126/125: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| de = 126/125
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-08 16:04:56 UTC</tt>.<br>
| en = 126/125
: The original revision id was <tt>244893409</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja =
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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<h4>Original Wikitext content:</h4>
{{Infobox Interval
<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">The starling comma or septimal semicomma, 126/125, is the only superparticular 7-limit comma which is not the difference between two  7 (or 9) limit consonances. Instead, it is the amount by which [[12_7|12/7]] falls short of three [[6_5|6/5]] minor thirds. 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]] or septimal semicomma diminished seventh chord.
| Name = starling comma, septimal semicomma
| Color name = zg<sup>3</sup>2, zotrigu 2nd,<br>Zotrigu comma
| Comma = yes
}}
{{Wikipedia|Septimal semicomma}}


The '''starling comma''' or '''septimal semicomma''', '''126/125''' (about 13.8 [[cent]]s), is the [[superparticular]] [[7-limit]] [[comma]] which is the difference between [[36/35]] (septimal quartertone) and [[50/49]] (jubilisma). In terms of just intervals, 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, [[25/18]]) fall short of the [[7/5]] [[tritone]], and the amount by which three 5/3's (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.


[[http://en.wikipedia.org/wiki/Septimal_semicomma]]</pre></div>
== Temperaments ==
<h4>Original HTML content:</h4>
Tempering it out alone in the 7-limit leads to the [[starling]] temperament, and enables [[starling chords]]. See [[Starling family]] for the rank-3 temperament family where it is tempered out. See [[starling temperaments]] for a collection of rank-2 temperaments where it is tempered out.  
<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;The starling comma or septimal semicomma, 126/125, is the only superparticular 7-limit comma which is not the difference between two  7 (or 9) limit consonances. 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. Tempering it out leads to &lt;a class="wiki_link" href="/Starling%20temperaments#Starling comma"&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;
== See also ==
&lt;br /&gt;
* [[Small comma]]
&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>
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]
 
[[Category:Starling]]
[[Category:Commas named after musical traditions]]

Latest revision as of 18:20, 13 March 2025

Interval information
Ratio 126/125
Factorization 2 × 32 × 5-3 × 7
Monzo [1 2 -3 1⟩
Size in cents 13.79477¢
Names starling comma,
septimal semicomma
Color name zg32, zotrigu 2nd,
Zotrigu comma
FJS name [math]\displaystyle{ \text{d2}^{7}_{5,5,5} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 13.9431
Weil height (log2 max(n, d)) 13.9546
Wilson height (sopfr(nd)) 30
Comma size small
Open this interval in xen-calc
English Wikipedia has an article on:

The starling comma or septimal semicomma, 126/125 (about 13.8 cents), is the superparticular 7-limit comma which is the difference between 36/35 (septimal quartertone) and 50/49 (jubilisma). In terms of just intervals, 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, 25/18) fall short of the 7/5 tritone, and the amount by which three 5/3's (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.

Temperaments

Tempering it out alone in the 7-limit leads to the starling temperament, and enables starling chords. See Starling family for the rank-3 temperament family where it is tempered out. See starling temperaments for a collection of rank-2 temperaments where it is tempered out.

See also

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