126/125: 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:

: This revision was by author [[User:~~hstraub~~|~~hstraub~~]] and made on <tt>2016-04-~~26 11~~:20:44 UTC</tt>.

: This revision was by author [[User:toddiharrop|toddiharrop]] and made on <tt>2016-11-23 16:06:29 UTC</tt>.

: The original revision id was <tt>~~581264315~~</tt>.

: The original revision id was <tt>600277782</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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<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">[[xenharmonie/126_125|Deutsch]]

The **starling comma** or **septimal semicomma**, 126/125, 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]].

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.

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<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"><html><head><title>126_125</title></head><body><a class="wiki_link" href="http://xenharmonie.wikispaces.com/126_125">Deutsch</a>

The starling comma or septimal semicomma, 126/125, is the only superparticular <a class="wiki_link" href="/7-limit">7-limit</a> <a class="wiki_link" href="/comma">comma</a> which is not the difference between two 7-limit superparticular ratios. Instead, it is the amount by which <a class="wiki_link" href="/12_7">12/7</a> falls short of three <a class="wiki_link" href="/6_5">6/5</a> minor thirds. It is also the amount by which two <a class="wiki_link" href="/5_3">5/3 major sixths</a> (octave-reduced) exceed the <a class="wiki_link" href="/7_5">7/5 tritone</a>, and the amount by which three 5/3s (octave-reduced) fall short of the <a class="wiki_link" href="/7_6">7/6 septimal minor third</a>.

The starling comma or septimal semicomma, 126/125 (about 13.8 cents), is the only superparticular <a class="wiki_link" href="/7-limit">7-limit</a> <a class="wiki_link" href="/comma">comma</a> which is not the difference between two 7-limit superparticular ratios. Instead, it is the amount by which <a class="wiki_link" href="/12_7">12/7</a> falls short of three <a class="wiki_link" href="/6_5">6/5</a> minor thirds. It is also the amount by which two <a class="wiki_link" href="/5_3">5/3 major sixths</a> (octave-reduced) exceed the <a class="wiki_link" href="/7_5">7/5 tritone</a>, and the amount by which three 5/3s (octave-reduced) fall short of the <a class="wiki_link" href="/7_6">7/6 septimal minor third</a>. 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 <a class="wiki_link" href="/Starling%20temperaments#Starling%20comma">starling temperament</a>, and three minor thirds plus a <a class="wiki_link" href="/7_6">7/6</a> subminor third, when 126/125 is tempered out, gives the <a class="wiki_link" href="/starling%20tetrad">starling tetrad</a> or septimal semicomma diminished seventh chord.

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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:hstraub|hstraub]] and made on <tt>2016-04-26 11:20:44 UTC</tt>.<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>581264315</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>
@@ Line 8: / Line 8: @@
 <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, 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]].
+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.
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 <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;
 &lt;/span&gt;&lt;br /&gt;
-The &lt;strong&gt;starling comma&lt;/strong&gt; or &lt;strong&gt;septimal semicomma&lt;/strong&gt;, 126/125, 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;.&lt;br /&gt;
+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;
 &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;