29edo: 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:~~guest~~|~~guest~~]] and made on <tt>2011-12-~~07 02~~:29:23 UTC</tt>.<br>

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 01:52:57 UTC</tt>.<br>

: The original revision id was <tt>~~283165452~~</tt>.<br>

: The original revision id was <tt>288886697</tt>.<br>

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

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=<span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;">29 tone equal temperament</span>=

29edo divides the 2:1 [[xenharmonic/octave|octave]] into 29 equal steps of approximately 41.37931 [[~~xenharmonic/~~cent|~~cent~~]]s.

29edo divides the 2:1 [[xenharmonic/octave|octave]] into 29 equal steps of approximately 41.37931 [[cent|cents]]. It is the 10th [[prime numbers|prime]] edo, following [[23edo]] and coming before [[31edo]].

29 is the lowest edo which approximates the [[xenharmonic/3_2|3:2]] just fifth more accurately than [[xenharmonic/12edo|12edo]]: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a [[xenharmonic/positive temperament|positive temperament]] -- a Superpythagorean instead of a Meantone system.

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<h1 id="toc0"><a name="x29 tone equal temperament"></a><span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;">29 tone equal temperament</span></h1>

<br />

29edo divides the 2:1 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave">octave</a> into 29 equal steps of approximately 41.37931 <a class="wiki_link" href="~~http:~~//~~xenharmonic~~.~~wikispaces.com~~/~~cent~~">~~cent~~</a>s.<br />

29edo divides the 2:1 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave">octave</a> into 29 equal steps of approximately 41.37931 <a class="wiki_link" href="/cent">cents</a>. It is the 10th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/23edo">23edo</a> and coming before <a class="wiki_link" href="/31edo">31edo</a>.<br />

<br />

29 is the lowest edo which approximates the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/3_2">3:2</a> just fifth more accurately than <a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12edo</a>: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/positive%20temperament">positive temperament</a> -- a Superpythagorean instead of a Meantone system.<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:guest|guest]] and made on <tt>2011-12-07 02:29:23 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 01:52:57 UTC</tt>.<br>
-: The original revision id was <tt>283165452</tt>.<br>
+: The original revision id was <tt>288886697</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 12: / Line 12: @@
 =&lt;span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;29 tone equal temperament&lt;/span&gt;=
-edo divides the 2:1 [[xenharmonic/octave|octave]] into 29 equal steps of approximately 41.37931 [[xenharmonic/cent|cent]]s.
+edo divides the 2:1 [[xenharmonic/octave|octave]] into 29 equal steps of approximately 41.37931 [[cent|cents]]. It is the 10th [[prime numbers|prime]] edo, following [[23edo]] and coming before [[31edo]].
 is the lowest edo which approximates the [[xenharmonic/3_2|3:2]] just fifth more accurately than [[xenharmonic/12edo|12edo]]: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a [[xenharmonic/positive temperament|positive temperament]] -- a Superpythagorean instead of a Meantone system.
@@ Line 105: / Line 105: @@
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x29 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;29 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-edo divides the 2:1 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave"&gt;octave&lt;/a&gt; into 29 equal steps of approximately 41.37931 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
+edo divides the 2:1 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave"&gt;octave&lt;/a&gt; into 29 equal steps of approximately 41.37931 &lt;a class="wiki_link" href="/cent"&gt;cents&lt;/a&gt;. It is the 10th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 is the lowest edo which approximates the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/3_2"&gt;3:2&lt;/a&gt; just fifth more accurately than &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo"&gt;12edo&lt;/a&gt;: 3/2 = 701.955... cents; 17 degrees of 29edo = 703.448... cents. Since the fifth is slightly sharp, 29edo is a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/positive%20temperament"&gt;positive temperament&lt;/a&gt; -- a Superpythagorean instead of a Meantone system.&lt;br /&gt;