50/49: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<span style="display: block; text-align: right;">[[:de:50/49 Deutsch]]</span>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-11-23 15:16:58 UTC</tt>.<br>
: The original revision id was <tt>622274741</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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/50_49|Deutsch]]
&lt;/span&gt;
The **septimal sixth-tone** or **jubilisma**, 50/49, is the only [[superparticular]] [[comma]] aside from [[126_125|126/125]] which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = ([[10_7|10/7]])/([[7_5|7/5]]). [[tempering out|Tempering it out]] equates the two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include [[12edo|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]] and [[54edo]].


[[http://en.wikipedia.org/wiki/Septimal_sixth-tone]]</pre></div>
The '''septimal sixth-tone''' or '''jubilisma''', 50/49, is the only [[superparticular|superparticular]] [[Comma|comma]] aside from [[126/125|126/125]] which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = ([[10/7|10/7]])/([[7/5|7/5]]). [[tempering_out|Tempering it out]] equates the two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include [[12edo|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]] and [[54edo|54edo]].
<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;50_49&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/50_49"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
[http://en.wikipedia.org/wiki/Septimal_sixth-tone http://en.wikipedia.org/wiki/Septimal_sixth-tone]      [[Category:comma]]
&lt;/span&gt;&lt;br /&gt;
[[Category:definition]]
The &lt;strong&gt;septimal sixth-tone&lt;/strong&gt; or &lt;strong&gt;jubilisma&lt;/strong&gt;, 50/49, is the only &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; aside from &lt;a class="wiki_link" href="/126_125"&gt;126/125&lt;/a&gt; which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = (&lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;)/(&lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;). &lt;a class="wiki_link" href="/tempering%20out"&gt;Tempering it out&lt;/a&gt; equates the two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt; and &lt;a class="wiki_link" href="/54edo"&gt;54edo&lt;/a&gt;.&lt;br /&gt;
[[Category:interval]]
&lt;br /&gt;
[[Category:jubilisma]]
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_sixth-tone" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Septimal_sixth-tone&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:ratio]]

Revision as of 00:00, 17 July 2018

de:50/49 Deutsch

The septimal sixth-tone or jubilisma, 50/49, is the only superparticular comma aside from 126/125 which has a numerator which is neither square nor triangular, meaning it is not the difference between septimal superparticular rations with numerators differing by either one or two; instead, 50/49 = (10/7)/(7/5). Tempering it out equates the two, leading to temperaments where the square root of two does service for both. Equal temperaments tempering out 50/49 include 12, 22, 26, 38, 48 and 54edo.

http://en.wikipedia.org/wiki/Septimal_sixth-tone