Diatonic functional harmony: Difference between revisions

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=== Scale Degree Functions ===

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

In addition to the aforemented Basic Diatonic 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]].

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'''Varicant''' - Just as a Mediant lies roughly in the middle of the 3/2 interval separating the Tonic and the Dominant above it, a Varicant lies roughly in the middle of the 4/3 interval separating the Dominant and the Tonic above it. Intervals in this region often don’t consistently act as either sixths or sevenths, or even act as a cross between a sixth and a seventh- effectively straddling the border between these two diatonic categories, hence the name "Varicant", from Latin "vāricō"<ref>[[Wiktionary: varico #Latin]]</ref>. This is a note that occurs roughly at intervals between 128/75 and 225/128 away from the Tonic in the scale's direction of construction. In Bass-Up Tonality, this functionality is first encountered in the form of the [[7/4]] interval, though [[12/7]] is another notable interval included in this range. While many microtonalists think of 7/4 as being purely a type of seventh- and indeed, it most commonly acts as a sort of subminor seventh- Aura counterargues based on this same interval's relationships with 11/8 in particular that 7/4 is not merely a type of seventh, but rather, a type of a cross between a sixth and a seventh, with such a property explaining why [[14/11]] is generally considered to be a type of third.

'''Contravaricant''' - This is a note that occurs roughly at intervals between 256/225 and 75/64 away from the Tonic in the scale's direction of construction. ~~This~~ region ~~is characterized by~~ intervals ~~that don’t~~ consistently act as either seconds or thirds. In Bass-Up tonality, this functionality ~~has its roots~~ in the ~~seventh subharmonic~~, though 7/6 is another notable interval included in this range.

'''Contravaricant''' - This is a note that occurs roughly at intervals between 256/225 and 75/64 away from the Tonic in the scale's direction of construction, lying roughly in the middle of the 4/3 interval separating the Tonic and the Serviant above it. Much like how intervals in the Varicant region often don’t consistently act as either sixths or sevenths, or even act as a cross between a sixth and a seventh, intervals in the Contravaricant region often don't consistently act as either seconds or thirds, or even act as a cross between a second and a third. In Bass-Up tonality, this functionality this functionality is first encountered in the form of [[8/7]], though [[7/6]] is another notable interval included in this range.

'''Varicodominant''' - This is a note that occurs roughly at intervals between 32/21 and 25/16 away from the Tonic in the scale's direction of construction. Accordingly, this region is characterized by intervals that don’t consistently act as either fifths or sixths, or even act as a cross between a fifth and a sixth, as well as by intervals that act as parachromatic alterations of either the Dominant or the Contramediant. The name of this region comes from "Varicant" and "Dominant", with a linking "-o-" in place of the "-ant" of "Varicant".

'''Varicoserviant''' - This is a note that occurs roughly at intervals between 32/25 and 21/16 away from the Tonic in the scale's direction of construction. Accordingly, this region is characterized by intervals that don’t consistently act as either thirds or fourths, or even act as a cross between a third and a fourth, as well as by intervals that act as parachromatic alterations of either the Mediant or the Serviant. The name of this region comes from "Varicant" and "Serviant", with a linking "-o-" in place of the "-ant" of "Varicant".

=== Circumtonic Regions ===

'''Supercommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 20 cents above the Tonic. These intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance, or for a slightly less resolved version of a Unison or Octave.

'''Superdietic''' - This is a note that occurs at intervals between roughly 20 cents above the Tonic and 28/27 above the Tonic. These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Contralead. However, while some microtonalists would question the idea of there being a distinct Superdietic region, preferring to think of the quartertones in this region as being simply the junction between the Supercommatic and Contralead regions, there there are actually a few functional differences between a Superdietic and a Contralead in Bass-Up Tonality that are worth considering. For starters, Superdietics are often more likely to be passing tones than Contraleads, and, when they’re not merely passing non-chord tones, they are just as liable to resolve upward to some form of Contralead or even Supertonic as they are to resolve downwards toward the Tonic, a property which intervals like [[33/32]] in particular are apt to demonstrate. Furthermore, whereas a Contralead can resolve to the Tonic in part through a strong harmonic connection, a Superdietic is much more likely to do so through sheer brute force when such a resolution is noticeable.

'''Subdietic''' - This is a note that occurs at intervals between roughly 27/14 above the Tonic and roughly 20 cents below the octave reduplication of the Tonic. These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Lead- however, there are functional differences between a Subdietic and a Lead in Bass-Up Tonality. In Bass-Up Tonality, Subdietics are often more likely to be passing tones than Leads, and, when they’re not merely passing non-chord tones, they are often harder to approach and or follow up without creating some kind of tonal disconnect, with such a disconnect being especially noticeable for intervals like [[64/33]]. Furthermore, whereas a Lead can resolve to the Tonic in part through a strong harmonic connection, a Subdietic is much more likely to do so through sheer brute force.

'''Subcommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 20 cents below the Tonic. As with Supercommatic intervals, these intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance.

== Additional Functions ==

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'''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.

'''Acuotyrant''' - This is a note that occurs at intervals ranging from 10/7 to 36/25 away from the Tonic. Although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless operates more on the side of brute force when it contrasts with the Tonic.

'''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.

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'''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.

'''Gravosycophant''' - This is a note that occurs at intervals ranging from 25/18 to 7/5 away from the Tonic. Although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless often runs a high risk of tonicizing either the Dominant or the Gravodominant.

'''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.

@@ Line 29: / Line 29: @@
 === Scale Degree Functions ===
-In addition to the aforemented Basic Functions, Aura contends that the following scale degree functions also exist:
+In addition to the aforemented Basic Diatonic 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]].
@@ Line 69: / Line 69: @@
 '''Varicant''' - Just as a Mediant lies roughly in the middle of the 3/2 interval separating the Tonic and the Dominant above it, a Varicant lies roughly in the middle of the 4/3 interval separating the Dominant and the Tonic above it.  Intervals in this region often don’t consistently act as either sixths or sevenths, or even act as a cross between a sixth and a seventh- effectively straddling the border between these two diatonic categories, hence the name "Varicant", from Latin "vāricō"<ref>[[Wiktionary: varico #Latin]]</ref>.  This is a note that occurs roughly at intervals between 128/75 and 225/128 away from the Tonic in the scale's direction of construction.  In Bass-Up Tonality, this functionality is first encountered in the form of the [[7/4]] interval, though [[12/7]] is another notable interval included in this range.  While many microtonalists think of 7/4 as being purely a type of seventh- and indeed, it most commonly acts as a sort of subminor seventh- Aura counterargues based on this same interval's relationships with 11/8 in particular that 7/4 is not merely a type of seventh, but rather, a type of a cross between a sixth and a seventh, with such a property explaining why [[14/11]] is generally considered to be a type of third.
-'''Contravaricant''' - This is a note that occurs roughly at intervals between 256/225 and 75/64 away from the Tonic in the scale's direction of construction.  This region is characterized by intervals that don’t consistently act as either seconds or thirds.  In Bass-Up tonality, this functionality has its roots in the seventh subharmonic, though 7/6 is another notable interval included in this range.
+'''Contravaricant''' - This is a note that occurs roughly at intervals between 256/225 and 75/64 away from the Tonic in the scale's direction of construction, lying roughly in the middle of the 4/3 interval separating the Tonic and the Serviant above it.  Much like how intervals in the Varicant region often don’t consistently act as either sixths or sevenths, or even act as a cross between a sixth and a seventh, intervals in the Contravaricant region often don't consistently act as either seconds or thirds, or even act as a cross between a second and a third.  In Bass-Up tonality, this functionality this functionality is first encountered in the form of [[8/7]], though [[7/6]] is another notable interval included in this range.
+'''Varicodominant''' - This is a note that occurs roughly at intervals between 32/21 and 25/16 away from the Tonic in the scale's direction of construction.  Accordingly, this region is characterized by intervals that don’t consistently act as either fifths or sixths, or even act as a cross between a fifth and a sixth, as well as  by intervals that act as parachromatic alterations of either the Dominant or the Contramediant.  The name of this region comes from "Varicant" and "Dominant", with a linking "-o-" in place of the "-ant" of "Varicant".
+'''Varicoserviant''' - This is a note that occurs roughly at intervals between 32/25 and 21/16 away from the Tonic in the scale's direction of construction.  Accordingly, this region is characterized by intervals that don’t consistently act as either thirds or fourths, or even act as a cross between a third and a fourth, as well as by intervals that act as parachromatic alterations of either the Mediant or the Serviant.  The name of this region comes from "Varicant" and "Serviant", with a linking "-o-" in place of the "-ant" of "Varicant".
+=== Circumtonic Regions ===
+'''Supercommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 20 cents above the Tonic.  These intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance, or for a slightly less resolved version of a Unison or Octave.
+'''Superdietic''' - This is a note that occurs at intervals between roughly 20 cents above the Tonic and 28/27 above the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Contralead.  However, while some microtonalists would question the idea of there being a distinct Superdietic region, preferring to think of the quartertones in this region as being simply the junction between the Supercommatic and Contralead regions, there there are actually a few functional differences between a Superdietic and a Contralead in Bass-Up Tonality that are worth considering.  For starters, Superdietics are often more likely to be passing tones than Contraleads, and, when they’re not merely passing non-chord tones, they are just as liable to resolve upward to some form of Contralead or even Supertonic as they are to resolve downwards toward the Tonic, a property which intervals like [[33/32]] in particular are apt to demonstrate.  Furthermore, whereas a Contralead can resolve to the Tonic in part through a strong harmonic connection, a Superdietic is much more likely to do so through sheer brute force when such a resolution is noticeable.
+'''Subdietic''' - This is a note that occurs at intervals between roughly 27/14 above the Tonic and roughly 20 cents below the octave reduplication of the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Lead- however, there are functional differences between a Subdietic and a Lead in Bass-Up Tonality.   In Bass-Up Tonality, Subdietics are often more likely to be passing tones than Leads, and, when they’re not merely passing non-chord tones, they are often harder to approach and or follow up without creating some kind of tonal disconnect, with such a disconnect being especially noticeable for intervals like [[64/33]].  Furthermore, whereas a Lead can resolve to the Tonic in part through a strong harmonic connection, a Subdietic is much more likely to do so through sheer brute force.
+'''Subcommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 20 cents below the Tonic.  As with Supercommatic intervals, these intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance.
 == Additional Functions ==
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 '''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.
+'''Acuotyrant''' - This is a note that occurs at intervals ranging from 10/7 to 36/25 away from the Tonic.  Although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless operates more on the side of brute force when it contrasts with the Tonic.
 '''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.
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 '''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.
+'''Gravosycophant''' - This is a note that occurs at intervals ranging from 25/18 to 7/5 away from the Tonic.  Although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless often runs a high risk of tonicizing either the Dominant or the Gravodominant.
 '''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.