28edo: 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:~~JosephRuhf~~|~~JosephRuhf~~]] and made on <tt>~~2015~~-03-~~28 16~~:38:01 UTC</tt>.<br>

: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-10 14:48:39 UTC</tt>.<br>

: The original revision id was <tt>~~545657998~~</tt>.<br>

: The original revision id was <tt>591574624</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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=Basic properties=

28edo, a multiple of both [[xenharmonic/7edo|7edo]] and [[xenharmonic/14edo|14edo]] (and of course [[xenharmonic/2edo|2edo]] and [[xenharmonic/4edo|4edo]]), has a step size of 42.857 [[xenharmonic/cent|cent]]s. It shares three intervals with [[xenharmonic/12edo|12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[xenharmonic/tempering out|tempers out]] the [[xenharmonic/greater diesis|greater diesis]] [[xenharmonic/648_625|648:625]]. It does not however temper out the [[xenharmonic/128_125|128:125]] [[xenharmonic/lesser diesis|lesser diesis]], as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as ~~14edo~~. It also has decent approximations of several septimal intervals, of which [[xenharmonic/9_7|9/7]] and its inversion [[xenharmonic/14_9|14/9]] are also found in 14edo.

28edo, a multiple of both [[xenharmonic/7edo|7edo]] and [[xenharmonic/14edo|14edo]] (and of course [[xenharmonic/2edo|2edo]] and [[xenharmonic/4edo|4edo]]), has a step size of 42.857 [[xenharmonic/cent|cent]]s. It shares three intervals with [[xenharmonic/12edo|12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[xenharmonic/tempering out|tempers out]] the [[xenharmonic/greater diesis|greater diesis]] [[xenharmonic/648_625|648:625]]. It does not however temper out the [[xenharmonic/128_125|128:125]] [[xenharmonic/lesser diesis|lesser diesis]], as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[xenharmonic/9_7|9/7]] and its inversion [[xenharmonic/14_9|14/9]] are also found in 14edo.

=Subgroups=

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<br />

<h1 id="toc0"><a name="Basic properties"></a>Basic properties</h1>

28edo, a multiple of both <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edo">14edo</a> (and of course <a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo">4edo</a>), has a step size of 42.857 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. It shares three intervals with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12edo</a>: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/greater%20diesis">greater diesis</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/648_625">648:625</a>. It does not however temper out the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/128_125">128:125</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lesser%20diesis">lesser diesis</a>, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as ~~14edo~~. It also has decent approximations of several septimal intervals, of which <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_7">9/7</a> and its inversion <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_9">14/9</a> are also found in 14edo.<br />

28edo, a multiple of both <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo">7edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edo">14edo</a> (and of course <a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo">2edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo">4edo</a>), has a step size of 42.857 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">cent</a>s. It shares three intervals with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo">12edo</a>: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/greater%20diesis">greater diesis</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/648_625">648:625</a>. It does not however temper out the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/128_125">128:125</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lesser%20diesis">lesser diesis</a>, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_7">9/7</a> and its inversion <a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_9">14/9</a> are also found in 14edo.<br />

<br />

<h1 id="toc1"><a name="Subgroups"></a>Subgroups</h1>

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-28 16:38:01 UTC</tt>.<br>
+: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-10 14:48:39 UTC</tt>.<br>
-: The original revision id was <tt>545657998</tt>.<br>
+: The original revision id was <tt>591574624</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 10: / Line 10: @@
 =Basic properties=
-edo, a multiple of both [[xenharmonic/7edo|7edo]] and [[xenharmonic/14edo|14edo]] (and of course [[xenharmonic/2edo|2edo]] and [[xenharmonic/4edo|4edo]]), has a step size of 42.857 [[xenharmonic/cent|cent]]s. It shares three intervals with [[xenharmonic/12edo|12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[xenharmonic/tempering out|tempers out]] the [[xenharmonic/greater diesis|greater diesis]] [[xenharmonic/648_625|648:625]]. It does not however temper out the [[xenharmonic/128_125|128:125]] [[xenharmonic/lesser diesis|lesser diesis]], as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, of which [[xenharmonic/9_7|9/7]] and its inversion [[xenharmonic/14_9|14/9]] are also found in 14edo.
+edo, a multiple of both [[xenharmonic/7edo|7edo]] and [[xenharmonic/14edo|14edo]] (and of course [[xenharmonic/2edo|2edo]] and [[xenharmonic/4edo|4edo]]), has a step size of 42.857 [[xenharmonic/cent|cent]]s. It shares three intervals with [[xenharmonic/12edo|12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[xenharmonic/tempering out|tempers out]] the [[xenharmonic/greater diesis|greater diesis]] [[xenharmonic/648_625|648:625]]. It does not however temper out the [[xenharmonic/128_125|128:125]] [[xenharmonic/lesser diesis|lesser diesis]], as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[xenharmonic/9_7|9/7]] and its inversion [[xenharmonic/14_9|14/9]] are also found in 14edo.
 =Subgroups=
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 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Basic properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Basic properties&lt;/h1&gt;
-edo, a multiple of both &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo"&gt;7edo&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edo"&gt;14edo&lt;/a&gt; (and of course &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo"&gt;2edo&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo"&gt;4edo&lt;/a&gt;), has a step size of 42.857 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent"&gt;cent&lt;/a&gt;s. It shares three intervals with &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo"&gt;12edo&lt;/a&gt;: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out"&gt;tempers out&lt;/a&gt; the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/greater%20diesis"&gt;greater diesis&lt;/a&gt; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/648_625"&gt;648:625&lt;/a&gt;. It does not however temper out the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/128_125"&gt;128:125&lt;/a&gt; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/lesser%20diesis"&gt;lesser diesis&lt;/a&gt;, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, of which &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_7"&gt;9/7&lt;/a&gt; and its inversion &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_9"&gt;14/9&lt;/a&gt; are also found in 14edo.&lt;br /&gt;
+edo, a multiple of both &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo"&gt;7edo&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/14edo"&gt;14edo&lt;/a&gt; (and of course &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/2edo"&gt;2edo&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/4edo"&gt;4edo&lt;/a&gt;), has a step size of 42.857 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent"&gt;cent&lt;/a&gt;s. It shares three intervals with &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/12edo"&gt;12edo&lt;/a&gt;: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out"&gt;tempers out&lt;/a&gt; the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/greater%20diesis"&gt;greater diesis&lt;/a&gt; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/648_625"&gt;648:625&lt;/a&gt;. It does not however temper out the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/128_125"&gt;128:125&lt;/a&gt; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/lesser%20diesis"&gt;lesser diesis&lt;/a&gt;, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_7"&gt;9/7&lt;/a&gt; and its inversion &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_9"&gt;14/9&lt;/a&gt; are also found in 14edo.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Subgroups"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Subgroups&lt;/h1&gt;