Diatonic functional harmony: Difference between revisions

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== Facets Derived from Viennese Theory ==

Among the chief ideas that come from Viennese Theory is the idea that each degree has its own function relative to the Tonic. However, while in Viennese Theory proper, the degrees are strictly defined only relative to the cycle of fifths, Aura, for the realm of Microtonality, additionally considers [[Wikipedia:Ivan Wyschnegradsky|Wyschnegradsky]]'s [[Wikipedia:Major fourth and minor fifth|Major Fourth]] interval to be a second axis for defining many of the various microtonal functions, and also takes things like Bass-Up Tonality (that is, music built from the Bass upwards) and Treble-Down Tonality (that is, music built from the Treble downards) into consideration. On top of that, Aura also contends that many of the functions described by Viennese Theory find their roots in specific combinations of different operations on the different basic functions described in German Theory.

Among the chief ideas that come from Viennese Theory is the idea that each degree has its own function relative to the Tonic. However, while in Viennese Theory proper, the degrees are strictly defined only relative to the cycle of fifths, Aura, for the realm of Microtonality, additionally takes things like Bass-Up Tonality (that is, music built from the Bass upwards) and Treble-Down Tonality (that is, music built from the Treble downards) into consideration. On top of that, Aura also contends that many of the functions described by Viennese Theory find their roots in specific combinations of different operations on the different basic functions described in German Theory.

=== Scale Degree Functions ===

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'''Subtonic''' - This function is easily derivable through a combination of the Dominant Parallel function of [[9/5]] and Double Serviant function of [[16/9]], or at least that's the case in Bass-Up Tonality, and especially in meantone contexts where the two intervals are equated. As with the Supertonic, however, Aura would argue that due to both the close proximity of 9/5 and 16/9 even in non-meantone settings and the shared Pretonic functionalities of both scale degrees, these two functions often overlap to some degree or other. This is the note that occurs roughly at intervals between 225/128 and 1024/567 above the Tonic as the seventh scale degree.

== Additional Diatonic Functions ==

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== Paradiatonic Functions ==

In addition to all the aforementioned Diatonic functions, Aura takes a more just version of [[Wikipedia:Ivan Wyschnegradsky|Wyschnegradsky]]'s [[Wikipedia:Major fourth and minor fifth|Major Fourth]] interval (under a different name) to be a second axis for defining many of the various microtonal functions, which, in relation to the Diatonic functions, he dubs "'''paradiatonic functions'''".

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 == Facets Derived from Viennese Theory ==
-Among the chief ideas that come from Viennese Theory is the idea that each degree has its own function relative to the Tonic.  However, while in Viennese Theory proper, the degrees are strictly defined only relative to the cycle of fifths, Aura, for the realm of Microtonality, additionally considers [[Wikipedia:Ivan Wyschnegradsky|Wyschnegradsky]]'s [[Wikipedia:Major fourth and minor fifth|Major Fourth]] interval to be a second axis for defining many of the various microtonal functions, and also takes things like Bass-Up Tonality (that is, music built from the Bass upwards) and Treble-Down Tonality (that is, music built from the Treble downards) into consideration.  On top of that, Aura also contends that many of the functions described by Viennese Theory find their roots in specific combinations of different operations on the different basic functions described in German Theory.
+Among the chief ideas that come from Viennese Theory is the idea that each degree has its own function relative to the Tonic.  However, while in Viennese Theory proper, the degrees are strictly defined only relative to the cycle of fifths, Aura, for the realm of Microtonality, additionally takes things like Bass-Up Tonality (that is, music built from the Bass upwards) and Treble-Down Tonality (that is, music built from the Treble downards) into consideration.  On top of that, Aura also contends that many of the functions described by Viennese Theory find their roots in specific combinations of different operations on the different basic functions described in German Theory.
 === Scale Degree Functions ===
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 '''Subtonic''' - This function is easily derivable through a combination of the Dominant Parallel function of [[9/5]] and Double Serviant function of [[16/9]], or at least that's the case in Bass-Up Tonality, and especially in meantone contexts where the two intervals are equated.  As with the Supertonic, however, Aura would argue that due to both the close proximity of 9/5 and 16/9 even in non-meantone settings and the shared Pretonic functionalities of both scale degrees, these two functions often overlap to some degree or other.  This is the note that occurs roughly at intervals between 225/128 and 1024/567 above the Tonic as the seventh scale degree.
 == Additional Diatonic Functions ==
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+== Paradiatonic Functions ==
+In addition to all the aforementioned Diatonic functions, Aura takes a more just version of [[Wikipedia:Ivan Wyschnegradsky|Wyschnegradsky]]'s [[Wikipedia:Major fourth and minor fifth|Major Fourth]] interval (under a different name) to be a second axis for defining many of the various microtonal functions, which, in relation to the Diatonic functions, he dubs "'''paradiatonic functions'''".