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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>
| | | de = 7/5 |
| : 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 comment was: <tt></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}} |
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| Another just tritone is the [[3-limit]] 729/512, 611.7¢, and this is literally a tritone, since it is (9/8)<span style="vertical-align: super;">3</span>. 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]]. |
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| 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>
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| <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>7_5</title></head><body>In <a class="wiki_link" href="/7-limit">7-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 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 <a class="wiki_link" href="/12edo">12edo</a> and every even-numbered <a class="wiki_link" href="/EDO">EDO</a>. It represents the difference between <a class="wiki_link" href="/7_4">7/4</a> and <a class="wiki_link" href="/5_4">5/4</a>. 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 <a class="wiki_link" href="/10_7">10/7</a>, which measures about 617.5¢, and these two septimal tritones differ by the <a class="wiki_link" href="/superparticular">superparticular</a> interval <a class="wiki_link" href="/50_49">50/49</a>, about 35.0¢. Systems which temper out 50/49 will equate 7/5 and 10/7, usually to the 600¢ half-octave.<br />
| | 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. |
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| Another just tritone is the <a class="wiki_link" href="/3-limit">3-limit</a> 729/512, 611.7¢, and this is literally a tritone, since it is (9/8)<span style="vertical-align: super;">3</span>. And yet another is <a class="wiki_link" href="/45_32">45/32</a>, about 590.2¢, which appears in the <a class="wiki_link" href="/5-limit">5-limit</a>. See also <a class="wiki_link" href="/13_9">13/9</a>, <a class="wiki_link" href="/18_13">18/13</a>, <a class="wiki_link" href="/17_12">17/12</a> and <a class="wiki_link" href="/24_17">24/17</a>.<br /> | | 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]]. |
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| | == Approximation == |
| See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | | {{Interval edo approximation|7/5}} |
| | == See also == |
| | |
| | * [[10/7]] – its [[octave complement]] |
| | * [[15/14]] – its [[fifth complement]] |
| | * [[Gallery of just intervals]] |
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| | [[Category:Tritone]] |
| | [[Category:Over-5 intervals]] |
| | [[Category:Taxicab-2 intervals]] |