7/5: Difference between revisions

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| Ratio = 7/5

| Monzo = 0 0 -1 1

| Cents = 582.51219

| Name = narrow tritone, Huygens' tritone

| 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 [[~~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]]. 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.

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.

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.

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]].

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* [[10/7]] – its [[octave 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:Over-5]]

@@ Line 8: / Line 8: @@
 | Ratio = 7/5
 | Monzo = 0 0 -1 1
 | Cents = 582.51219
-| Name = narrow tritone, <br>Huygens' tritone
+| 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 [[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]]. 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.
-/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.
+/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.
 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]].
@@ Line 25: / Line 26: @@
 * [[10/7]] – its [[octave 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:Over-5]]