50edo: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<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>

|| | -6 -8 2 5 &gt; ||&gt; 1.12 ||= 420175/419904 ||  ||  ||

|| |-11 2 7 -3 &gt; ||&gt; 1.63 ||= 703125/702464 ||  ||  ||

|| |-13 10 0 -1 &gt; ||&gt; 50.72 ||= 59049/57344 || Harrison's comma ||  ||

|| | 2 3 1 -2 -1 &gt; ||&gt; 3.21 ||= 540/539 || Swets' comma || Swetisma ||

&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 0 2 0 1 -3 &gt; 2.36 2200/2197 Parizek comma&lt;/span&gt;

&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 1 1 1 0 -1 &gt; 16.57 105/104 small tridecimal comma&lt;/span&gt;

<h4>Original HTML content:</h4>

<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;50edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;em&gt;50edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 50 equal parts of precisely 24 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. In the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, it tempers out 81/80, making it a &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; system, and in that capacity has historically has drawn some notice. In &amp;quot;Harmonics or the Philosophy of Musical Sounds&amp;quot; (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the &lt;a class="wiki_link" href="/Target%20tunings"&gt;least squares&lt;/a&gt; tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; extends meantone with a &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; which is nearly pure, 50 has a flat 7/4 but both &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; and &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; are nearly pure.&lt;br /&gt;

         &lt;td style="text-align: right;"&gt;5.57&lt;br /&gt;

&lt;/td&gt;

&lt;/td&gt;

         &lt;td&gt;&lt;br /&gt;

&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 0 2 0 1 -3 &amp;gt; 2.36 2200/2197 Parizek comma&lt;/span&gt;&lt;br /&gt;

&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 1 1 1 0 -1 &amp;gt; 16.57 105/104 small tridecimal comma&lt;/span&gt;&lt;br /&gt;

&lt;/table&gt;