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{{Infobox Interval
{{Infobox Interval
| JI glyph = [[File:ji_glyph_7_5.png|x48px]]
| Name = narrow tritone, lesser septimal tritone, Huygens' tritone, septimal diminished fifth
| Ratio = 7/5
| Monzo = 0 0 -1 1
| Cents = 582.51219
| Name = narrow tritone, <br>Huygens' tritone
| Color name = zg5, zogu 5th
| Color name = zg5, zogu 5th
| FJS name = d5<sup>7</sup><sub>5</sub>
| Sound = jid_7_5_pluck_adu_dr220.mp3
| Sound = jid_7_5_pluck_adu_dr220.mp3
}}
}}
{{Wikipedia|Septimal tritone}}


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]]. 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 heptatonic scale that demonstrates [[Wikipedia:Rothenberg propriety|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.
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]]. It being classified as a diminished fifth in both [[Functional Just System|FJS]] and [[Helmholtz-Ellis notation|HEJI]], it can also be named the '''septimal diminished fifth''', as found in the context [[5:6:7|septimal diminished triad (5:6:7)]] and [[4:5:6:7|harmonic seventh chord. (4:5:6:7)]].  


7/5 is notable for its low [[Harmonic Entropy|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]], 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.
While found contextually as a diminished fifth in JI harmony, in some situations it can actually be found as more of a augmented fourth – 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.


Another just tritone is the [[3-limit]] 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]].
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 [[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 also ==


* [[10/7]] – its [[octave complement]]
* [[10/7]] – its [[octave complement]]
* [[15/14]] – its [[fifth complement]]
* [[15/14]] – its [[fifth complement]]
* [[Gallery of Just Intervals]]
* [[Gallery of just intervals]]
* [[Wikipedia:Septimal_tritone|Septimal tritone - Wikipedia]]


[[Category:7-limit]]
[[Category:interval]]
[[Category:just_interval]]
[[Category:ratio]]
[[Category:Tritone]]
[[Category:Tritone]]
[[Category:Over-5]]
[[Category:Over-5 intervals]]
[[Category:Taxicab-2 intervals]]
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