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28/27: Difference between revisions

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**Imported revision 245078677 - Original comment: **
Rewrite; simplify essentially duplicate names; - "small septimal chroma", not attested anywhere
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox Interval
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = septimal third-tone, septimal minor second, subminor second, trienstonic comma
: This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-09 15:10:21 UTC</tt>.<br>
| Color name = z2, zo 2nd
: The original revision id was <tt>245078677</tt>.<br>
| Sound = jid_28_27_pluck_adu_dr220.mp3
: The revision comment was: <tt></tt><br>
| Comma = yes
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>
{{Wikipedia| Septimal third tone }}
<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 septimal chroma or septimal third-tone is the [[superparticular]] interval 28/27, which has the seventh triangular number as a numerator and which is the difference between 15/14 and 10/9, 9/8 and 7/6, 9/7 and 4/3, 3/2 and 14/9, 12/7 and 16/9 and 9/5 and 28/25.


[[http://en.wikipedia.org/wiki/Septimal_third-tone]]</pre></div>
In [[7-limit]] [[just intonation]], '''28/27''', measuring about 63.0 [[cent]]s, is conventionally known as the '''septimal third-tone'''. It arises as the difference between [[15/14]] and [[10/9]], between [[9/8]] and [[7/6]], between [[9/7]] and [[4/3]], between [[3/2]] and [[14/9]], between [[12/7]] and [[16/9]], and between [[9/5]] and [[28/15]]. Since it is flat of the [[Pythagorean limma]] by a [[64/63|septimal comma (64/63)]], it may be called the '''septimal (sub)minor second''' if treated as an interval in its own right, analogous to the septimal major second [[8/7]], which has the same relationship with [[9/8]], and such classification suggests the function of a strong leading tone added to the traditional harmony.
<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;28_27&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The septimal chroma or septimal third-tone is the &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; interval 28/27, which has the seventh triangular number as a numerator and which is the difference between 15/14 and 10/9, 9/8 and 7/6, 9/7 and 4/3, 3/2 and 14/9, 12/7 and 16/9 and 9/5 and 28/25.&lt;br /&gt;
Finally, since it is a [[superparticular ratio]] which has the seventh [[triangular number]] as a numerator, it a [[triangle-particular]] ratio with factorization ([[49/48]])⋅(64/63).  
&lt;br /&gt;
 
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_third-tone" rel="nofollow"&gt;http://en.wikipedia.org/wiki/Septimal_third-tone&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
== Approximation ==
This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
 
{{Interval edo approximation|28/27}}
 
== Temperaments ==
If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic''' temperament.
 
See [[Trienstonic clan]] for the rank-2 [[clan]] of temperaments where it is tempered out.
 
== Notation ==
=== Sagittal notation ===
In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal| (|\ }} and is called the '''7 large diesis''', or '''7L''' for short, because the simplest interval it notates is 7/1 (equivalently, 7/4), as for example in C–A{{nbhsp}}{{sagittal | (|\ }}. The primary role of {{sagittal| (|\ }} is [[8505/8192 #Sagittal notation|8505/8192]] (35L). The downward version is called '''1/7L''' or '''7L down''' and is represented (in a secondary role) by {{sagittal| (!/ }}.
 
== See also ==
* [[27/14]] – its [[octave complement]]
* [[81/56]] – its [[fifth complement]]
* [[9/7]] – its [[fourth complement]]
* [[List of superparticular intervals]]
* [[Gallery of just intervals]]
* [[Trienstonoschisma]], the difference by which a stack of five 28/27's falls short of [[6/5]]
 
[[Category:Second]]
[[Category:Semitone]]
[[Category:Third tone]]
[[Category:Chroma]]
[[Category:Trienstonic]]
[[Category:Commas named for the intervals they stack]]
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