100/99: Difference between revisions

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-19 19:26:43 UTC</tt>.<br>

: The original revision id was <tt>266601380</tt>.<br>

<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">In [[Just Intonation]],100/99 is a [[superparticular]] interval (the ptolemisma) of around 17.4¢ which makes the difference between [[11_10|11/10]], the greater undecimal neutral second of about 165¢, and [[10_9|10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81_80|81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9_8|9/8]]. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11_8|11/8]] and two [[6_5|6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5.

<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;100_99&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;,100/99 is a &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; interval (the ptolemisma) of around 17.4¢ which makes the difference between &lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt;, the greater undecimal neutral second of about 165¢, and &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;, the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;, which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; and two &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;s fall short of an octave, so that tempering out 100/99 allows for the &lt;a class="wiki_link" href="/ptolemismic%20triad"&gt;ptolemismic triad&lt;/a&gt; which has intervals of 11/8, 6/5, 6/5.&lt;br /&gt;