57edo: 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>2011-03-~~18 18~~:48:57 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-19 12:53:38 UTC</tt>.<br>

: The original revision id was <tt>~~211901286~~</tt>.<br>

: The original revision id was <tt>211993418</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="color: #006118;">57 tone equal temperament</span>=

//57edo// divides the [[octave]] into 57 parts of size 21.053. It can be used to tune [[mothra temperament]], and is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]].

//57edo// divides the [[octave]] into 57 parts of size 21.053. It can be used to tune [[mothra temperament]], and is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]]. One way to describe 57 is that it has a [[5-limit]] part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the [[19-limit]] 46&57 temperament.

[[5-limit]] [[comma]]s: 81/80, 3125/3072

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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>57edo</title></head><body><h1 id="toc0"><a name="x57 tone equal temperament"></a><span style="color: #006118;">57 tone equal temperament</span></h1>

<br />

<em>57edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 57 parts of size 21.053. It can be used to tune <a class="wiki_link" href="/mothra%20temperament">mothra temperament</a>, and is an excellent tuning for the 2.5/3.7.11.13.17.19 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>.<br />

<em>57edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 57 parts of size 21.053. It can be used to tune <a class="wiki_link" href="/mothra%20temperament">mothra temperament</a>, and is an excellent tuning for the 2.5/3.7.11.13.17.19 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. One way to describe 57 is that it has a <a class="wiki_link" href="/5-limit">5-limit</a> part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the <a class="wiki_link" href="/19-limit">19-limit</a> 46&amp;57 temperament.<br />

<br />

<a class="wiki_link" href="/5-limit">5-limit</a> <a class="wiki_link" href="/comma">comma</a>s: 81/80, 3125/3072<br />

@@ 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>2011-03-18 18:48:57 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-19 12:53:38 UTC</tt>.<br>
-: The original revision id was <tt>211901286</tt>.<br>
+: The original revision id was <tt>211993418</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="color: #006118;"&gt;57 tone equal temperament&lt;/span&gt;=
-//57edo// divides the [[octave]] into 57 parts of size 21.053. It can be used to tune [[mothra temperament]], and is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]].
+//57edo// divides the [[octave]] into 57 parts of size 21.053. It can be used to tune [[mothra temperament]], and is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]]. One way to describe 57 is that it has a [[5-limit]] part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the [[19-limit]] 46&amp;57 temperament.
 [[5-limit]] [[comma]]s: 81/80, 3125/3072
@@ Line 78: / Line 78: @@
 <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;57edo&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="x57 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #006118;"&gt;57 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;em&gt;57edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 57 parts of size 21.053. It can be used to tune &lt;a class="wiki_link" href="/mothra%20temperament"&gt;mothra temperament&lt;/a&gt;, and is an excellent tuning for the 2.5/3.7.11.13.17.19 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;.&lt;br /&gt;
+&lt;em&gt;57edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 57 parts of size 21.053. It can be used to tune &lt;a class="wiki_link" href="/mothra%20temperament"&gt;mothra temperament&lt;/a&gt;, and is an excellent tuning for the 2.5/3.7.11.13.17.19 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. One way to describe 57 is that it has a &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; 46&amp;amp;57 temperament.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s: 81/80, 3125/3072&lt;br /&gt;