class="wiki_link" href="/Ragismic%20microtemperaments">Abigail</a>: <a class="wiki_link" href="/1258edo">1258edo</a> 46&amp;178 8.856</body></html></pre></div> | <a class="wiki_link" href="/Ragismic%20microtemperaments">Abigail</a>: <a class="wiki_link" href="/1258edo">1258edo</a> 46&amp;178 8.856<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-13-limit rank three"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit rank three</h2> | |||
Name: Optimal patent val: Val name: 10^5 * badness<br /> | |||
<a class="wiki_link" href="/Marvel%20family">Deecee</a>: <a class="wiki_link" href="/72edo">72edo</a> 9&amp;22&amp;41 92.048<br /> | |||
<a class="wiki_link" href="/Marvel%20family">Tripod</a>: <a class="wiki_link" href="/91edo">91edo</a> 9&amp;10&amp;31 74.546<br /> | |||
<a class="wiki_link" href="/Marvel%20family">Marvell</a>: <a class="wiki_link" href="/166edo">166edo</a> 9&amp;31&amp;63 86.160</body></html></pre></div> | |||