Optimal patent val: Difference between revisions
Wikispaces>genewardsmith **Imported revision 204556432 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 204561394 - 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>2011-02-23 23: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-23 23:46:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>204561394</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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[[Tetracot family|Octacot]]: [[41edo]] [<1 1 1 2 2 4|, <0 8 18 11 20 -4|] 23.276 | [[Tetracot family|Octacot]]: [[41edo]] [<1 1 1 2 2 4|, <0 8 18 11 20 -4|] 23.276 | ||
[[Starling temperaments|Sensi]]: [[46edo]] 19&27 25.474 | [[Starling temperaments|Sensi]]: [[46edo]] 19&27 25.474 | ||
[[Gamelismic clan|Manna]]: [[72edo]] 41&72 17.012 | |||
[[Gamelismic clan|Benediction]]: [[103edo]] 31&72 15.715 | [[Gamelismic clan|Benediction]]: [[103edo]] 31&72 15.715 | ||
[[ | [[Ragismic microtemperaments|Octoid]]: [[224edo]] 72&224 15.274 | ||
[[Ragismic microtemperaments|Hemiennealimmal]]: [[270edo]] 72&198 12.505 | |||
[[Ragismic microtemperaments|Abigail]]: [[1258edo]] 46&178 8.856</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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<a class="wiki_link" href="/Tetracot%20family">Octacot</a>: <a class="wiki_link" href="/41edo">41edo</a> [&lt;1 1 1 2 2 4|, &lt;0 8 18 11 20 -4|] 23.276<br /> | <a class="wiki_link" href="/Tetracot%20family">Octacot</a>: <a class="wiki_link" href="/41edo">41edo</a> [&lt;1 1 1 2 2 4|, &lt;0 8 18 11 20 -4|] 23.276<br /> | ||
<a class="wiki_link" href="/Starling%20temperaments">Sensi</a>: <a class="wiki_link" href="/46edo">46edo</a> 19&amp;27 25.474<br /> | <a class="wiki_link" href="/Starling%20temperaments">Sensi</a>: <a class="wiki_link" href="/46edo">46edo</a> 19&amp;27 25.474<br /> | ||
<a class="wiki_link" href="/Gamelismic%20clan">Manna</a>: <a class="wiki_link" href="/72edo">72edo</a> 41&amp;72 17.012<br /> | |||
<a class="wiki_link" href="/Gamelismic%20clan">Benediction</a>: <a class="wiki_link" href="/103edo">103edo</a> 31&amp;72 15.715<br /> | <a class="wiki_link" href="/Gamelismic%20clan">Benediction</a>: <a class="wiki_link" href="/103edo">103edo</a> 31&amp;72 15.715<br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/Ragismic%20microtemperaments">Octoid</a>: <a class="wiki_link" href="/224edo">224edo</a> 72&amp;224 15.274<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="/Ragismic%20microtemperaments">Abigail</a>: <a class="wiki_link" href="/1258edo">1258edo</a> 46&amp;178 8.856</body></html></pre></div> | |||