7/5: Difference between revisions

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{{Infobox Interval

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

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

| Color name = zg5, zogu 5th

| Sound = jid_7_5_pluck_adu_dr220.mp3

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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]].

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)]].

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.

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.

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]].

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 ==

== See also ==

@@ Line 6: / Line 6: @@
 }}
 {{Infobox Interval
-| Name = narrow tritone, lesser septimal tritone, Huygens' tritone
+| Name = narrow tritone, lesser septimal tritone, Huygens' tritone, septimal diminished fifth
 | Color name = zg5, zogu 5th
 | Sound = jid_7_5_pluck_adu_dr220.mp3
@@ Line 12: / Line 12: @@
 {{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]].
+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)]].
-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.
+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.
 /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]].
+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}}
+{{Interval edo approximation|7/5}}
 == See also ==