23edo: 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~~:13:22 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 13:59:40 UTC</tt>.<br>

: The original revision id was <tt>~~211896084~~</tt>.<br>

: The original revision id was <tt>216466006</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: #007a1b; display: block;">23 tone equal temperament</span>=

~~23-tET~~, or 23-EDO, is a tuning system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]].

23et, or 23-EDO, is a tuning system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of 17-limit 46et, the larger subgroup 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes.

==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>23edo</title></head><body><h1 id="toc0"><a name="x23 tone equal temperament"></a><span style="color: #007a1b; display: block;">23 tone equal temperament</span></h1>

<br />

~~23-tET~~, or 23-EDO, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>.<br />

23et, or 23-EDO, is a tuning system which divides the <a class="wiki_link" href="/octave">octave</a> into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. If to this subgroup is added the commas of 17-limit 46et, the larger subgroup 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes. <br />

<br />

<h2 id="toc1"><a name="x23 tone equal temperament-Intervals"></a>Intervals</h2>

@@ 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 18:13:22 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 13:59:40 UTC</tt>.<br>
-: The original revision id was <tt>211896084</tt>.<br>
+: The original revision id was <tt>216466006</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: #007a1b; display: block;"&gt;23 tone equal temperament&lt;/span&gt;=
--tET, or 23-EDO, is a tuning system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]].
+et, or 23-EDO, is a tuning system which divides the [[octave]] into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of 17-limit 46et, the larger subgroup 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes.
 ==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">&lt;html&gt;&lt;head&gt;&lt;title&gt;23edo&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="x23 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #007a1b; display: block;"&gt;23 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
--tET, or 23-EDO, is a tuning system which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;.&lt;br /&gt;
+et, or 23-EDO, is a tuning system which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 23 equal parts of approximately 52.173913 cents. It has good approximations for 5/3, 11/7, 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. If to this subgroup is added the commas of 17-limit 46et, the larger subgroup 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit 46, and may be regarded as a basis for analyzing the harmony of 23-EDO so far as approximations to just intervals goes. &lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x23 tone equal temperament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals&lt;/h2&gt;