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

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 === Circumserviant Regions ===
-The circumserviant regions are the two main regions on either side of the Serviant proper, and since the uncanny valley around the Serviant is around half the size of the one around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities.  Note that antitonic and paradiatonic functions falling in this region are not covered in this section.
+The circumserviant regions are the two main regions on either side of the Serviant proper, and since the uncanny valley around the Serviant is around half the size of the one around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities.
 '''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from about 16 cents to about 32 cents beyond the 4/3 perfect fourth in the scale's direction of construction.  Although often overlooked or even outright shunned by traditional theorists, the Geminodominant is a legitimate diatonic function in terms of this analysis- albeit one only existing in non-meantone environments in which it is easily derived from the Serviant through detempering, occurring in 5-limit diatonic environments, and acting as a sort of "fraternal twin" to the Serviant, hence its name.  As typified by intervals like [[27/20]], Geminoserviants are dissonant intervals that often act as a sort of predominant and or as the inverses of Geminodominants.  The dissonance of this function relative to a chord root is useful in preventing tonicization of chords built on the Supertonic, Subtonic, the Mediant and the Contramediant, but outside of these usages and well supported chords, this kind of thing is best avoided.  Apart from diatonic contexts, Geminoserviants only rise to prominence in systems where what might otherwise function as a Serviant is found just beyond the sweet spot range near the standard issue 4/3.
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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, 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.
-=== Neutralization ===
+=== Derivative Paradiatonic Functions ===
-In addition to the six known Diatonic Function-Deriving Operations listed above, there's also one Paradiatonic Function-Deriving Operation known as Neutralization, which, as the name suggests, creates paradiatonic functions from the neutralization and hybridization of Major and Minor Diatonic scale degrees.
+In addition to the six known Diatonic Function-Deriving Operations listed above, there's also one Paradiatonic Function-Deriving Operation known as '''Neutralization''', which, as the name suggests, creates paradiatonic functions from the neutralization and hybridization of Major and Minor Diatonic scale degrees.
-=== Derivative Paradiatonic Functions ===
 '''Neutral Mediant''' - As per the name, this is nothing other than a neutralized Mediant, and thus, it has the Tonic Parallel, Serviant Adjacent, Preserviant and Predominant functions that you expect from a Mediant, only, it doesn't serve well at phrase endings, rather, its Tonic Parallel function is only appropriate during the middle of musical phrases.
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 '''Neutral Contramediant''' -  As per the name, this is nothing other than a neutralized Contramediant, and thus, it has the Tonic Parallel, Dominant Adjacent, Preserviant and Predominant functions that you expect from a Contramediant, but, like with the Neutral Mediant, it doesn't serve well at phrase endings, rather, its Tonic Parallel function is only appropriate during the middle of musical phrases.
-'''Subgradient''' - This is a note that occurs at intervals between roughly 48/25 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 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 Subtonic.  As if that weren't enough, the Subgradient also has the Antintersubiant function.
+'''Subgradient''' - This is a note that occurs at intervals between roughly 48/25 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 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 Subtonic.  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 a related composite function (see below on Composite Functions).
-'''Supergradient''' - This is a note that occurs at intervals between roughly 20 cents above the Tonic and 25/24 above the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Contralead.  However, there there are a few functional differences between a Supergradient and a Contralead in Bass-Up Tonality that are worth considering.  For starters, Supergradients 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 thought some sort of semitone-like motion to some form of Contralead, Semicontralead, or even a 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 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.
+'''Supergradient''' - This is a note that occurs at intervals between roughly 20 cents above the Tonic and 25/24 above the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Contralead.  However, there there are a few functional differences between a Supergradient and a Contralead in Bass-Up Tonality that are worth considering.  For starters, Supergradients 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 thought some sort of semitone-like motion to some form of Contralead, Semicontralead, or even a 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 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 a related composite function (see below on Composite Functions).
 === Basic Parachromatic Functions ===