14/11: Difference between revisions

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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), 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 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.

== See also ==

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-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), 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 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.
 == See also ==