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 ==
== See also ==
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[11/7]] -- its [[octave complement]]
* [[gentle chords]]
* [[gentle chords]]
* [[List of root-3rd-P5 triads in JI]]
* [[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]


[[Category:11-limit]]
[[Category:Interval ratio]]
[[Category:Major third]]
[[Category:Major third]]
[[Category:Supermajor]]
[[Category:Supermajor third]]
[[Category:Undecimal]]
[[Category:11-limit]]
[[Category:Third]]
[[Category:Third]]
[[Category:Interval]]
[[Category:Listen]]

Revision as of 22:12, 13 June 2020

Interval information
Ratio 14/11
Factorization 2 × 7 × 11-1
Monzo [1 0 0 1 -1
Size in cents 417.508¢
Name undecimal major third
Color name 1uz4, luzo 4th
FJS name [math]\displaystyle{ \text{P4}^{7}_{11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.26679
Weil norm (log2 max(n, d)) 7.61471
Wilson norm (sopfr(nd)) 20

[sound info]
Open this interval in xen-calc

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 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-reducing.

See also