14/11: Difference between revisions

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In [[11-limit]] [[~~Just~~ intonation]], '''14/11''' is a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th overtones of the [[~~OverToneSeries|~~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|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 ==

* [[Gallery of just intervals]]

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

* [[gentle chords]]

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

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

[[Category:11-limit]]

[[Category:Interval ratio]]

[[Category:Major third]]

[[Category:Supermajor]]

[[Category:Supermajor third]]

~~[[Category:Undecimal]]~~

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

[[Category:Third]]

[[Category:~~Interval~~]]

[[Category:Listen]]

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-In [[11-limit]] [[Just intonation]], '''14/11''' is a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th overtones of the [[OverToneSeries|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|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 ==
 * [[Gallery of just intervals]]
+* [[11/7]] -- its [[octave complement]]
 * [[gentle chords]]
 * [[List of root-3rd-P5 triads in JI]]
 * [http://dkeenan.com/Music/NobleMediant.txt The Noble Mediant]
+[[Category:11-limit]]
+[[Category:Interval ratio]]
 [[Category:Major third]]
-[[Category:Supermajor]]
+[[Category:Supermajor third]]
-[[Category:Undecimal]]
-[[Category:11-limit]]
 [[Category:Third]]
-[[Category:Interval]]
+[[Category:Listen]]