14/11: Difference between revisions

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14/11 can 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¢. 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.

Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth.

Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth. It also appears in the chord [[7:9:11:14]], which consists of three thirds stacked to an octave, but in a diatonic system three thirds would stack to a type of seventh, so one of the intervals would have to be considered a type of fourth instead. In FJS and other systems, 14/11 is considered an imperfect fourth, but 9/7 is wider than it, so it may be considered a diminished fourth in this context instead. In short, this interval shows that diatonic interval classification is far from perfect, and such ambiguity also occurs with [[13/10]] and [[7/5]].

It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.

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 /11 can 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¢. 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.
-Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth.
+Despite being around a third in size, due to being notated as an imperfect fourth in many systems, many chords involving it are awkward to notate in terms of diatonic degrees. For example, in [[11:14:16:20]], if [[16/11]] is considered a type of fifth and 14/11 is considered a type of third, then [[8/7]] would be considered a type of third, which is awkward due to its size, but actually makes sense if its inversion 7/4 sometimes considered a sixth. It also appears in the chord [[7:9:11:14]], which consists of three thirds stacked to an octave, but in a diatonic system three thirds would stack to a type of seventh, so one of the intervals would have to be considered a type of fourth instead. In FJS and other systems, 14/11 is considered an imperfect fourth, but 9/7 is wider than it, so it may be considered a diminished fourth in this context instead. In short, this interval shows that diatonic interval classification is far from perfect, and such ambiguity also occurs with [[13/10]] and [[7/5]].
 It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament.