11/7: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = undecimal minor sixth, pentacircle minor sixth

~~| Ratio = 11/7~~

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

~~| Cents = 782.49204~~

| Name = undecimal minor sixth, ~~ undecimal augmented fifth~~

| Color name = 1or5, loru 5th

~~| FJS name = P5117~~

| Sound = jid_11_7_pluck_adu_dr220.mp3

}}

In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', measuring about 782.5¢. It is the inversion of [[14/11]], the ~~undecimal~~ major third.

In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5 [[cent]]s. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].

~~11/7 is flat of the Pythagorean minor sixth of~~ [[~~128/81~~]] ~~(about 792.2¢) by a pentacircle comma~~, [[~~896/891~~]]~~. It~~ is ~~flat of the 5-limit minor sixth of~~ [[8/5]] ~~(about 813.7¢) by~~ [[56/55]]~~. It~~ is ~~sharp of the 7-limit subminor sixth~~ of [[14/9]] ~~(about 764.9¢) by~~ a ~~mothwellsma,~~ [[99/98]]~~. And finally~~, ~~it is sharp~~ of the ~~classic augmented fifth of~~ [[~~25/16~~]] ~~(about 772~~.~~6¢) by a valinorsma~~, [[~~176/175~~]].

In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].

11/~~7 is~~ [[22/21]] (about 80.5¢) ~~above~~ the [[3/2]] ~~perfect fifth~~, ~~allowing~~ the ~~possibility~~ of ~~a resolution down~~ by a ~~step from~~ 11/7 to 3/2.

However, it is only flat of the [[128/81|Pythagorean minor sixth]] (about 792.2{{c}}) by a [[896/891|pentacircle comma (896/891)]], which makes it function sometimes as a minor sixth, hence the names. For one thing, as it is 22/21 (about 80.5{{c}}) above the perfect fifth, it can be resolved down by a step to the perfect fifth.

It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7{{c}}) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9{{c}}) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6{{c}}) by a valinorsma, [[176/175]].

== Approximation ==

== Proximity with acoustic pi ==

[[22/7]], one octave higher, is a fraction convergent to the continued fraction of acoustic pi. Such is the exactness, that 22/7π is an [[unnoticeable comma]] of only 0.7 cents.

== See also ==

* [[14/11]] – its octave complement

* [[14/11]] – its [[octave complement]]

* [[21/11]] – its [[twelfth complement]]

* [[Ed11/7]]

* [[Gallery of just intervals]]

* [[:File:Ji-11-7-csound-foscil-220hz.mp3]] – another sound example

~~[[Category:11-limit]]~~

[[Category:Over-7 intervals]]

[[Category:Over-7]]

[[Category:Sixth]]

[[Category:Minor sixth]]

[[Category:Subminor sixth]]

[[Category:Pentacircle]]

[[Category:Taxicab-2 intervals]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = undecimal minor sixth, pentacircle minor sixth
-| Ratio = 11/7
-| Monzo = 0 0 0 -1 1
-| Cents = 782.49204
-| Name = undecimal minor sixth, <br>undecimal augmented fifth
 | Color name = 1or5, loru 5th
-| FJS name = P5<sup>11</sup><sub>7</sub>
 | Sound = jid_11_7_pluck_adu_dr220.mp3
 }}
-In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', measuring about 782.5¢. It is the inversion of [[14/11]], the undecimal major third.
+In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5 [[cent]]s. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]].
-/7 is flat of the Pythagorean minor sixth of [[128/81]] (about 792.2¢) by a pentacircle comma, [[896/891]]. It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7¢) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9¢) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6¢) by a valinorsma, [[176/175]].
+In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. It functions as such in voicings of the harmonic eleventh chord, [[4:5:6:7:9:11]].
-/7 is [[22/21]] (about 80.5¢) above the [[3/2]] perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2.
+However, it is only flat of the [[128/81|Pythagorean minor sixth]] (about 792.2{{c}}) by a [[896/891|pentacircle comma (896/891)]], which makes it function sometimes as a minor sixth, hence the names. For one thing, as it is 22/21 (about 80.5{{c}}) above the perfect fifth, it can be resolved down by a step to the perfect fifth.
+It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7{{c}}) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9{{c}}) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6{{c}}) by a valinorsma, [[176/175]].
+== Approximation ==
+{{Interval edo approximation|11/7}}
+== Proximity with acoustic pi ==
+[[22/7]], one octave higher, is a fraction convergent to the continued fraction of acoustic pi. Such is the exactness, that 22/7π is an [[unnoticeable comma]] of only 0.7 cents.
 == See also ==
-* [[14/11]] – its octave complement
+* [[14/11]] – its [[octave complement]]
+* [[21/11]] – its [[twelfth complement]]
+* [[Ed11/7]]
 * [[Gallery of just intervals]]
 * [[:File:Ji-11-7-csound-foscil-220hz.mp3]] – another sound example
-[[Category:11-limit]]
+[[Category:Over-7 intervals]]
-[[Category:Over-7]]
 [[Category:Sixth]]
 [[Category:Minor sixth]]
 [[Category:Subminor sixth]]
 [[Category:Pentacircle]]
+[[Category:Taxicab-2 intervals]]