7/5: Difference between revisions

Wikispaces>Andrew_Heathwaite
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-28 20:21:44 UTC</tt>.<br>
| en = 7/5
: The original revision id was <tt>259406376</tt>.<br>
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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">In [[7-limit]] [[Just Intonation]], 7/5 is a narrow 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]]. It is often reported to sound more consonant than the half-octave tritone, and 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, usually to the 600¢ half-octave.
| Name = narrow tritone, lesser septimal tritone, Huygens' tritone
| Color name = zg5, zogu 5th
| Sound = jid_7_5_pluck_adu_dr220.mp3
}}
{{Wikipedia|Septimal tritone}}


Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tritone, since it is (9/8)&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;. And yet another is [[45_32|45/32]], about 590.2¢, which appears in the [[5-limit]]. See also [[13_9|13/9]], [[18_13|18/13]], [[17_12|17/12]] and [[24_17|24/17]].
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]].  


See: [[Gallery of Just Intervals]]</pre></div>
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.
<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;7_5&lt;/title&gt;&lt;/head&gt;&lt;body&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 tritone 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;. It is often reported to sound more consonant than the half-octave tritone, and 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 10/7, usually to the 600¢ half-octave.&lt;br /&gt;
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.
&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 tritone, since it is (9/8)&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;. And 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;. 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; and &lt;a class="wiki_link" href="/24_17"&gt;24/17&lt;/a&gt;.&lt;br /&gt;
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]].
&lt;br /&gt;
== Approximation ==
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>
{{Interval edo approximation|7/5}}
== See also ==
 
* [[10/7]] – its [[octave complement]]
* [[15/14]] – its [[fifth complement]]
* [[Gallery of just intervals]]
 
[[Category:Tritone]]
[[Category:Over-5 intervals]]
[[Category:Taxicab-2 intervals]]
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