EDOs to ETs: Difference between revisions

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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:genewardsmith|genewardsmith]] and made on <tt>2011-07-23 19:12:23 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-23 19:13:36 UTC</tt>.<br>

: The original revision id was <tt>~~242564505~~</tt>.<br>

: The original revision id was <tt>242564587</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">==<span style="font-size: 18px; line-height: 27px;">Approaches to Connecting EDOs to Temperaments</span>==

"Equal temperaments" (ETs), also known as "rank-1 temperaments", are temperaments which map JI intervals of a given prime-limit or subgroup to iterations of a single generator. "Equal divisions of the octave" (EDOs) are exactly what they sound like, a division of a Just 2/1 ratio into some number of equal parts. An equal temperament is defined by a p-limit val for some odd prime p, but an EDO is defined a 2-limit val: that is, by only the number of steps to an octave, and nothing else.

"Equal temperaments" (ETs), also known as "rank-1 temperaments", are temperaments which map JI intervals of a given prime-limit or subgroup to iterations of a single generator. "Equal divisions of the octave" (EDOs) are exactly what they sound like, a division of a Just 2/1 ratio into some number of equal parts. An equal temperament is defined by a p-limit val for some odd prime p, but an EDO is defined as a 2-limit val: that is, by only the number of steps to an octave, and nothing else.

===Support for higher-rank temperaments===

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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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>EDOs to ETs</title></head><body><h2 id="toc0"><a name="x-Approaches to Connecting EDOs to Temperaments"></a><span style="font-size: 18px; line-height: 27px;">Approaches to Connecting EDOs to Temperaments</span></h2>

<br />

&quot;Equal temperaments&quot; (ETs), also known as &quot;rank-1 temperaments&quot;, are temperaments which map JI intervals of a given prime-limit or subgroup to iterations of a single generator. &quot;Equal divisions of the octave&quot; (EDOs) are exactly what they sound like, a division of a Just 2/1 ratio into some number of equal parts. An equal temperament is defined by a p-limit val for some odd prime p, but an EDO is defined a 2-limit val: that is, by only the number of steps to an octave, and nothing else.<br />

&quot;Equal temperaments&quot; (ETs), also known as &quot;rank-1 temperaments&quot;, are temperaments which map JI intervals of a given prime-limit or subgroup to iterations of a single generator. &quot;Equal divisions of the octave&quot; (EDOs) are exactly what they sound like, a division of a Just 2/1 ratio into some number of equal parts. An equal temperament is defined by a p-limit val for some odd prime p, but an EDO is defined as a 2-limit val: that is, by only the number of steps to an octave, and nothing else.<br />

<br />

<h3 id="toc1"><a name="x-Approaches to Connecting EDOs to Temperaments-Support for higher-rank temperaments"></a>Support for higher-rank temperaments</h3>

@@ Line 1: / Line 1: @@
 <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:genewardsmith|genewardsmith]] and made on <tt>2011-07-23 19:12:23 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-23 19:13:36 UTC</tt>.<br>
-: The original revision id was <tt>242564505</tt>.<br>
+: The original revision id was <tt>242564587</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">==&lt;span style="font-size: 18px; line-height: 27px;"&gt;Approaches to Connecting EDOs to Temperaments&lt;/span&gt;==
-"Equal temperaments" (ETs), also known as "rank-1 temperaments", are temperaments which map JI intervals of a given prime-limit or subgroup to iterations of a single generator. "Equal divisions of the octave" (EDOs) are exactly what they sound like, a division of a Just 2/1 ratio into some number of equal parts. An equal temperament is defined by a p-limit val for some odd prime p, but an EDO is defined a 2-limit val: that is, by only the number of steps to an octave, and nothing else.
+"Equal temperaments" (ETs), also known as "rank-1 temperaments", are temperaments which map JI intervals of a given prime-limit or subgroup to iterations of a single generator. "Equal divisions of the octave" (EDOs) are exactly what they sound like, a division of a Just 2/1 ratio into some number of equal parts. An equal temperament is defined by a p-limit val for some odd prime p, but an EDO is defined as a 2-limit val: that is, by only the number of steps to an octave, and nothing else.
 ===Support for higher-rank temperaments===
@@ Line 71: / Line 71: @@
 <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;EDOs to ETs&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Approaches to Connecting EDOs to Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="font-size: 18px; line-height: 27px;"&gt;Approaches to Connecting EDOs to Temperaments&lt;/span&gt;&lt;/h2&gt;
   &lt;br /&gt;
-&amp;quot;Equal temperaments&amp;quot; (ETs), also known as &amp;quot;rank-1 temperaments&amp;quot;, are temperaments which map JI intervals of a given prime-limit or subgroup to iterations of a single generator. &amp;quot;Equal divisions of the octave&amp;quot; (EDOs) are exactly what they sound like, a division of a Just 2/1 ratio into some number of equal parts. An equal temperament is defined by a p-limit val for some odd prime p, but an EDO is defined a 2-limit val: that is, by only the number of steps to an octave, and nothing else.&lt;br /&gt;
+&amp;quot;Equal temperaments&amp;quot; (ETs), also known as &amp;quot;rank-1 temperaments&amp;quot;, are temperaments which map JI intervals of a given prime-limit or subgroup to iterations of a single generator. &amp;quot;Equal divisions of the octave&amp;quot; (EDOs) are exactly what they sound like, a division of a Just 2/1 ratio into some number of equal parts. An equal temperament is defined by a p-limit val for some odd prime p, but an EDO is defined as a 2-limit val: that is, by only the number of steps to an octave, and nothing else.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Approaches to Connecting EDOs to Temperaments-Support for higher-rank temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Support for higher-rank temperaments&lt;/h3&gt;