28/27: Difference between revisions

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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, small septimal chroma, subminor second, septimal minor second, septimal subminor second, trienstonic comma

~~: This revision was by author [[User:spt3125~~|~~spt3125]] and made on <tt>2014~~-~~06-30 20:45:11 UTC</tt>.<br>~~

| Color name = z2, zo 2nd

~~: The original revision id was <tt>515316436</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>~~

~~<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">**28/27**

|~~2 -3 0 1>~~

~~62.9609 cents~~

~~[[media type~~=~~"file" key="jid_28_27_pluck_adu_dr220.mp3"]] [[file:xenharmonic/~~jid_28_27_pluck_adu_dr220.mp3|~~sound sample]]~~

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.

The [[superparticular]] interval '''28/27''', '''septimal third-tone''' has the seventh [[triangular number]] as a numerator and 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 [[28/15]].

~~[[http://en.wikipedia.org/wiki/Septimal_third-tone]]</pre></div>~~

== Terminology ==

~~<h4>Original HTML content:</h4>~~

28/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz–Ellis notation]], and the [[Functional Just System]], viewed as the [[256/243|Pythagorean limma (256/243)]] altered by the [[64/63|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is 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.

~~<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>28_27</title></head><body><strong>~~28/27~~<~~/~~strong><br~~ /~~>~~

|~~2 -3 0 1&gt;<br~~ /~~>~~

== Approximation ==

~~62.9609 cents<br~~ /~~>~~

This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.

~~<embed src~~=~~"/s/mediaplayer.swf" pluginspage~~=~~"http:~~/~~/www~~.~~macromedia~~.~~com/go/getflashplayer" type~~=~~"application/x-shockwave-flash" quality~~=~~"high" width~~=~~"240" height~~=~~"20" wmode~~=~~"transparent" flashvars~~=~~"file~~=~~http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_28_27_pluck_adu_dr220.mp3?file_extension~~=~~mp3&autostart~~=~~false&repeat~~=~~false&showdigits=true&showfsbutton=false&width=240&height=20"></embed> <~~a ~~href="http://xenharmonic.wikispaces.com/file/view/jid_28_27_pluck_adu_dr220.mp3/515315664/jid_28_27_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink~~('~~http:~~//~~xenharmonic~~.~~wikispaces.com~~/~~file~~/~~view/jid_28_27_pluck_adu_dr220~~.~~mp3~~/~~515315664/jid_28_27_pluck_adu_dr220.mp3~~')~~;">sound sample<~~/~~a><br />~~

~~<br />~~

== Temperaments ==

~~The septimal chroma or septimal third-tone is the <a class~~=~~"wiki_link" href~~=~~"/superparticular">superparticular</a> 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.<br />~~

If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic temperaments'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out.

~~<br />~~

~~<a class="wiki_link_ext" href="http~~:~~//en.wikipedia.org/wiki/Septimal_third-~~tone~~" rel="nofollow">http~~:~~//en.wikipedia.org/wiki/Septimal_third-tone</a></body></html></pre></div>~~

== 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]]

* [[Trienstonisma]], 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]]

@@ Line 1: / Line 1: @@
-<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, small septimal chroma, subminor second, septimal minor second, septimal subminor second, trienstonic comma
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2014-06-30 20:45:11 UTC</tt>.<br>
+| Color name = z2, zo 2nd
-: The original revision id was <tt>515316436</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">**28/27**
-|2 -3 0 1&gt;
-.9609 cents
-[[media type="file" key="jid_28_27_pluck_adu_dr220.mp3"]] [[file:xenharmonic/jid_28_27_pluck_adu_dr220.mp3|sound sample]]
-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.
+The [[superparticular]] interval '''28/27''', '''septimal third-tone''' has the seventh [[triangular number]] as a numerator and 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 [[28/15]].
-[[http://en.wikipedia.org/wiki/Septimal_third-tone]]</pre></div>
+== Terminology ==
-<h4>Original HTML content:</h4>
+/27 is traditionally called the '''small septimal chroma''', perhaps for its proximity (and conflation in systems like [[septimal meantone]]) with the classic chroma, [[25/24]]. However, it is a ''[[diatonic semitone]]'' in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz–Ellis notation]], and the [[Functional Just System]], viewed as the [[256/243|Pythagorean limma (256/243)]] altered by the [[64/63|septimal comma (64/63)]]. Hence, it may be described as the '''septimal minor second''' or '''septimal subminor second''' if treated as an interval in its own right. This is 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.
-<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;&lt;strong&gt;28/27&lt;/strong&gt;&lt;br /&gt;
-|2 -3 0 1&amp;gt;&lt;br /&gt;
+== Approximation ==
-.9609 cents&lt;br /&gt;
+This interval is very accurately approximated by [[19edo]] (1\19), and hence the [[enneadecal]] temperament.
-&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_28_27_pluck_adu_dr220.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;jid_28_27_pluck_adu_dr220.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fjid_28_27_pluck_adu_dr220.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt; &lt;a href="http://xenharmonic.wikispaces.com/file/view/jid_28_27_pluck_adu_dr220.mp3/515315664/jid_28_27_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_28_27_pluck_adu_dr220.mp3/515315664/jid_28_27_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
+== Temperaments ==
-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;
+If treated as a [[comma]] to be tempered out, 28/27 may be called the '''trienstonic comma''', which leads to the '''trienstonic temperaments'''. See [[Trienstonic clan]] for the rank-2 clan of temperaments where it is tempered out.
-&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>
+== 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]]
+* [[Trienstonisma]], 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]]
+{{Todo| improve synopsis }}