14/11: Difference between revisions

Line 6:

| 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 [[Neo-Gothic]] major third, as it falls between [[5/4]] and [[9/7]]. Indeed, it is the [[~~mediant|~~mediant]] ratio between those simpler intervals, as it is (5+9)/(4+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¢), which can be generated by stacking four [[3/2]] perfect fifths and [[octave-reduce|octave-reducing]].

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 [[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). 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¢), which can be generated by stacking four [[3/2]] perfect fifths and [[octave-reduce|octave-reducing]].

== See also ==

* [[11/7]] – its [[octave complement]]

* [[33/28]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[~~11/7]] -- its [[octave complement]]~~

* [[Gentle chords]]

* [[gentle chords]]

* [[List of root-3rd-P5 triads in JI]]

* [http://dkeenan.com/Music/NobleMediant.txt The Noble Mediant]

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

[[Category:11-limit]]

@@ Line 6: / Line 6: @@
 | 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 [[Neo-Gothic]] major third, as it falls between [[5/4]] and [[9/7]]. Indeed, it is the [[mediant|mediant]] ratio between those simpler intervals, as it is (5+9)/(4+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¢), which can be generated by stacking four [[3/2]] perfect fifths and [[octave-reduce|octave-reducing]].
+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 [[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). 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¢), which can be generated by stacking four [[3/2]] perfect fifths and [[octave-reduce|octave-reducing]].
 == See also ==
+* [[11/7]] – its [[octave complement]]
+* [[33/28]] – its [[fifth complement]]
 * [[Gallery of just intervals]]
-* [[11/7]] -- its [[octave complement]]
+* [[Gentle chords]]
-* [[gentle chords]]
 * [[List of root-3rd-P5 triads in JI]]
-* [http://dkeenan.com/Music/NobleMediant.txt The Noble Mediant]
+* [http://dkeenan.com/Music/NobleMediant.txt ''The Noble Mediant'' by Margo Schulter and David Keenan]
 [[Category:11-limit]]