Patent val: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 250601336 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 250603118 - 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>2011-09-04 10:00:29 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 10:20:04 UTC</tt>.<br>
: The original revision id was <tt>250601336</tt>.<br>
: The original revision id was <tt>250603118</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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=Patent vals from real numbers=
=Patent vals from real numbers=
Instead of assuming the patent val for N-edo comes from an integer N, we could define a patent val for X-edo, where X is any real number, in just the same way. For instance, the [[Z-function]] maximum at 48.9451 leads to a 13-limit X-edo val of &lt;49 78 114 137 169 181|, whereas the minimum at 49.1412 leads to an X-edo val of &lt;49 78 114 138 170 182|. Meanwhile, the patent val, which is the X-edo val for X=49.0000 exactly, is &lt;49 78 114 138 170 181|.</pre></div>
Instead of assuming the patent val for N-edo comes from an integer N, we could define a patent val for X-edo, where X is any real number, in just the same way. For instance, the [[The Riemann Zeta Function and Tuning#The Z function|Z-function]] maximum at 48.9451 leads to a 13-limit X-edo val of &lt;49 78 114 137 169 181|, whereas the minimum at 49.1412 leads to an X-edo val of &lt;49 78 114 138 170 182|. Meanwhile, the patent val, which is the X-edo val for X=49.0000 exactly, is &lt;49 78 114 138 170 181|.</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Patent val&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Definition"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Definition&lt;/h1&gt;
<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;Patent val&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Definition"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Definition&lt;/h1&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Patent vals from real numbers"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Patent vals from real numbers&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Patent vals from real numbers"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Patent vals from real numbers&lt;/h1&gt;
Instead of assuming the patent val for N-edo comes from an integer N, we could define a patent val for X-edo, where X is any real number, in just the same way. For instance, the &lt;a class="wiki_link" href="/Z-function"&gt;Z-function&lt;/a&gt; maximum at 48.9451 leads to a 13-limit X-edo val of &amp;lt;49 78 114 137 169 181|, whereas the minimum at 49.1412 leads to an X-edo val of &amp;lt;49 78 114 138 170 182|. Meanwhile, the patent val, which is the X-edo val for X=49.0000 exactly, is &amp;lt;49 78 114 138 170 181|.&lt;/body&gt;&lt;/html&gt;</pre></div>
Instead of assuming the patent val for N-edo comes from an integer N, we could define a patent val for X-edo, where X is any real number, in just the same way. For instance, the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#The Z function"&gt;Z-function&lt;/a&gt; maximum at 48.9451 leads to a 13-limit X-edo val of &amp;lt;49 78 114 137 169 181|, whereas the minimum at 49.1412 leads to an X-edo val of &amp;lt;49 78 114 138 170 182|. Meanwhile, the patent val, which is the X-edo val for X=49.0000 exactly, is &amp;lt;49 78 114 138 170 181|.&lt;/body&gt;&lt;/html&gt;</pre></div>