User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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'''Preparation''' - These are notes that "prepare the way" for either a Dominant or a Serviant through any of the above operations, or through some other mechanism. Functions which have this kind of role relative are denoted with a "pre-" prefix here. | '''Preparation''' - These are notes that "prepare the way" for either a Dominant or a Serviant through any of the above operations, or through some other mechanism. Functions which have this kind of role relative are denoted with a "pre-" prefix here. | ||
''' | '''Detempering''' - These are notes that appear when the comma or subchroma that separates them from the Tonic or from one of the primary Nontonic functions are not tempered out, and often, though not always, fall within the uncanny valleys of the three primary functions. | ||
''' | '''Neutralization''' - These are notes that are the result of neutralization and hybridization of Major and Minor Diatonic scale degrees. | ||
== Facets Derived from Viennese Theory == | == Facets Derived from Viennese Theory == | ||
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Out of the various functions found in the Paradiatonic scale, four of them- specifically, the tII/dbIII, tIV, dV and tVI/dbVII- can be considered basic, while the other three are first derivatives. As with the three basic diatonic functions, the four most basic paradiatonic functions have their roots in LCJI. In the order listed, the tII/dbIII, tIV, dV and tVI/dbVII functions are the following... | Out of the various functions found in the Paradiatonic scale, four of them- specifically, the tII/dbIII, tIV, dV and tVI/dbVII- can be considered basic, while the other three are first derivatives. As with the three basic diatonic functions, the four most basic paradiatonic functions have their roots in LCJI. In the order listed, the tII/dbIII, tIV, dV and tVI/dbVII functions are the following... | ||
'''Contravaricant''' - Named in contrast to the Varicant function, this is an interval that maps to both 1\5 and 5\24 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. 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, only without potential for crowding in chords. In Bass-Up tonality, this functionality is first encountered in the form of [[8/7]], though [[7/6]] is another notable interval included in this range, with intervals in this range having Predominant, Preserviant, and Dominant Parallel functions, as well as an overlap between Tonic Adjacent and Tonic Parallel functions. There are two different subtypes of this function that differ from each other based on how they are approached in interval stacking, the "''' | '''Contravaricant''' - Named in contrast to the Varicant function, this is an interval that maps to both 1\5 and 5\24 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. 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, only without potential for crowding in chords. In Bass-Up tonality, this functionality is first encountered in the form of [[8/7]], though [[7/6]] is another notable interval included in this range, with intervals in this range having Predominant, Preserviant, and Dominant Parallel functions, as well as an overlap between Tonic Adjacent and Tonic Parallel functions. There are two different subtypes of this function that differ from each other based on how they are approached in interval stacking, the "'''Pseudobidominant'''", which arises from stacking two Pseudodominants, and the "'''Pseudotriserviant'''", which arises from stacking three Pseudoserviants. | ||
'''Intersubiant''' - This is an interval that maps to both 3\7 and 11\24 in the scale's direction of construction. Like both the Serviant and the Sycophant, intervals in this region have a Predominant function, however, this predominant function is weaker than that of the surrounding interval regions since they neither act as a counterweight to the Dominant like a Serviant nor do they completely tonicize the Dominant like a Sycophant- at least to those who are more familiar with quartertones. What is even less expected is that these same intervals also have Preserviant and Mocktyrant functions. Since the Intersubiant is not found in the Tonic's quartertone field, there is a tendency for Intersubiant chords to be preceded and or followed by other chords with roots in the same quartertone field, though one could also reasonably approach it from the Tonic, the Contramediant, the Serviant, or the Supertonic. Furthermore, since Intersubiant intervals are either not on the Tonic's circle of fifths, or at least located very far away from the Tonic along the circle of fifths, there is a tendency for chords rooted on these intervals to have impure fifths- sometimes markedly so. In Bass-Up tonality, this functionality has its roots in the eleventh harmonic, and indeed 11/8 is perhaps one of the best examples of an interval within this range. | '''Intersubiant''' - This is an interval that maps to both 3\7 and 11\24 in the scale's direction of construction. Like both the Serviant and the Sycophant, intervals in this region have a Predominant function, however, this predominant function is weaker than that of the surrounding interval regions since they neither act as a counterweight to the Dominant like a Serviant nor do they completely tonicize the Dominant like a Sycophant- at least to those who are more familiar with quartertones. What is even less expected is that these same intervals also have Preserviant and Mocktyrant functions. Since the Intersubiant is not found in the Tonic's quartertone field, there is a tendency for Intersubiant chords to be preceded and or followed by other chords with roots in the same quartertone field, though one could also reasonably approach it from the Tonic, the Contramediant, the Serviant, or the Supertonic. Furthermore, since Intersubiant intervals are either not on the Tonic's circle of fifths, or at least located very far away from the Tonic along the circle of fifths, there is a tendency for chords rooted on these intervals to have impure fifths- sometimes markedly so. In Bass-Up tonality, this functionality has its roots in the eleventh harmonic, and indeed 11/8 is perhaps one of the best examples of an interval within this range. | ||
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'''Interregnant''' - This is an interval that maps to both 4\7 and 13\24 in the scale's direction of construction. Accordingly, intervals in this region behave as a cross between a Tyrant Antitonic on one hand and a Dominant on the other in that they often contrast with the Tonic through some combination of harmonic connection and brute force contrast, though it unexpectedly has decent Predominant and Mocksycophant functions. However, it also has Mocksycophant Functions. Like the Intersubiant, the Interregnant is not found in the Tonic's quartertone field and is either very distant from the Tonic along the circle of fifths or is completely missed by said circle of fifths, thus, there is a tendency for Interregnant chords to be preceded and or followed by other chords with roots in the same quartertone field, and or to have impure fifths. Conspicuously, the distance between the Interregnant is only about a Minor Second- or, at the very most, a Supraminor Second- away from the Intersubiant, so as a result, the Interregnant can be both a set-up and a follow-up to the Intersubiant. In Bass-Up tonality, the Interregnant functionality has its roots in the eleventh subharmonic, and indeed [[16/11]] is perhaps one of the best examples of an interval within this range. | '''Interregnant''' - This is an interval that maps to both 4\7 and 13\24 in the scale's direction of construction. Accordingly, intervals in this region behave as a cross between a Tyrant Antitonic on one hand and a Dominant on the other in that they often contrast with the Tonic through some combination of harmonic connection and brute force contrast, though it unexpectedly has decent Predominant and Mocksycophant functions. However, it also has Mocksycophant Functions. Like the Intersubiant, the Interregnant is not found in the Tonic's quartertone field and is either very distant from the Tonic along the circle of fifths or is completely missed by said circle of fifths, thus, there is a tendency for Interregnant chords to be preceded and or followed by other chords with roots in the same quartertone field, and or to have impure fifths. Conspicuously, the distance between the Interregnant is only about a Minor Second- or, at the very most, a Supraminor Second- away from the Intersubiant, so as a result, the Interregnant can be both a set-up and a follow-up to the Intersubiant. In Bass-Up tonality, the Interregnant functionality has its roots in the eleventh subharmonic, and indeed [[16/11]] is perhaps one of the best examples of an interval within this range. | ||
'''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, only without potential for crowding in chords- effectively straddling the border between these two diatonic categories, hence the name "Varicant", from Latin "vāricō"<ref>[[Wiktionary: varico #Latin]]</ref>. This is an interval that maps to both 4\5 and 19\24 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- I counterargue 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. Furthermore, in contrast to the Subtonics of Bass-Up Tonality, Varicants are liable to acts as Predominants and Preserviants, but not as Dominant Parallels. There are two different subtypes of this function that differ from each other based on how they are approached in interval stacking, the "'''Pseudotridominant'''", which arises from stacking three Pseudodominants, and the "''' | '''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, only without potential for crowding in chords- effectively straddling the border between these two diatonic categories, hence the name "Varicant", from Latin "vāricō"<ref>[[Wiktionary: varico #Latin]]</ref>. This is an interval that maps to both 4\5 and 19\24 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- I counterargue 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. Furthermore, in contrast to the Subtonics of Bass-Up Tonality, Varicants are liable to acts as Predominants and Preserviants, but not as Dominant Parallels. There are two different subtypes of this function that differ from each other based on how they are approached in interval stacking, the "'''Pseudotridominant'''", which arises from stacking three Pseudodominants, and the "'''Pseudobiserviant'''", which arises from stacking two Pseudoserviants. | ||
=== Derivative Paradiatonic Functions === | === Derivative Paradiatonic Functions === | ||
'''Subgradient''' - This is a note that occurs at intervals between roughly 48/25 above the Tonic and roughly 25 cents below the octave reduplication of the Tonic. These intervals tend to act as parachromatic alterations of either the Tonic, or, more rarely in Bass-Up Tonality, the Lead- however, there are functional differences between a Subgradient and a Lead in Bass-Up Tonality. In Bass-Up Tonality, Subgradients 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 awkward 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 Subgradient is much more likely to do so through sheer brute force, and even these cases require a proper set-up, as otherwise, the awkward tonal disconnect between the Subdietic and the Tonic is likely to result in the Subgradient resolving back down to either the Lead or the Semilead. As if that weren't enough, the Subgradient also has the Antintersubiant function. This function used to be called the "Subdietic", though that term has since been restricted to a related composite function (see below on Composite Functions). | '''Subgradient''' - This is a note that occurs at intervals between roughly 48/25 above the Tonic and roughly 25 cents below the octave reduplication of the Tonic. These intervals tend to act as parachromatic alterations of either the Tonic, or, more rarely in Bass-Up Tonality, the Lead- however, there are functional differences between a Subgradient and a Lead in Bass-Up Tonality. In Bass-Up Tonality, Subgradients 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 awkward 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 Subgradient is much more likely to do so through sheer brute force, and even these cases require a proper set-up, as otherwise, the awkward tonal disconnect between the Subdietic and the Tonic is likely to result in the Subgradient resolving back down to either the Lead or the Semilead. As if that weren't enough, the Subgradient also has the Antintersubiant function. This function used to be called the "Subdietic", though that term has since been restricted to a related composite function (see below on Composite Functions). | ||
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These are quartertone functions that are not on the Paradiatonic Scale. Of these, there are only two basic functions... | These are quartertone functions that are not on the Paradiatonic Scale. Of these, there are only two basic functions... | ||
''' | '''Superobstant''' - This is a note which, in Bass-Up tonality, is mapped to 9\24. 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. Although originally named the "Varicoserviant" region- the name coming from "Varicant" and "Serviant", with a linking "-o-" in place of the "-ant" of "Varicant"- the fact is that intervals in this region are also generally more dissonant and have a tendency to disrupt both chords and melodies, leading to their avoidance in chords outside of deliberate dissonances, has lead to a name change for the region as a whole. The new name of this region comes from "super-" and "obstant" which comes from Latin "obstō"<ref>[[Wiktionary: obsto #Latin]]</ref>. Chords of this type have Preserviant, Preintersubiant and Preinterregnant functions as well as Premediant functions. | ||
''' | '''Subobstant''' - This is a note which, in Bass-Up tonality, is mapped to 15\24. 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. Although originally named the "Varicodominant" region- the name coming from "Varicant" and "Dominant", with a linking "-o-" in place of the "-ant" of "Varicant"- the fact that intervals in this region are also generally more dissonant, leading to their avoidance in chords outside of deliberate dissonances, has lead to a name change for the region as a whole. The new name of this region comes from "sub-" and "obstant", which, as mentioned before, comes from Latin "obstō". Chords of this type have Predominant, Preintersubiant and Preinterregnant functions, as well as Precontramediant functions, and, perhaps very tellingly, tend to utilize Diminished Fourths instead of Major Thirds due to the functions of the Subgradient- which usually gets incorporated into these kinds of chords. | ||
== Diatonic, Paradiatonic, and the Tonic's Proximal Pythagorean Aura == | == Diatonic, Paradiatonic, and the Tonic's Proximal Pythagorean Aura == | ||