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

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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...
-'''Contravaricant''' - Named in contrast to the Varicant function, 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.  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.
+'''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.
-'''Intersubiant''' - This is a note that occurs roughly at intervals ranging from 256/187 to [[25/18]] away from the Tonic in the scale's direction of construction.  Like both the Serviant and the Sycophant, intervals in this region tend to have a Predominant function, however, the way these intervals carry out this function is rather different from both as 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.  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, since, as its name implies, it has a decent Predominant function without the risks of tonicizing the Dominant that arise with Sycophant Antitonics, while also having Preserviant functions.
+'''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 tend to have a Predominant function, however, the way these intervals carry out this function is rather different from both as 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.  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, since, as its name implies, it has a decent Predominant function without the risks of tonicizing the Dominant that arise with Sycophant Antitonics, while also having Preserviant functions.
 What's less expected, however, is that the Intersubiant also has Mocktyrant Functions.
-'''Interregnant''' - This is a note that occurs roughly at intervals ranging from [[36/25]] to 187/128 away from the Tonic 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.  In Bass-Up tonality, this 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, since, as its name implies, it has decent Preserviant and Predominant functions.  However, it also has Mocksycophant Functions.
+'''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.  In Bass-Up tonality, this 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, since, as its name implies, it has decent Preserviant and Predominant functions.  However, it also has Mocksycophant Functions.
-'''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 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- 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.
+'''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 ===