Tenney–Euclidean tuning: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-05-09 14:56:21 UTC</tt>.<br>

: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-07-27 14:06:05 UTC</tt>.<br>

: The original revision id was <tt>~~582561047~~</tt>.<br>

: The original revision id was <tt>588204515</tt>.<br>

: The revision comment was: <tt></tt><br>

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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]]

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]]. Just as the TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, the TE tuning minimizes the maximum TE-weighted error of any interval.

Just as the TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, the TE tuning minimizes the maximum TE-weighted error of any interval.

=Temperaments=

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Tenney-Euclidean tuning is a variant of <a class="wiki_link" href="/TOP%20tuning">TOP tuning</a> which employs the <a class="wiki_link" href="/Tenney-Euclidean%20metrics">TE norm</a>. ~~While there are theoretical arguments favoring TOP, the advantages of using a Euclidean norm provides a powerful argument in favor of TE tuning.<br />~~

Tenney-Euclidean tuning is a variant of <a class="wiki_link" href="/TOP%20tuning">TOP tuning</a> which employs the <a class="wiki_link" href="/Tenney-Euclidean%20metrics">TE norm</a>. Just as the TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, the TE tuning minimizes the maximum TE-weighted error of any interval.<br />

~~<br />~~

Just as the TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, the TE tuning minimizes the maximum TE-weighted error of any interval.<br />

<br />

<h1 id="toc0"><a name="Temperaments"></a>Temperaments</h1>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2016-05-09 14:56:21 UTC</tt>.<br>
+: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-07-27 14:06:05 UTC</tt>.<br>
-: The original revision id was <tt>582561047</tt>.<br>
+: The original revision id was <tt>588204515</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>
@@ Line 8: / Line 8: @@
 <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]]. Just as the TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, the TE tuning minimizes the maximum TE-weighted error of any interval.
-Just as the TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, the TE tuning minimizes the maximum TE-weighted error of any interval.
 =Temperaments=
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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;. Just as the TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, the TE tuning minimizes the maximum TE-weighted error of any interval.&lt;br /&gt;
-&lt;br /&gt;
-Just as the TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, the TE tuning minimizes the maximum TE-weighted error of any interval.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Temperaments&lt;/h1&gt;