Diatonic functional harmony: Difference between revisions

Line 60:

=== Basic Paradiatonic Functions ===

As with the three basic diatonic functions, the two most basic basic paradiatonic functions have their roots in LCJI.

'''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.

Line 66:

Line 68:

=== Interstep Functions ===

These intervals fall between the scale steps as defined by Viennese Theory, hence their collective label, and even some aspects of their individual names.

'''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- 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- Aura counterargues 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.

Line 76:

Line 80:

=== Neutral Degree Functions ===

While some neutralized scale degrees, such as the Neutral third and Neutral sixth, have the same diatonic functions as the adjacent Major and Minor scale degrees, this is not the case for neutral seconds and neutral sevenths.

'''Semicontralead''' - This is a note that occurs roughly at intervals between 14/13 and 567/512 above the Tonic as the second scale degree. Naturally, this interval functions as a sort of cross between a Contralead and a Supertonic, and indeed chords built on this can function as some sort of cross between a Neapolitan chord and a Supertonic chord. However, there are ways in which the Semicontralead is distinct from both. Notably, set-ups and follow-ups for a Semicontralead- apart from root motion by a fifth- are generally best when moving in a given Tonality's direction of construction, as intervals like this moving stepwise in the opposite direction are likely to create a disjunct without proper context. The [[12/11]] neutral second is a rather typical example of an interval with this function.

@@ Line 60: / Line 60: @@
 === Basic Paradiatonic Functions ===
+As with the three basic diatonic functions, the two most basic basic paradiatonic functions have their roots in LCJI.
 '''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.
@@ Line 66: / Line 68: @@
 === Interstep Functions ===
+These intervals fall between the scale steps as defined by Viennese Theory, hence their collective label, and even some aspects of their individual names.
 '''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- 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- Aura counterargues 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.
@@ Line 76: / Line 80: @@
 === Neutral Degree Functions ===
+While some neutralized scale degrees, such as the Neutral third and Neutral sixth, have the same diatonic functions as the adjacent Major and Minor scale degrees, this is not the case for neutral seconds and neutral sevenths.
 '''Semicontralead''' - This is a note that occurs roughly at intervals between 14/13 and 567/512 above the Tonic as the second scale degree.  Naturally, this interval functions as a sort of cross between a Contralead and a Supertonic, and indeed chords built on this can function as some sort of cross between a Neapolitan chord and a Supertonic chord.  However, there are ways in which the Semicontralead is distinct from both.  Notably, set-ups and follow-ups for a Semicontralead- apart from root motion by a fifth- are generally best when moving in a given Tonality's direction of construction, as intervals like this moving stepwise in the opposite direction are likely to create a disjunct without proper context.  The [[12/11]] neutral second is a rather typical example of an interval with this function.