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

'''Intersubiant''' - This is an interval that maps to both 3\7 and 11\24 in the scale's direction of construction and comprises the intervals ranging from around 3.5 cents short of [[15/11]] to around 3.5 cents beyond [[11/8]].  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 Serviant, some kind of Contramediant, some kind of Supervicinant, or, in some tuning systems, certain kinds of Mediant.  In Bass-Up tonality, this functionality has its roots in the eleventh harmonic.

'''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.