Diatonic functional harmony: Difference between revisions

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'''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.

'''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, 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.

'''Lead''' - This is the note typically referred to when people say "the leading-tone". This is a note that occurs at intervals between 13/7 and 27/14 away from the Tonic, which serves as a leading tone in the scale's direction of construction. In Bass-Up Tonality, this functionality has its roots in the fifteenth harmonic. Although triads built on this scale degree are regarded by some as simply incomplete Dominant Seventh chords, Aura's own analysis, while acknowledging the functional similarities between the Lead and the Dominant, sees this interval as functionally distinct from the Dominant due to the the Lead also being related to the Mediant in the same way that the Dominant is related to the Tonic- a key functionality that is often exploited in [[Wikipedia:Vi–ii–V–I|circle progression]]s.

== Additional Diatonic Functions ==

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*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.

=== Circumdominant Regions ===

The circumdomimant regions are the two main regions on either side of the Dominant proper, and there are several functions located in these regions, one of which is an actual diatonic function. Note that antitonic and paradiatonic functions falling in this region are not covered in this section.

'''Mocktyrant''' - In Bass-Up Tonality, this is an interval that ranges from 13/10 to 7/5 which acts as a type of fifth rather than either a type of fourth or a type of third. These intervals are generally not that common outside of Jazz and Blues.

'''Gravodominant''' - This is a note that occurs roughly at intervals ranging from 187/128 away from the Tonic to about 3.5 cents short of the 3/2 perfect fifth in the scale's direction of construction. Although often overlooked or even outright shunned by traditional theorists, Aura actually considers the Gravodominant to be a legitimate diatonic function- albeit one only existing in non-meantone environments. Specifically, as typified by intervals like 40/27, Gravodominants are dissonant intervals that simultaneously act as alternatives to the Dominant in both chord progressions and chord construction, and often require resolution. Apart from this, Gravodominants only rise to prominence in systems where what might otherwise function as a Dominant is found just short of the sweetspot range near the standard issue 3/2.

'''Acuodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond the 3/2 perfect fifth to 32/21 away from the Tonic in the scale's direction of construction. These only rise to prominence in systems where what might otherwise function as a Dominant is found just beyond the sweetspot range near the standard issue 3/2.

'''Mockdominant''' - This is a note that occurs at intervals ranging from 32/21 to 64/39, specifically one which acts as a type of diminished fourth in contrast to a more typical function as a Contramediant, or else, acts as a surrogate for a note that would otherwise function as a Dominant. These only rise to prominence in systems where there’s no proper Dominant, and where what might otherwise function as a Dominant is found too far away from the standard issue 3/2. Beyond this, they tend mostly to be found in augmented chords, and in modes like Lydian Augmented in which the fifth is augmented.

=== Circumserviant Regions ===

The circumserviant regions are the two main regions on either side of the Serviant proper, and there are two functions located in these regions, one of which is an actual diatonic function. Note that antitonic and paradiatonic functions falling in this region are not covered in this section.

'''Mockserviant''' - This is a note that occurs at intervals ranging from 39/32 to 21/16, specifically one which acts as a type of diminished fourth in contrast to a more typical function as a Mediant, or else, acts as a surrogate for a note that would otherwise function as a Serviant. Thus, these intervals only rise to prominence either in modes like Superlocrian where the fourth is diminished or in systems where there’s no proper Serviant, and where what might otherwise function as a Serviant is found too far away from the standard issue 4/3.

'''Gravoserviant''' - This is a note that occurs roughly at intervals ranging from about 21/16 away from the Tonic to about 3.5 cents short of the 4/3 perfect fourth in the scale's direction of construction. These only rise to prominence in systems where what might otherwise function as a Serviant is found just short of the sweetspot range near the standard issue 4/3.

'''Acuoserviant''' - This is a note that occurs roughly at intervals ranging from 3.5 cents beyond the 4/3 perfect fourth to 256/187 away from the Tonic in the scale's direction of construction. As typified by intervals like 27/20, Acuoserviants are dissonant intervals that often act as a sort of predominant and or as the inverses of Gravodominants, making the Acuoserviant a legitimate diatonic function in terms of Aura's analysis. Apart from this, Acuoserviants only rise to prominence in systems where what might otherwise function as a Serviant is found just beyond the sweetspot range near the standard issue 4/3.

'''Mocksycophant''' - In Bass-Up Tonality, this is an interval that ranges from 10/7 to 20/13 which acts as a type of fourth rather than either a type of fifth or a type of sixth. These intervals are generally not that common outside of Jazz and Blues.

== Paradiatonic Functions ==

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 '''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.
+'''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, 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.
+'''Lead''' - This is the note typically referred to when people say "the leading-tone".  This is a note that occurs at intervals between 13/7 and 27/14 away from the Tonic, which serves as a leading tone in the scale's direction of construction.  In Bass-Up Tonality, this functionality has its roots in the fifteenth harmonic.  Although triads built on this scale degree are regarded by some as simply incomplete Dominant Seventh chords, Aura's own analysis, while acknowledging the functional similarities between the Lead and the Dominant, sees this interval as functionally distinct from the Dominant due to the the Lead also being related to the Mediant in the same way that the Dominant is related to the Tonic- a key functionality that is often exploited in [[Wikipedia:Vi–ii–V–I|circle progression]]s.
 == Additional Diatonic Functions ==
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 *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.
+=== Circumdominant Regions ===
+The circumdomimant regions are the two main regions on either side of the Dominant proper, and there are several functions located in these regions, one of which is an actual diatonic function.  Note that antitonic and paradiatonic functions falling in this region are not covered in this section.
+'''Mocktyrant''' - In Bass-Up Tonality, this is an interval that ranges from 13/10 to 7/5 which acts as a type of fifth rather than either a type of fourth or a type of third.  These intervals are generally not that common outside of Jazz and Blues.
+'''Gravodominant''' - This is a note that occurs roughly at intervals ranging from 187/128 away from the Tonic to about 3.5 cents short of the 3/2 perfect fifth in the scale's direction of construction.  Although often overlooked or even outright shunned by traditional theorists, Aura actually considers the Gravodominant to be a legitimate diatonic function- albeit one only existing in non-meantone environments.  Specifically, as typified by intervals like 40/27, Gravodominants are dissonant intervals that simultaneously act as alternatives to the Dominant in both chord progressions and chord construction, and often require resolution.  Apart from this, Gravodominants only rise to prominence in systems where what might otherwise function as a Dominant is found just short of the sweetspot range near the standard issue 3/2.
+'''Acuodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond the 3/2 perfect fifth to 32/21 away from the Tonic in the scale's direction of construction.  These only rise to prominence in systems where what might otherwise function as a Dominant is found just beyond the sweetspot range near the standard issue 3/2.
+'''Mockdominant''' - This is a note that occurs at intervals ranging from 32/21 to 64/39, specifically one which acts as a type of diminished fourth in contrast to a more typical function as a Contramediant, or else, acts as a surrogate for a note that would otherwise function as a Dominant.  These only rise to prominence in systems where there’s no proper Dominant, and where what might otherwise function as a Dominant is found too far away from the standard issue 3/2.  Beyond this, they tend mostly to be found in augmented chords, and in modes like Lydian Augmented in which the fifth is augmented.
+=== Circumserviant Regions ===
+The circumserviant regions are the two main regions on either side of the Serviant proper, and there are two functions located in these regions, one of which is an actual diatonic function.  Note that antitonic and paradiatonic functions falling in this region are not covered in this section.
+'''Mockserviant''' - This is a note that occurs at intervals ranging from 39/32 to 21/16, specifically one which acts as a type of diminished fourth in contrast to a more typical function as a Mediant, or else, acts as a surrogate for a note that would otherwise function as a Serviant.  Thus, these intervals only rise to prominence either in modes like Superlocrian where the fourth is diminished or in systems where there’s no proper Serviant, and where what might otherwise function as a Serviant is found too far away from the standard issue 4/3.
+'''Gravoserviant''' - This is a note that occurs roughly at intervals ranging from about 21/16 away from the Tonic to about 3.5 cents short of the 4/3 perfect fourth in the scale's direction of construction.  These only rise to prominence in systems where what might otherwise function as a Serviant is found just short of the sweetspot range near the standard issue 4/3.
+'''Acuoserviant''' - This is a note that occurs roughly at intervals ranging from 3.5 cents beyond the 4/3 perfect fourth to 256/187 away from the Tonic in the scale's direction of construction.  As typified by intervals like 27/20, Acuoserviants are dissonant intervals that often act as a sort of predominant and or as the inverses of Gravodominants, making the Acuoserviant a legitimate diatonic function in terms of Aura's analysis.  Apart from this, Acuoserviants only rise to prominence in systems where what might otherwise function as a Serviant is found just beyond the sweetspot range near the standard issue 4/3.
+'''Mocksycophant''' - In Bass-Up Tonality, this is an interval that ranges from 10/7 to 20/13 which acts as a type of fourth rather than either a type of fifth or a type of sixth.  These intervals are generally not that common outside of Jazz and Blues.
 == Paradiatonic Functions ==