10/7: Difference between revisions

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{{Infobox Interval

~~| Ratio = 10/7~~

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

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

~~| Cents = 617.48781~~

| Name = high tritone, ~~ ~~Euler's tritone

| Color name = ry4, ruyo 4th

~~| FJS name = A457~~

| Sound = jid_10_7_pluck_adu_dr220.mp3

}}

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. ~~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 heptatonic scale that demonstrates [[~~Wikipedia:Rothenberg propriety|Rothenberg propriety~~]].

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]].

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]]~~

* [[Gallery of just intervals]]

* [[Wikipedia:Septimal_tritone|Septimal tritone - Wikipedia]]

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

~~[[Category:Interval ratio]]~~

~~[[Category:Just interval]]~~

[[Category:Tritone]]

[[Category:Over-7]]

[[Category:Over-7 intervals]]

~~[[Category:Pages with internal sound examples~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 10/7
+| Name = high tritone, greater septimal tritone, Euler's tritone
-| Monzo = 1 0 1 -1
-| Cents = 617.48781
-| Name = high tritone, <br>Euler's tritone
 | Color name = ry4, ruyo 4th
-| FJS name = A4<sup>5</sup><sub>7</sub>
 | Sound = jid_10_7_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Septimal tritone}}
-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. 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 heptatonic scale that demonstrates [[Wikipedia:Rothenberg propriety|Rothenberg propriety]].
+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]].
+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]]
+* [[Gallery of just intervals]]
-* [[Wikipedia:Septimal_tritone|Septimal tritone - Wikipedia]]
-[[Category:7-limit]]
-[[Category:Interval ratio]]
-[[Category:Just interval]]
 [[Category:Tritone]]
-[[Category:Over-7]]
+[[Category:Over-7 intervals]]
-[[Category:Pages with internal sound examples]]