7/5: Difference between revisions

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{{Infobox Interval

~~| Ratio = 7/5~~

| Name = narrow tritone, lesser septimal tritone, Huygens' tritone

~~| Monzo = 0 0 -1 1~~

~~| Cents = 582.51219~~

| Name = narrow tritone, ~~ ~~lesser septimal tritone, ~~ ~~Huygens' tritone

| Color name = zg5, zogu 5th

~~| FJS name = d575~~

| Sound = jid_7_5_pluck_adu_dr220.mp3

}}

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.

~~Another just tritone~~ is ~~the~~ [[~~3-limit~~]] ~~729/512, 611.7¢~~, and ~~this~~ is ~~literally a tri~~-~~tone, since~~ it ~~is (9/8)3, 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)3, 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 ==

== See also ==

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* [[Gallery of just intervals]]

~~[[Category:7-limit]]~~

[[Category:Tritone]]

[[Category:Over-5]]

[[Category:Over-5 intervals]]

[[Category:Taxicab-2 intervals]]

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 }}
 {{Infobox Interval
-| Ratio = 7/5
+| Name = narrow tritone, lesser septimal tritone, Huygens' tritone
-| Monzo = 0 0 -1 1
-| Cents = 582.51219
-| Name = narrow tritone, <br>lesser septimal tritone, <br>Huygens' tritone
 | Color name = zg5, zogu 5th
-| FJS name = d5<sup>7</sup><sub>5</sub>
 | 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 [[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.
-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]].
+/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 ==
@@ Line 28: / Line 27: @@
 * [[Gallery of just intervals]]
-[[Category:7-limit]]
 [[Category:Tritone]]
-[[Category:Over-5]]
+[[Category:Over-5 intervals]]
+[[Category:Taxicab-2 intervals]]