Optimal patent val: Difference between revisions
Wikispaces>genewardsmith **Imported revision 205393376 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 205449966 - 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>2011-02-27 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-27 16:22:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>205449966</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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[[Starling family|Bluebird]]: [[58edo]] 12&15&31 91.548 | [[Starling family|Bluebird]]: [[58edo]] 12&15&31 91.548 | ||
[[Starling family|Aplonis]]: [[58edo]] 19&31&58 82.078 | [[Starling family|Aplonis]]: [[58edo]] 19&31&58 82.078 | ||
[[Breed family|Jofur]]: [[58edo]] 10&31&58 74.932 | |||
[[Marvel family|Deecee]]: [[72edo]] 9&22&41 92.048 | [[Marvel family|Deecee]]: [[72edo]] 9&22&41 92.048 | ||
[[Marvel family|Tripod]]: [[91edo]] 9&10&31 74.546 | [[Marvel family|Tripod]]: [[91edo]] 9&10&31 74.546 | ||
| Line 322: | Line 323: | ||
[[Marvel family|Marvell]]: [[166edo]] 9&31&63 86.160 | [[Marvel family|Marvell]]: [[166edo]] 9&31&63 86.160 | ||
[[Gamelismic family|Portentous]]: [[190edo]] 15&31&56 66.119 | [[Gamelismic family|Portentous]]: [[190edo]] 15&31&56 66.119 | ||
[[Werckismic temperaments|History]]: [[289edo]] 15&29&43 53.955</pre></div> | [[Breed family|Agni]]: [[212edo]] 6&31&72 | ||
[[Breed family|Jove]]: [[243edo]] 41&58&72 62.380 | |||
[[Werckismic temperaments|History]]: [[289edo]] 15&29&43 53.955 | |||
[[Breed family|Vili]]: [[643edo]] 37&93&103 73.821 | |||
[[Breed family|Baldur]]: [[940edo]] 58&72&198 44.343 | |||
[[Breed family|Ennealimmic]]: [[981edo]] 27&72&171 | |||
[[Breed family|Zisa]]: [[1241edo]] 21&31&109 82.974 | |||
[[Breed family|Frigg]]: [[1344edo]] 6&58&103 93.387 | |||
[[Breed family|Freya]]: [[2615edo]] 10&31&229 85.515</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="/Starling%20family">Bluebird</a>: <a class="wiki_link" href="/58edo">58edo</a> 12&amp;15&amp;31 91.548<br /> | <a class="wiki_link" href="/Starling%20family">Bluebird</a>: <a class="wiki_link" href="/58edo">58edo</a> 12&amp;15&amp;31 91.548<br /> | ||
<a class="wiki_link" href="/Starling%20family">Aplonis</a>: <a class="wiki_link" href="/58edo">58edo</a> 19&amp;31&amp;58 82.078 <br /> | <a class="wiki_link" href="/Starling%20family">Aplonis</a>: <a class="wiki_link" href="/58edo">58edo</a> 19&amp;31&amp;58 82.078 <br /> | ||
<a class="wiki_link" href="/Breed%20family">Jofur</a>: <a class="wiki_link" href="/58edo">58edo</a> 10&amp;31&amp;58 74.932<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">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">Tripod</a>: <a class="wiki_link" href="/91edo">91edo</a> 9&amp;10&amp;31 74.546<br /> | ||
| Line 640: | Line 650: | ||
<a class="wiki_link" href="/Marvel%20family">Marvell</a>: <a class="wiki_link" href="/166edo">166edo</a> 9&amp;31&amp;63 86.160<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<br /> | ||
<a class="wiki_link" href="/Gamelismic%20family">Portentous</a>: <a class="wiki_link" href="/190edo">190edo</a> 15&amp;31&amp;56 66.119<br /> | <a class="wiki_link" href="/Gamelismic%20family">Portentous</a>: <a class="wiki_link" href="/190edo">190edo</a> 15&amp;31&amp;56 66.119<br /> | ||
<a class="wiki_link" href="/Werckismic%20temperaments">History</a>: <a class="wiki_link" href="/289edo">289edo</a> 15&amp;29&amp;43 53.955</body></html></pre></div> | <a class="wiki_link" href="/Breed%20family">Agni</a>: <a class="wiki_link" href="/212edo">212edo</a> 6&amp;31&amp;72<br /> | ||
<a class="wiki_link" href="/Breed%20family">Jove</a>: <a class="wiki_link" href="/243edo">243edo</a> 41&amp;58&amp;72 62.380<br /> | |||
<a class="wiki_link" href="/Werckismic%20temperaments">History</a>: <a class="wiki_link" href="/289edo">289edo</a> 15&amp;29&amp;43 53.955<br /> | |||
<a class="wiki_link" href="/Breed%20family">Vili</a>: <a class="wiki_link" href="/643edo">643edo</a> 37&amp;93&amp;103 73.821<br /> | |||
<a class="wiki_link" href="/Breed%20family">Baldur</a>: <a class="wiki_link" href="/940edo">940edo</a> 58&amp;72&amp;198 44.343<br /> | |||
<a class="wiki_link" href="/Breed%20family">Ennealimmic</a>: <a class="wiki_link" href="/981edo">981edo</a> 27&amp;72&amp;171<br /> | |||
<a class="wiki_link" href="/Breed%20family">Zisa</a>: <a class="wiki_link" href="/1241edo">1241edo</a> 21&amp;31&amp;109 82.974<br /> | |||
<a class="wiki_link" href="/Breed%20family">Frigg</a>: <a class="wiki_link" href="/1344edo">1344edo</a> 6&amp;58&amp;103 93.387<br /> | |||
<a class="wiki_link" href="/Breed%20family">Freya</a>: <a class="wiki_link" href="/2615edo">2615edo</a> 10&amp;31&amp;229 85.515</body></html></pre></div> | |||