38edo: 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:~~Osmiorisbendi~~|~~Osmiorisbendi~~]] and made on <tt>2011-06-~~24 18~~:35:40 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-07-01 11:50:37 UTC</tt>.<br>

: The original revision id was <tt>~~238638717~~</tt>.<br>

: The original revision id was <tt>239662669</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>

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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="background-color: #e1e1e1; color: #008693; font-size: 110%;">38 tone equal temperament</span>=

//38edo// divides the octave into 38 equal parts of 31.579 ~~cents~~. Since 38 = 2*19, it can be thought of as two parallel [[19edo]]s. It tempers out the same 5-limit commas as 19, namely 81/80, 3125/3072 and 15625/15552. In the 7-limit, we can add 50/49, and tempering out 81/80 and 50/49 gives [[Meantone family|injera temperament]], for which 38 is the [[optimal patent val]]. In the 11-limit, we can add 121/120 and 176/175.

**38edo** divides the octave into 38 equal parts of 31.579 [[cent]]s. Since 38 = 2*19, it can be thought of as two parallel [[19edo]]s. It [[tempering out|tempers out]] the same [[5-limit]] commas as [[19edo|19]], namely 81/80, 3125/3072 and 15625/15552. In the [[7-limit]], we can add 50/49, and tempering out 81/80 and 50/49 gives [[Meantone family|injera temperament]], for which 38 is the [[optimal patent val]]. In the [[11-limit]], we can add 121/120 and 176/175.

===38-EDO Intervals:===

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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>38edo</title></head><body><h1 id="toc0"><a name="x38 tone equal temperament"></a><span style="background-color: #e1e1e1; color: #008693; font-size: 110%;">38 tone equal temperament</span></h1>

<br />

<em>38edo</em> divides the octave into 38 equal parts of 31.579 ~~cents~~. Since 38 = 2*19, it can be thought of as two parallel <a class="wiki_link" href="/19edo">19edo</a>s. It tempers out the same 5-limit commas as 19, namely 81/80, 3125/3072 and 15625/15552. In the 7-limit, we can add 50/49, and tempering out 81/80 and 50/49 gives <a class="wiki_link" href="/Meantone%20family">injera temperament</a>, for which 38 is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>. In the 11-limit, we can add 121/120 and 176/175.<br />

<strong>38edo</strong> divides the octave into 38 equal parts of 31.579 <a class="wiki_link" href="/cent">cent</a>s. Since 38 = 2*19, it can be thought of as two parallel <a class="wiki_link" href="/19edo">19edo</a>s. It <a class="wiki_link" href="/tempering%20out">tempers out</a> the same <a class="wiki_link" href="/5-limit">5-limit</a> commas as <a class="wiki_link" href="/19edo">19</a>, namely 81/80, 3125/3072 and 15625/15552. In the <a class="wiki_link" href="/7-limit">7-limit</a>, we can add 50/49, and tempering out 81/80 and 50/49 gives <a class="wiki_link" href="/Meantone%20family">injera temperament</a>, for which 38 is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>. In the <a class="wiki_link" href="/11-limit">11-limit</a>, we can add 121/120 and 176/175.<br />

<br />

<h3 id="toc1"><a name="x38 tone equal temperament--38-EDO Intervals:"></a>38-EDO Intervals:</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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-06-24 18:35:40 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-07-01 11:50:37 UTC</tt>.<br>
-: The original revision id was <tt>238638717</tt>.<br>
+: The original revision id was <tt>239662669</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="background-color: #e1e1e1; color: #008693; font-size: 110%;"&gt;38 tone equal temperament&lt;/span&gt;=
-//38edo// divides the octave into 38 equal parts of 31.579 cents. Since 38 = 2*19, it can be thought of as two parallel [[19edo]]s. It tempers out the same 5-limit commas as 19, namely 81/80, 3125/3072 and 15625/15552. In the 7-limit, we can add 50/49, and tempering out 81/80 and 50/49 gives [[Meantone family|injera temperament]], for which 38 is the [[optimal patent val]]. In the 11-limit, we can add 121/120 and 176/175.
+**38edo** divides the octave into 38 equal parts of 31.579 [[cent]]s. Since 38 = 2*19, it can be thought of as two parallel [[19edo]]s. It [[tempering out|tempers out]] the same [[5-limit]] commas as [[19edo|19]], namely 81/80, 3125/3072 and 15625/15552. In the [[7-limit]], we can add 50/49, and tempering out 81/80 and 50/49 gives [[Meantone family|injera temperament]], for which 38 is the [[optimal patent val]]. In the [[11-limit]], we can add 121/120 and 176/175.
 ===38-EDO Intervals:===
@@ Line 53: / Line 53: @@
 <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;38edo&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="x38 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="background-color: #e1e1e1; color: #008693; font-size: 110%;"&gt;38 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;em&gt;38edo&lt;/em&gt; divides the octave into 38 equal parts of 31.579 cents. Since 38 = 2*19, it can be thought of as two parallel &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;s. It tempers out the same 5-limit commas as 19, namely 81/80, 3125/3072 and 15625/15552. In the 7-limit, we can add 50/49, and tempering out 81/80 and 50/49 gives &lt;a class="wiki_link" href="/Meantone%20family"&gt;injera temperament&lt;/a&gt;, for which 38 is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt;. In the 11-limit, we can add 121/120 and 176/175.&lt;br /&gt;
+&lt;strong&gt;38edo&lt;/strong&gt; divides the octave into 38 equal parts of 31.579 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. Since 38 = 2*19, it can be thought of as two parallel &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;s. It &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the same &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; commas as &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, namely 81/80, 3125/3072 and 15625/15552. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, we can add 50/49, and tempering out 81/80 and 50/49 gives &lt;a class="wiki_link" href="/Meantone%20family"&gt;injera temperament&lt;/a&gt;, for which 38 is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt;. In the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;, we can add 121/120 and 176/175.&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="x38 tone equal temperament--38-EDO Intervals:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;38-EDO Intervals:&lt;/h3&gt;