7/5: Difference between revisions

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~~[[:de:~~7/5|~~Deutsch]]<~~/~~span>~~

{{interwiki

| de = 7/5

| en = 7/5

| es =

| ja =

}}

{{Infobox Interval

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

| Color name = zg5, zogu 5th

| Sound = jid_7_5_pluck_adu_dr220.mp3

}}

~~{| class="wikitable"~~

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]].

|-

|-

~~| | JI glyph for~~ 7/5

|}

~~'''~~7/5~~'''~~

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.

|~~0 0 -1 1>~~

~~582~~.~~51219 cents~~

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.

[[~~File:jid_7_5_pluck_adu_dr220~~.~~mp3~~]] [[~~:File:jid_7_5_pluck_adu_dr220~~.~~mp3|sound sample~~]]

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 ==

In [[7~~-limit|7-limit~~]] [[~~Just_intonation|Just Intonation]], 7/5 is a narrow [http://en.wikipedia.org/wiki/Tritone tritone] measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-~~octave ~~(square root of 2) tritone of [[12edo|12edo~~]] ~~and every even-numbered~~ [[~~EDO|EDO~~]]~~. It represents the difference between~~ [[~~7/4|7/4~~]] ~~and~~ [[~~5/4|5/4~~]].

* [[10/7]] – its [[octave complement]]

* [[15/14]] – its [[fifth complement]]

* [[Gallery of just intervals]]

~~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|10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular|superparticular]] interval [[50/49|50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7|10/7]]~~, usually to the 600¢ half-octave.~~

[[Category:Tritone]]

[[Category:Over-5 intervals]]

~~Another just tritone is the~~ [[~~3-limit|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|45/32]], about 590.2¢, which appears in the [[5~~-~~limit|~~5~~-limit]] (inversion is [[64/45|64/45]]). See also [[13/9|13/9]], [[18/13|18/13]], [[17/12|17/12]], [[24/17|24/17]], [[25/18|25/18]] and [[36/25|36/25~~]].

[[Category:Taxicab-2 intervals]]

~~See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~ [[Category:7-~~limit]]~~

~~[[Category:interval]]~~

~~[[Category:just_interval]]~~

~~[[Category:ratio~~]]

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-<span style="display: block; text-align: right;">[[:de:7/5|Deutsch]]</span>
+{{interwiki
+| de = 7/5
+| en = 7/5
+| es =
+| ja =
+}}
+{{Infobox Interval
+| Name = narrow tritone, lesser septimal tritone, Huygens' tritone
+| Color name = zg5, zogu 5th
+| Sound = jid_7_5_pluck_adu_dr220.mp3
+}}
+{{Wikipedia|Septimal tritone}}
-{| class="wikitable"
+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]].
-|-
-| | [[File:ji_glyph_7_5.png|alt=ji glyph 7 5.png|147x116px|ji glyph 7 5.png]]
-|-
-| | JI glyph for 7/5
-|}
-'''7/5'''
+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.
-|0 0 -1 1&gt;
-.51219 cents
+/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.
-[[File:jid_7_5_pluck_adu_dr220.mp3]] [[:File:jid_7_5_pluck_adu_dr220.mp3|sound sample]]
+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 ==
-In [[7-limit|7-limit]] [[Just_intonation|Just Intonation]], 7/5 is a narrow [http://en.wikipedia.org/wiki/Tritone tritone] measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of [[12edo|12edo]] and every even-numbered [[EDO|EDO]]. It represents the difference between [[7/4|7/4]] and [[5/4|5/4]].
+* [[10/7]] – its [[octave complement]]
+* [[15/14]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
-/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|10/7]], which measures about 617.5¢, and these two septimal tritones differ by the [[superparticular|superparticular]] interval [[50/49|50/49]], about 35.0¢. Systems which temper out 50/49 will equate 7/5 and [[10/7|10/7]], usually to the 600¢ half-octave.
+[[Category:Tritone]]
+[[Category:Over-5 intervals]]
-Another just tritone is the [[3-limit|3-limit]] 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)<span style="vertical-align: super;">3</span>, or three "whole tones". Yet another is [[45/32|45/32]], about 590.2¢, which appears in the [[5-limit|5-limit]] (inversion is [[64/45|64/45]]). See also [[13/9|13/9]], [[18/13|18/13]], [[17/12|17/12]], [[24/17|24/17]], [[25/18|25/18]] and [[36/25|36/25]].
+[[Category:Taxicab-2 intervals]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:7-limit]]
-[[Category:interval]]
-[[Category:just_interval]]
-[[Category:ratio]]