14/11: Difference between revisions

| Name = undecimal major third, pentacircle major third

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.

 

== See also ==

* [[Gallery of just intervals]]

* [[Gentle chords]]

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

 

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

 

 

[[Category:Third]]

[[Category:Major third]]

[[Category:Supermajor third]]

[[Category:Neo-gothic]]