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7/5: 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 = 7/5
: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-10 07:29:06 UTC</tt>.<br>
| en = 7/5
: The original revision id was <tt>591563482</tt>.<br>
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: 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">[[image:ji glyph 7 5.png width="147" height="116" caption="JI glyph for 7/5"]]
| Name = narrow tritone, lesser septimal tritone, Huygens' tritone
| Color name = zg5, zogu 5th
| Sound = jid_7_5_pluck_adu_dr220.mp3
}}
{{Wikipedia|Septimal tritone}}


**7/5**
In [[7-limit]] [[just intonation]], '''7/5''' is a '''narrow [[tritone]]''' (or '''Huygens' tritone''') measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[edo]]. It represents the difference between [[7/4]] and [[5/4]].
|0 0 -1 1&gt;
582.51219 cents
[[media type="file" key="jid_7_5_pluck_adu_dr220.mp3" width="240" height="20"]] [[file:xenharmonic/jid_7_5_pluck_adu_dr220.mp3|sound sample]]


In [[7-limit]] [[Just Intonation]], 7/5 is a narrow [[@http://en.wikipedia.org/wiki/Tritone|tritone]] measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo]] and every even-numbered [[EDO]]. It represents the difference between [[7_4|7/4]] and [[5_4|5/4]].
While in the context of the [[harmonic seventh chord]], it is rightly recognized as a type of diminished fifth, it can also be argued on the basis of the fact that 7/5 interval is smaller than 600 cents that it acts more as a type of augmented fourth than a diminished fifth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]]. This is one of the reasons why 7/4 can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.


7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the 4:5:6:7 tetrad that forms the basis of consonance in 7-limit JI. Its inversion is [[10_7|10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50_49|50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10_7|10/7]], usually to the 600¢ half-octave.
7/5 is notable for its low [[harmonic entropy]], and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the harmonic seventh chord that forms the basis of consonance in 7-limit JI. Its inversion is [[10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular]] interval [[50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7]], usually to the 600¢ half-octave.


Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;, or three "whole tones". Yet another is [[45_32|45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64_45|64/45]]). See also [[13_9|13/9]], [[18_13|18/13]], [[17_12|17/12]], [[24_17|24/17]], [[25_18|25/18]] and [[36_25|36/25]].
Another just tritone is [[729/512]] (611.7¢), and this is literally a tri-tone, since it is (9/8)<sup>3</sup>, or three "whole tones". Yet another is [[45/32]], about 590.2¢, which appears in the [[5-limit]] (inversion is [[64/45]]). See also [[13/9]], [[18/13]], [[17/12]], [[24/17]], [[25/18]] and [[36/25]].
== Approximation ==
{{Interval edo approximation|7/5}}
== See also ==


See: [[Gallery of Just Intervals]]</pre></div>
* [[10/7]] – its [[octave complement]]
<h4>Original HTML content:</h4>
* [[15/14]] – its [[fifth complement]]
<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;7_5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextLocalImageRule:1:&amp;lt;img src=&amp;quot;/file/view/ji%20glyph%207%205.png/545214466/147x116/ji%20glyph%207%205.png&amp;quot; alt=&amp;quot;JI glyph for 7/5&amp;quot; title=&amp;quot;JI glyph for 7/5&amp;quot; style=&amp;quot;height: 116px; width: 147px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="/file/view/ji%20glyph%207%205.png/545214466/147x116/ji%20glyph%207%205.png" alt="ji glyph 7 5.png" title="ji glyph 7 5.png" style="height: 116px; width: 147px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;JI glyph for 7/5&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1 --&gt;&lt;br /&gt;
* [[Gallery of just intervals]]
&lt;br /&gt;
 
&lt;strong&gt;7/5&lt;/strong&gt;&lt;br /&gt;
[[Category:Tritone]]
|0 0 -1 1&amp;gt;&lt;br /&gt;
[[Category:Over-5 intervals]]
582.51219 cents&lt;br /&gt;
[[Category:Taxicab-2 intervals]]
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/jid_7_5_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_7_5_pluck_adu_dr220.mp3&amp;amp;quot; width=&amp;amp;quot;240&amp;amp;quot; height=&amp;amp;quot;20&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_7_5_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_7_5_pluck_adu_dr220.mp3/513183034/jid_7_5_pluck_adu_dr220.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/jid_7_5_pluck_adu_dr220.mp3/513183034/jid_7_5_pluck_adu_dr220.mp3');"&gt;sound sample&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
In &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20Intonation"&gt;Just Intonation&lt;/a&gt;, 7/5 is a narrow &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tritone" rel="nofollow" target="_blank"&gt;tritone&lt;/a&gt; measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and every even-numbered &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;. It represents the difference between &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; and &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
7/5 is notable for its low &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt;, and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the 4:5:6:7 tetrad that forms the basis of consonance in 7-limit JI. Its inversion is &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;, which measures about 617.5¢, and these two septimal tritones differ by the &lt;a class="wiki_link" href="/superparticular"&gt;superparticular&lt;/a&gt; interval &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, about 35.0¢. Systems which temper out 50/49 will equate 7/5 and &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;, usually to the 600¢ half-octave.&lt;br /&gt;
&lt;br /&gt;
Another just tritone is the &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt; 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;, or three &amp;quot;whole tones&amp;quot;. Yet another is &lt;a class="wiki_link" href="/45_32"&gt;45/32&lt;/a&gt;, about 590.2¢, which appears in the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; (inversion is &lt;a class="wiki_link" href="/64_45"&gt;64/45&lt;/a&gt;). See also &lt;a class="wiki_link" href="/13_9"&gt;13/9&lt;/a&gt;, &lt;a class="wiki_link" href="/18_13"&gt;18/13&lt;/a&gt;, &lt;a class="wiki_link" href="/17_12"&gt;17/12&lt;/a&gt;, &lt;a class="wiki_link" href="/24_17"&gt;24/17&lt;/a&gt;, &lt;a class="wiki_link" href="/25_18"&gt;25/18&lt;/a&gt; and &lt;a class="wiki_link" href="/36_25"&gt;36/25&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
See: &lt;a class="wiki_link" href="/Gallery%20of%20Just%20Intervals"&gt;Gallery of Just Intervals&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/7/5"