Diatonic functional harmony: Difference between revisions

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'''Parallelism''' - Notes located in the same primary [[tetrachord]] as either the Tonic, the Dominant, or the Serviant take on similar functions to said notes, with the caveat that functions derived from the Tonic in this fashion are still technically nontonic functions. This process creates what in traditional music theory are referred to as [[Wikipedia:Parallel and counter parallel|"''parallels''" and "''counter parallels''"]].

'''~~Doubling~~''' - The notes that are arrived at through stacking ~~two~~ instances of either 3/2 or 4/3 (or their tempered counterparts) are dubbed the "Double Dominant" ~~and~~ "Double Serviant" respectively. This comes from German's way of referring to the chord built on the second scale degree of the Diatonic scale as the "Doppeldominante", which literally means "Double Dominant".

'''Stacking''' - The notes that are arrived at through stacking multiple instances of either 3/2 or 4/3 (or their tempered counterparts) are dubbed according to the number of instances stacked, and the nature of the notes separated by the interval being stacked. Thus, stacking two instances of the Dominant or the Serviant results in the creation of the "Double Dominant" or "Double Serviant" respectively. This idea comes from German's way of referring to the chord built on the second scale degree of the Diatonic scale as the "Doppeldominante", which literally means "Double Dominant".

== 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.

=== Scale Degree Functions ===

In addition to the aforemented Basic Functions, Aura contends that the following scale degree functions also exist:

'''Contralead''' - Although this function is not found in Viennese Theory proper and various schools of thought take different positions, Aura contends that due to a combination of this scale degree being native to Phrygian mode, often approaching the Tonic from above in a manner reminiscent of a [[Wikipedia:Leading-tone|leading tone]], and simultaneously serving as the root of the [[Wikipedia:Neapolitan chord|Neapolitan chord]], this lowered second scale degree in Bass-Up Tonality should be considered as more than just a simple chromatic alteration of the Supertonic. Furthermore, taking this idea into the realm of Microtonality, the Contralead is an interval that occurs at intervals between 28/27 and 14/13 away from the Tonic, and, which not only serves as a leading tone in the direction opposite that of the scale's direction of construction, but also contains all the functions of a Neapolitan chord, with both functionalities having their roots in [[16/15]].

'''Supertonic''' - This function is easily derivable through a combination of the Subdominant Parallel function of [[10/9]] and Double Dominant function of [[9/8]], or at least that's the case in Bass-Up Tonality, and especially in [[meantone]] contexts where the two intervals are equated. However, Aura would argue that due to both the close proximity of 10/9 and 9/8 even in non-meantone settings and the shared Predominant functionalities of both scale degrees, these two functions often overlap to some degree or other. Accordingly, this is the note that occurs roughly at intervals between 567/512 and 256/225 above the Tonic as the second scale degree.

'''Mediant''' - This is the note that occurs roughly at intervals between 75/64 and 32/25 away from the Tonic in the scale's direction of construction, and is named due to being roughly halfway between the Tonic and the Dominant. This is the first of the two diatonic scale degrees with the most possibilities for realization, though it is most often within 20 cents of either [[6/5]] or [[5/4]] due to these two LCJI intervals coming the closest to the halfway point between the Tonic and the Dominant. From a functional standpoint, the Mediant has multiple possible functions ranging from the Tonic Counter Parallel and Preserviant functions of both 5/4 and 6/5, which overlap with the Triple Serviant Function of [[32/27]] on one side, and the Quadruple Dominant function of [[81/64]] on the other side.

'''Contramediant''' - Compared to the term "''Submediant''" from traditional music theory, the term "Contramediant" may have a slightly different frame of reference, as while a "Submediant" is halfway between the Tonic and a "Subdominant", the "Contramediant" is halfway between the Tonic and the Serviant. The Contramediant is a note that occurs roughly at intervals between 25/16 and 128/75 away from the Tonic in the scale's direction of construction, and is the second of two scale degrees with the most possibilities for the realization. From a functional standpoint, the Contramediant has multiple possible functions ranging from the Tonic Parallel and Predominant functions of both 8/5 and 5/3, which overlap with the Triple Dominant Function of [[27/16]] on one side, and the Quadruple Serviant function of [[128/81]] on the other side.

'''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 ==

In addition to the Functions derived from both German theory and Viennese theory, there have been other functions described by Aura and others.

=== Antitonic Region ===

Notes that occur around half an octave away from the Tonic- especially the region extending from 7/5 to 10/7- on account of harmonies built on notes in this area tend to oppose that of the Tonic, thus leading to the term '''Antitonic''' being used to describe the region as a whole. The exact outcome of this opposition depends on the exact distance of the Antitonic from the Tonic:

*If the Antitonic is between 7/5 and 600 cents away from the Tonic and functions as an augmented fourth, it tends to cause the Dominant to become a new Tonic unless followed up by a different note- one that is usually a Major 7th away from the Tonic. Because of this tendency to "kiss up to" and tonicize the Dominant, this type of Antitonic can be dubbed a "'''Sycophant'''", with the prototypical Sycophant being 45/32.

*Conversely, if the Antitonic is between 600 cents and 10/7 away from the Tonic and functions as a diminished fifth, it tends to contrast with the Tonic in a manner somewhat akin to that of a Dominant, but by sheer brute force and contrary harmonic nature- e.g. if the Tonic harmony is Minor in nature, the Antitonic harmony will be Major- or more rarely, Supermajor- in nature. Furthermore, in scales such as the Locrian scale, any type of Serviant harmony tends to resolve towards either this type of Antitonic, or some other type of substitute for a Dominant. Because of these Dominant-esque tendencies, this type of Antitonic can be dubbed a "'''Tyrant'''", with the prototypical Tyrant being 64/45.

*If the Antitonic is between 7/5 and 600 cents away from the Tonic and functions as a diminished fifth, it demonstrates a mixture of both Sycophant-like and Tyrant-like properties, but because it is found just below the range of a typical Tyrant, it is called a '''Gravotyrant''' in Bass-Up tonality. A classic example of such an interval is 1024/729.

*If the Antitonic is between 600 cents and 10/7 away from the Tonic and functions as an augmented fourth, it demonstrates a mixture of both Sycophant-like and Tyrant-like properties, but because it is found just above the range of a typical Sycophant, it is called an '''Acuosycophant''' in Bass-Up Tonality. A classic example of such an interval is 729/512.

[[Category:Terms]]

[[Category:Theory]]

[[Category:Method]]

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 '''Parallelism''' - Notes located in the same primary [[tetrachord]] as either the Tonic, the Dominant, or the Serviant take on similar functions to said notes, with the caveat that functions derived from the Tonic in this fashion are still technically nontonic functions.  This process creates what in traditional music theory are referred to as [[Wikipedia:Parallel and counter parallel|"''parallels''" and "''counter parallels''"]].
-'''Doubling''' - The notes that are arrived at through stacking two instances of either 3/2 or 4/3 (or their tempered counterparts) are dubbed the "Double Dominant" and "Double Serviant" respectively.  This comes from German's way of referring to the chord built on the second scale degree of the Diatonic scale as the "Doppeldominante", which literally means "Double Dominant".
+'''Stacking''' - The notes that are arrived at through stacking multiple instances of either 3/2 or 4/3 (or their tempered counterparts) are dubbed according to the number of instances stacked, and the nature of the notes separated by the interval being stacked.  Thus, stacking two instances of the Dominant or the Serviant results in the creation of the "Double Dominant" or "Double Serviant" respectively.  This idea comes from German's way of referring to the chord built on the second scale degree of the Diatonic scale as the "Doppeldominante", which literally means "Double Dominant".
 == 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.
+=== Scale Degree Functions ===
+In addition to the aforemented Basic Functions, Aura contends that the following scale degree functions also exist:
+'''Contralead''' - Although this function is not found in Viennese Theory proper and various schools of thought take different positions, Aura contends that due to a combination of this scale degree being native to Phrygian mode, often approaching the Tonic from above in a manner reminiscent of a [[Wikipedia:Leading-tone|leading tone]], and simultaneously serving as the root of the [[Wikipedia:Neapolitan chord|Neapolitan chord]], this lowered second scale degree in Bass-Up Tonality should be considered as more than just a simple chromatic alteration of the Supertonic.  Furthermore, taking this idea into the realm of Microtonality, the Contralead is an interval that occurs at intervals between 28/27 and 14/13 away from the Tonic, and, which not only serves as a leading tone in the direction opposite that of the scale's direction of construction, but also contains all the functions of a Neapolitan chord, with both functionalities having their roots in [[16/15]].
+'''Supertonic''' - This function is easily derivable through a combination of the Subdominant Parallel function of [[10/9]] and Double Dominant function of [[9/8]], or at least that's the case in Bass-Up Tonality, and especially in [[meantone]] contexts where the two intervals are equated.  However, Aura would argue that due to both the close proximity of 10/9 and 9/8 even in non-meantone settings and the shared Predominant functionalities of both scale degrees, these two functions often overlap to some degree or other.  Accordingly, this is the note that occurs roughly at intervals between 567/512 and 256/225 above the Tonic as the second scale degree.
+'''Mediant''' - This is the note that occurs roughly at intervals between 75/64 and 32/25 away from the Tonic in the scale's direction of construction, and is named due to being roughly halfway between the Tonic and the Dominant. This is the first of the two diatonic scale degrees with the most possibilities for realization, though it is most often within 20 cents of either [[6/5]] or [[5/4]] due to these two LCJI intervals coming the closest to the halfway point between the Tonic and the Dominant.  From a functional standpoint, the Mediant has multiple possible functions ranging from the Tonic Counter Parallel and Preserviant functions of both 5/4 and 6/5, which overlap with the Triple Serviant Function of [[32/27]] on one side, and the Quadruple Dominant function of [[81/64]] on the other side.
+'''Contramediant''' - Compared to the term "''Submediant''" from traditional music theory, the term "Contramediant" may have a slightly different frame of reference, as while a "Submediant" is halfway between the Tonic and a "Subdominant", the "Contramediant" is halfway between the Tonic and the Serviant.  The Contramediant is a note that occurs roughly at intervals between 25/16 and 128/75 away from the Tonic in the scale's direction of construction, and is the second of two scale degrees with the most possibilities for the realization.  From a functional standpoint, the Contramediant has multiple possible functions ranging from the Tonic Parallel and Predominant functions of both 8/5 and 5/3, which overlap with the Triple Dominant Function of [[27/16]] on one side, and the Quadruple Serviant function of [[128/81]] on the other side.
+'''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 ==
+In addition to the Functions derived from both German theory and Viennese theory, there have been other functions described by Aura and others.
+=== Antitonic Region ===
+Notes that occur around half an octave away from the Tonic- especially the region extending from 7/5 to 10/7- on account of harmonies built on notes in this area tend to oppose that of the Tonic, thus leading to the term '''Antitonic''' being used to describe the region as a whole.  The exact outcome of this opposition depends on the exact distance of the Antitonic from the Tonic:
+*If the Antitonic is between 7/5 and 600 cents away from the Tonic and functions as an augmented fourth, it tends to cause the Dominant to become a new Tonic unless followed up by a different note- one that is usually a Major 7th away from the Tonic.  Because of this tendency to "kiss up to" and tonicize the Dominant, this type of Antitonic can be dubbed a "'''Sycophant'''", with the prototypical Sycophant being 45/32.
+*Conversely, if the Antitonic is between 600 cents and 10/7 away from the Tonic and functions as a diminished fifth, it tends to contrast with the Tonic in a manner somewhat akin to that of a Dominant, but by sheer brute force and contrary harmonic nature- e.g. if the Tonic harmony is Minor in nature, the Antitonic harmony will be Major- or more rarely, Supermajor- in nature. Furthermore, in scales such as the Locrian scale, any type of Serviant harmony tends to resolve towards either this type of Antitonic, or some other type of substitute for a Dominant. Because of these Dominant-esque tendencies, this type of Antitonic can be dubbed a "'''Tyrant'''", with the prototypical Tyrant being 64/45.
+*If the Antitonic is between 7/5 and 600 cents away from the Tonic and functions as a diminished fifth, it demonstrates a mixture of both Sycophant-like and Tyrant-like properties, but because it is found just below the range of a typical Tyrant, it is called a '''Gravotyrant''' in Bass-Up tonality.  A classic example of such an interval is 1024/729.
+*If the Antitonic is between 600 cents and 10/7 away from the Tonic and functions as an augmented fourth, it demonstrates a mixture of both Sycophant-like and Tyrant-like properties, but because it is found just above the range of a typical Sycophant, it is called an '''Acuosycophant''' in Bass-Up Tonality.  A classic example of such an interval is 729/512.
 [[Category:Terms]]
 [[Category:Theory]]
 [[Category:Method]]