126/125: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<span style="display: block; text-align: right;">[[:de:126/125 Deutsch]]</span>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:toddiharrop|toddiharrop]] and made on <tt>2016-11-23 16:06:29 UTC</tt>.<br>
: The original revision id was <tt>600277782</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/126_125|Deutsch]]
&lt;/span&gt;
The **starling comma** or **septimal semicomma**, 126/125 (about 13.8 cents), is the only superparticular [[7-limit]] [[comma]] which is not the difference between two 7-limit superparticular ratios. Instead, it is the amount by which [[12_7|12/7]] falls short of three [[6_5|6/5]] minor thirds. It is also the amount by which two [[5_3|5/3 major sixths]] (octave-reduced) exceed the [[7_5|7/5 tritone]], and the amount by which three 5/3s (octave-reduced) fall short of the [[7_6|7/6 septimal minor third]]. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.


Tempering it out leads to [[Starling temperaments#Starling%20comma|starling temperament]], and three minor thirds plus a [[7_6|7/6]] subminor third, when 126/125 is tempered out, gives the [[starling tetrad]] or septimal semicomma diminished seventh chord.
The '''starling comma''' or '''septimal semicomma''', 126/125 (about 13.8 cents), is the only superparticular [[7-limit|7-limit]] [[Comma|comma]] which is not the difference between two 7-limit superparticular ratios. Instead, it is the amount by which [[12/7|12/7]] falls short of three [[6/5|6/5]] minor thirds. It is also the amount by which two [[5/3|5/3 major sixths]] (octave-reduced) exceed the [[7/5|7/5 tritone]], and the amount by which three 5/3s (octave-reduced) fall short of the [[7/6|7/6 septimal minor third]]. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.


Tempering it out leads to [[Starling_temperaments#Starling comma|starling temperament]], and three minor thirds plus a [[7/6|7/6]] subminor third, when 126/125 is tempered out, gives the [[starling_tetrad|starling tetrad]] or septimal semicomma diminished seventh chord.


[[http://en.wikipedia.org/wiki/Septimal_semicomma]]</pre></div>
[http://en.wikipedia.org/wiki/Septimal_semicomma http://en.wikipedia.org/wiki/Septimal_semicomma]      [[Category:7-limit]]
<h4>Original HTML content:</h4>
[[Category:comma]]
<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;126_125&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/126_125"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
[[Category:interval]]
&lt;/span&gt;&lt;br /&gt;
[[Category:septimal]]
The &lt;strong&gt;starling comma&lt;/strong&gt; or &lt;strong&gt;septimal semicomma&lt;/strong&gt;, 126/125 (about 13.8 cents), is the only superparticular &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; which is not the difference between two 7-limit superparticular ratios. Instead, it is the amount by which &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt; falls short of three &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt; minor thirds. It is also the amount by which two &lt;a class="wiki_link" href="/5_3"&gt;5/3 major sixths&lt;/a&gt; (octave-reduced) exceed the &lt;a class="wiki_link" href="/7_5"&gt;7/5 tritone&lt;/a&gt;, and the amount by which three 5/3s (octave-reduced) fall short of the &lt;a class="wiki_link" href="/7_6"&gt;7/6 septimal minor third&lt;/a&gt;. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.&lt;br /&gt;
[[Category:starling]]
&lt;br /&gt;
Tempering it out leads to &lt;a class="wiki_link" href="/Starling%20temperaments#Starling%20comma"&gt;starling temperament&lt;/a&gt;, and three minor thirds plus a &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; subminor third, when 126/125 is tempered out, gives the &lt;a class="wiki_link" href="/starling%20tetrad"&gt;starling tetrad&lt;/a&gt; or septimal semicomma diminished seventh chord.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_semicomma" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Septimal_semicomma&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

de:126/125 Deutsch

The starling comma or septimal semicomma, 126/125 (about 13.8 cents), is the only superparticular 7-limit comma which is not the difference between two 7-limit superparticular ratios. Instead, it is the amount by which 12/7 falls short of three 6/5 minor thirds. It is also the amount by which two 5/3 major sixths (octave-reduced) exceed the 7/5 tritone, and the amount by which three 5/3s (octave-reduced) fall short of the 7/6 septimal minor third. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.

Tempering it out leads to starling temperament, and three minor thirds plus a 7/6 subminor third, when 126/125 is tempered out, gives the starling tetrad or septimal semicomma diminished seventh chord.

http://en.wikipedia.org/wiki/Septimal_semicomma