10/7: Difference between revisions

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{| ~~class~~=~~"wikitable"~~

{{interwiki

|-

| de = 10/7

| en = 10/7

|-

| es =

| | ~~JI Glyph for 10/7~~

| ja =

|}

}}

{{Infobox Interval

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

| Color name = ry4, ruyo 4th

| Sound = jid_10_7_pluck_adu_dr220.mp3

}}

'''10/7'''

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]].

~~|1 0 1~~ -~~1>~~

~~617~~.~~48781 cents~~

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]]

~~Type: Utonal~~

[[Category:Tritone]]

[[Category:Over-7 intervals]]

[[~~File:jid_10_7_pluck_adu_dr220.mp3]] [[:File~~:~~jid_10_7_pluck_adu_dr220.mp3|sound sample~~]]

In [[7-limit|7-limit]] [[Just_intonation|Just Intonation]], 10/7 is a high tritone measuring about 617.5¢. It has a similar sound to its inversion, [[7/5|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|5/4]]) appears above the harmonic seventh ([[7/4|7/4]]), such as 4:~~6:7:10. (This particular chord is well-approximated in [[88cET|88cET]], which has a good approximation of 10/7 -~~- ~~but no~~ 7~~/5.)~~

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

~~[[Category:interval]]~~

~~[[Category:just_interval]]~~

~~[[Category:ratio]]~~

~~[[Category:tritone~~]]

@@ Line 1: / Line 1: @@
-{| class="wikitable"
+{{interwiki
-|-
+| de = 10/7
-| | [[File:ji_glyph_10_7.png|alt=ji glyph 10 7.png|148x118px|ji glyph 10 7.png]]
+| en = 10/7
-|-
+| es =
-| | JI Glyph for 10/7
+| ja =
-|}
+}}
+{{Infobox Interval
+| Name = high tritone, greater septimal tritone, Euler's tritone
+| Color name = ry4, ruyo 4th
+| Sound = jid_10_7_pluck_adu_dr220.mp3
+}}
+{{Wikipedia|Septimal tritone}}
-'''10/7'''
+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]].
-|1 0 1 -1&gt;
-.48781 cents
+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]]
-Type: Utonal
+[[Category:Tritone]]
+[[Category:Over-7 intervals]]
-[[File:jid_10_7_pluck_adu_dr220.mp3]] [[:File:jid_10_7_pluck_adu_dr220.mp3|sound sample]]
-In [[7-limit|7-limit]] [[Just_intonation|Just Intonation]], 10/7 is a high tritone measuring about 617.5¢. It has a similar sound to its inversion, [[7/5|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|5/4]]) appears above the harmonic seventh ([[7/4|7/4]]), such as 4:6:7:10. (This particular chord is well-approximated in [[88cET|88cET]], which has a good approximation of 10/7 -- but no 7/5.)
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:7-limit]]
-[[Category:interval]]
-[[Category:just_interval]]
-[[Category:ratio]]
-[[Category:tritone]]