7/5: Difference between revisions

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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 [[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]].

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]], 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 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 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)<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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 {{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 [[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]].
-/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]], 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 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.
+/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)<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]].