14/11: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = undecimal major third, pentacircle major third

~~| Ratio = 14/11~~

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

~~| Cents = 417.50796~~

| Name = undecimal major third

| Color name = 1uz4, luzo 4th

~~| FJS name = P4<sup>7</sup><sub>11</sub>~~

| Sound = jid_14_11_pluck_adu_dr220.mp3

}}

In [[11-limit]] [[just intonation]], '''14/11''' is the '''~~undecimal~~ major third''', a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th ~~overtones~~ of the [[harmonic series]] and ~~appears~~ in ~~chords such as 8~~:11~~:14~~, the ~~principal triad~~ of [[~~Orgonia~~|~~orgone~~]] ~~temperament~~. 14/11 ~~can also function as a~~ [[neogothic|~~neo-Gothic~~]] ~~major third, as it~~ falls between [[5/4]] and [[9/7]]~~. Indeed~~, it is the [[mediant]] ratio between those simpler intervals, as it is (5+9)/(4+7)~~, and~~ is [[56/55]] sharp of [[5/4]], [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5+14)/(4+11) = [[19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14+9)/(11+7) = [[23/18]], about 424.~~4¢. Also in this region is the Pythagorean ([[3-limit]]~~) ~~major third of [[81/64]] (about 407~~.~~8¢), of which~~ 14/11 ~~is sharp by [[896/891]]. The fact that this interval~~ functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth"- a cross between a sixth and a seventh- as opposed to merely a subminor seventh.

In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5 [[cent]]s. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].

In many notation systems based on the [[5L 2s|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3|perfect fourth (4/3)]] minus 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]].

However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891|pentacircle comma (896/891)]], which makes it function sometimes as a major third, hence the names. Indeed, 14/11 is the simplest [[neogothic major and minor|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. As such, it is used to form the gentle major triad, [[22:28:33]]<ref group="note">This is a [[minor minthmic chords|minor minthmic chord]] where 14/11 and [[13/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:28:32 ([[11:14:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of [[3/2]]; 11:14:16 can be voiced as 8:11:14 however, which is less dissonant. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}). The fact that 14/11 functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.

== Approximation ==

== See also ==

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* [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant''] by Margo Schulter and David Keenan

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

== Notes ==

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

[[Category:Third]]

[[Category:Major third]]

[[Category:Supermajor third]]

~~[[Category:Third]]~~

[[Category:Over-11 intervals]]

~~[[Category:Listen]]~~

[[Category:Over-11]]

[[Category:Pentacircle]]

[[Category:Gentle]]

[[Category:Neo-gothic]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = undecimal major third, pentacircle major third
-| Ratio = 14/11
-| Monzo = 1 0 0 1 -1
-| Cents = 417.50796
-| Name = undecimal major third
 | Color name = 1uz4, luzo 4th
-| FJS name = P4<sup>7</sup><sub>11</sub>
 | Sound = jid_14_11_pluck_adu_dr220.mp3
 }}
-In [[11-limit]] [[just intonation]], '''14/11''' is the '''undecimal major third''', a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th overtones of the [[harmonic series]] and appears in chords such as 8:11:14, the principal triad of [[Orgonia|orgone]] temperament. 14/11 can also function as a [[neogothic|neo-Gothic]] major third, as it falls between [[5/4]] and [[9/7]]. Indeed, it is the [[mediant]] ratio between those simpler intervals, as it is (5+9)/(4+7), and is [[56/55]] sharp of [[5/4]], [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5+14)/(4+11) = [[19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14+9)/(11+7) = [[23/18]], about 424.4¢. Also in this region is the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8¢), of which 14/11 is sharp by [[896/891]].  The fact that this interval functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth"- a cross between a sixth and a seventh- as opposed to merely a subminor seventh.
+In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''pentacircle major third''', a major or supermajor third of about 417.5 [[cent]]s. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]].
+In many notation systems based on the [[5L 2s|diatonic]] [[chain-of-fifths notation]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is a [[4/3|perfect fourth (4/3)]] minus 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]].
+However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8{{c}}) by a [[896/891|pentacircle comma (896/891)]], which makes it function sometimes as a major third, hence the names. Indeed, 14/11 is the simplest [[neogothic major and minor|neogothic major third]]. It falls between [[5/4]] and [[9/7]], and is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7). It is [[56/55]] sharp of [[5/4]], and [[99/98]] flat of [[9/7]]. As such, it is used to form the gentle major triad, [[22:28:33]]<ref group="note">This is a [[minor minthmic chords|minor minthmic chord]] where 14/11 and [[13/11]] sum to a perfect fifth. Shown here is the simplest JI representation. </ref>. Compare this to 22:28:32 ([[11:14:16]]), which has the much more dissonant [[16/11]] as the outside interval in place of [[3/2]]; 11:14:16 can be voiced as 8:11:14 however, which is less dissonant. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2{{c}}) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4{{c}}). The fact that 14/11 functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh – as opposed to merely a subminor seventh.
+== Approximation ==
+{{Interval edo approximation|14/11}}
 == See also ==
@@ Line 22: / Line 24: @@
 * [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant''] by Margo Schulter and David Keenan
-[[Category:11-limit]]
+== Notes ==
-[[Category:Interval ratio]]
+<references group="note"/>
+[[Category:Third]]
 [[Category:Major third]]
 [[Category:Supermajor third]]
-[[Category:Third]]
+[[Category:Over-11 intervals]]
-[[Category:Listen]]
-[[Category:Over-11]]
 [[Category:Pentacircle]]
 [[Category:Gentle]]
 [[Category:Neo-gothic]]