User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions

'''Preparation''' - Notes that "prepare the way" for either a Dominant or a Serviant through any of the above operations, or through some other mechanism, relate to said notes by this process.  Functions which have this kind of role relative are denoted with a "pre-" prefix here.

'''Sycophant''' - Named as such on account of it having a tendency to "kiss up to" and tonicize the Dominant- that is, to cause the Dominant to become a new Tonic- unless followed up by a different note such as a Subcollocant or Supercollocant, this type of Antitonic is mapped to both 3\7 and 12\24.  A prototypical example of this type of Antitonic is 45/32.

'''Tyrant''' - If the Antitonic is mapped to both 4\7 and 12\24, 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, and indeed these brute force Dominant-esque tendencies are the source the name "Tyrant".  For example, 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 some other type of substitute for a Dominant, often bypassing this type of Antitonic, though on rare occasions, a Tyrant will act as a leading tone to the Serviant.  A prototypical example of this type of Antitonic is 64/45.

'''Subdislocant''' - This is a note that is to either the Subcollocant what a Tyrant is to a Sycophant.  Specifically, it is the result of the Tonic being altered by some kind of chromatic semitone downwards and thus being displaced by a Nontonic function which leads away from the Tonic proper.

'''Pseudoserviant''' - This is a note that occurs roughly at intervals ranging from about 25 cents to about 3.5 cents short of the 4/3 perfect fourth in the scale's direction of construction.  Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Servient is found just short the sweet spot range near the standard issue 4/3.  However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Preserviant function.

'''Primary Adpositive Purity''' - This rule is that for every chord root located one step away from either the Tonic, Dominant or Serviant along the Circle of Fifths, there is a demand for the fifth of the chord in question to be within 3.5 cents of a just 3/2, however, chord roots that are located three or more steps away from the Tonic along the circle of fifths are not subject to the aforementioned restriction due to their distance.  This means that the Tonic, Dominant, Serviant, Supertonic and Subtonic chords all demand a perfect fifth as the fifth of the chord, whether you are building the Tonality upwards or downwards, but wolf fifths can occur easily as the fifth of chords which are located three or more steps away from the Tonic.

 

 

 

 

 

The Paradiatonic scales from a given tonic acts as a sort of "second shelf" of that tonality.   

I, tII/dbIII, dIII, tIV, dV, dVI, tVI/dbVII, tVII

I, dbII tII/dbIII, dIII, tIV, dV, dVI, tVI/dbVII

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...

'''Interregnant''' - This is an interval that maps to both 4\7 and 13\24 in the scale's direction of construction and comprises the intervals ranging from around 3.5 cents short of [[16/11]] to around 3.5 cents beyond [[22/15]].  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.  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.

'''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, Preserviants, and Serviant Parallels, 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 "'''Pseudotridominant'''", which arises from stacking three Pseudodominants, and the "'''Pseudobiserviant'''", which arises from stacking two Pseudoserviants.

'''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 Subcollocant- 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 Subgradient and the Tonic is likely to result in the Subgradient resolving back down to either the Lead or the Subabrogant.  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).

'''Supergradient''' - This is a note that occurs at intervals between roughly 25 cents above the Tonic and 25/24 above the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, more rarely in Bass-Up Tonality, the Supercollocant.  However, there are a few functional differences between a Supergradient and a Supercollocant in Bass-Up Tonality that are worth considering.  For starters, Supergradients are often more likely to be passing tones than Supercollocant, and, when they’re not merely passing non-chord tones, they are just as liable to resolve upward through some sort of semitone-like motion to some form of Supercollocant or Superabrogant, 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 Supercollocant can resolve to the Tonic in part through a strong harmonic connection, a Supergradient is much more likely to do so through sheer brute force when such a resolution is noticeable.  As if that weren't enough, the Subgradient also has the Antinterregnant function.  This function used to be called the "Superdietic", though that term has since been restricted to a related composite function (see below on Composite Functions).

'''Supersanguinant''' - This function is one of two "bleeding tone" functions- hence its Latin-derived name- and is a compositing of Supergradient and Proximosupercollocant functions, and thus, has a more tense feel than a Contralead alone.  It should be noted that this function is formed by the overlap between different functional regions rather than merely being located at a boundary.