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Tenney–Euclidean tuning: Difference between revisions

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**Imported revision 535153020 - Original comment: **
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**Imported revision 535153046 - 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:clumma|clumma]] and made on <tt>2014-12-14 22:39:22 UTC</tt>.<br>
: This revision was by author [[User:clumma|clumma]] and made on <tt>2014-12-14 22:39:41 UTC</tt>.<br>
: The original revision id was <tt>535153020</tt>.<br>
: The original revision id was <tt>535153046</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>
<h4>Original Wikitext content:</h4>
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<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]


Tenney-Euclidean tuning is a variant of [[TOP tuning]] which employs the [[Tenney-Euclidean metrics|TE norm]]. While there are theoretical arguments favoring TOP, the advantages of using a Euclidean norm provides a powerful argument in favor of TE tuning.
Tenney-Euclidean tuning is a variant of [[TOP tuning]] which employs the [[Tenney-Euclidean metrics|TE norm]]. While there are theoretical arguments favoring TOP, the advantages of using a Euclidean norm provides a powerful argument in favor of TE tuning.
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This sends monzos for 50/49, 64/63 etc to the unison monzo, and vals for 10et, 12et and 22et to themselves.</pre></div>
This sends monzos for 50/49, 64/63 etc to the unison monzo, and vals for 10et, 12et and 22et to themselves.</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;Tenney-Euclidean Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#Temperaments"&gt;Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#TE tuning"&gt;TE tuning&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#The pseudoinverse"&gt;The pseudoinverse&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Computing TE tuning using pseudoinverses"&gt;Computing TE tuning using pseudoinverses&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Pure octaves TE tuning"&gt;Pure octaves TE tuning&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#The Frobenius projection map"&gt;The Frobenius projection map&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Examples"&gt;Examples&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;
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&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#The pseudoinverse"&gt;The pseudoinverse&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Computing TE tuning using pseudoinverses"&gt;Computing TE tuning using pseudoinverses&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Pure octaves TE tuning"&gt;Pure octaves TE tuning&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Examples"&gt;Examples&lt;/a&gt;&lt;/div&gt;
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Tenney-Euclidean tuning is a variant of &lt;a class="wiki_link" href="/TOP%20tuning"&gt;TOP tuning&lt;/a&gt; which employs the &lt;a class="wiki_link" href="/Tenney-Euclidean%20metrics"&gt;TE norm&lt;/a&gt;. While there are theoretical arguments favoring TOP, the advantages of using a Euclidean norm provides a powerful argument in favor of TE tuning.&lt;br /&gt;
Tenney-Euclidean tuning is a variant of &lt;a class="wiki_link" href="/TOP%20tuning"&gt;TOP tuning&lt;/a&gt; which employs the &lt;a class="wiki_link" href="/Tenney-Euclidean%20metrics"&gt;TE norm&lt;/a&gt;. While there are theoretical arguments favoring TOP, the advantages of using a Euclidean norm provides a powerful argument in favor of TE tuning.&lt;br /&gt;
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