10/7: Difference between revisions

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{{Infobox Interval

| ~~Icon~~ = ~~[[File:ji_glyph_10_7.png|alt=ji glyph 10 7.png|148x118px|ji glyph 10 7.png]] <small><br/>JI Glyph</small>~~

| Name = high tritone, greater septimal tritone, Euler's tritone

| ~~Ratio~~ = ~~10/7~~

| Color name = ry4, ruyo 4th

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

~~| Cents = 617.48781~~

~~| Name = high tritone~~

| Sound = jid_10_7_pluck_adu_dr220.mp3

}}

~~Type~~: ~~Utonal~~

In [[7-limit]] [[just intonation]], '''10/7''' is a '''high [[tritone]]''' (or '''Euler's tritone''') measuring about 617.5¢. It has a similar sound to its inversion, [[7/5]], but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third ([[5/4]]) appears above the harmonic seventh ([[7/4]]), such as 4:6:7:10 – This particular chord is well-approximated in [[88cET]], which has a good approximation of 10/7, but no 7/5. It's well approximated by the Pythagorean augmented fourth [[729/512]], differing by [[5120/5103]].

In [[7~~-limit~~]] [[~~Just Intonation~~]], 10/7 ~~is a high tritone measuring about 617.5¢. It has a similar sound to its inversion,~~ [[7/5]]~~, but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third (~~[[~~5/4~~]]~~) appears above the harmonic seventh (~~[[7/4]]~~), such as 4:6:7:10. (This particular chord is well-approximated in~~ [[~~88cET~~]]~~, which has a good approximation~~ of ~~10/7 -- but no 7/5.)~~

While in the context of the [[harmonic seventh chord]], it is rightly recognized as a type of augmented fourth, it can also be argued on the basis of the fact that 10/7 interval is larger than 600 cents that it acts more as a type of diminished fifth than an augmented fourth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]].

== Approximation ==

== See also ==

* [[7/5]] – its [[octave complement]]

* [[21/20]] – its [[fifth complement]]

* [[Gallery of just intervals]]

~~:''See also [[Gallery of Just Intervals]]''~~

[[Category:Tritone]]

[[Category:Over-7 intervals]]

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

[[Category:~~interval]]~~

~~[[Category:just_interval]]~~

~~[[Category:ratio]]~~

~~[[Category:tritone~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon = [[File:ji_glyph_10_7.png|alt=ji glyph 10 7.png|148x118px|ji glyph 10 7.png]] <small><br/>JI Glyph</small>
+| Name = high tritone, greater septimal tritone, Euler's tritone
-| Ratio = 10/7
+| Color name = ry4, ruyo 4th
-| Monzo = 1 0 1 -1
-| Cents = 617.48781
-| Name = high tritone
 | Sound = jid_10_7_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Septimal tritone}}
-Type: Utonal
+In [[7-limit]] [[just intonation]], '''10/7''' is a '''high [[tritone]]''' (or '''Euler's tritone''') measuring about 617.5¢. It has a similar sound to its inversion, [[7/5]], but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third ([[5/4]]) appears above the harmonic seventh ([[7/4]]), such as 4:6:7:10 – This particular chord is well-approximated in [[88cET]], which has a good approximation of 10/7, but no 7/5. It's well approximated by the Pythagorean augmented fourth [[729/512]], differing by [[5120/5103]].
-In [[7-limit]] [[Just Intonation]], 10/7 is a high tritone measuring about 617.5¢. It has a similar sound to its inversion, [[7/5]], but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third ([[5/4]]) appears above the harmonic seventh ([[7/4]]), such as 4:6:7:10. (This particular chord is well-approximated in [[88cET]], which has a good approximation of 10/7 -- but no 7/5.)
+While in the context of the [[harmonic seventh chord]], it is rightly recognized as a type of augmented fourth, it can also be argued on the basis of the fact that 10/7 interval is larger than 600 cents that it acts more as a type of diminished fifth than an augmented fourth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]].
+== Approximation ==
+{{Interval edo approximation|10/7}}
+== See also ==
+* [[7/5]] – its [[octave complement]]
+* [[21/20]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
-:''See also [[Gallery of Just Intervals]]''
+[[Category:Tritone]]
+[[Category:Over-7 intervals]]
-[[Category:7-limit]]
-[[Category:interval]]
-[[Category:just_interval]]
-[[Category:ratio]]
-[[Category:tritone]]