Optimal patent val: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

[[Starling family|Nightingale]]: [[31edo]] 3&amp;15&amp;28 83.714

[[Starling family|Thrasher]]: [[34edo]] 12&amp;15&amp;19 87.636

[[Starling family|Thrush]]: [[58edo]] 31&amp;46&amp;58 67.663

[[Starling family|Bluebird]]: [[58edo]] 12&amp;15&amp;31 91.548

[[Marvel family|Deecee]]: [[72edo]] 9&amp;22&amp;41 92.048

[[Marvel family|Tripod]]: [[91edo]] 9&amp;10&amp;31 74.546

[[Marvel family|Marvell]]: [[166edo]] 9&amp;31&amp;63 86.160

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Optimal patent val&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Given any collection of p-limit commas, there is a finite list of p-limit &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt; 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 &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures"&gt;TE error&lt;/a&gt;; this is the &lt;em&gt;optimal (TE) patent val&lt;/em&gt; 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.&lt;br /&gt;

&lt;a class="wiki_link" href="/Starling%20family"&gt;Nightingale&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 3&amp;amp;15&amp;amp;28 83.714&lt;br /&gt;

&lt;a class="wiki_link" href="/Starling%20family"&gt;Thrasher&lt;/a&gt;: &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; 12&amp;amp;15&amp;amp;19 87.636&lt;br /&gt;

&lt;a class="wiki_link" href="/Starling%20family"&gt;Thrush&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 31&amp;amp;46&amp;amp;58 67.663&lt;br /&gt;

&lt;a class="wiki_link" href="/Starling%20family"&gt;Bluebird&lt;/a&gt;: &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; 12&amp;amp;15&amp;amp;31 91.548&lt;br /&gt;

&lt;a class="wiki_link" href="/Marvel%20family"&gt;Deecee&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 9&amp;amp;22&amp;amp;41 92.048&lt;br /&gt;

&lt;a class="wiki_link" href="/Marvel%20family"&gt;Tripod&lt;/a&gt;: &lt;a class="wiki_link" href="/91edo"&gt;91edo&lt;/a&gt; 9&amp;amp;10&amp;amp;31 74.546&lt;br /&gt;