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

← Older edit Newer edit →

VisualWikitext

@@ Line 39: / Line 39: @@
 === Derivative Diatonic Functions ===
-I should point out that all of the scale degree functions described in Viennese Theory, as well as a few additional functions listed on this page, can be classified as '''first derivative''' functions because only one instance of any given derivational process is needed to reach them.
+I should point out that all of the scale degree functions described in Viennese Theory, as well as a few additional functions listed on this page, can be classified as '''first derivative''' functions because only one instance of any given derivational process is needed to reach them.  Do note that of all the original Viennese functions, only the Mediant remains virtually unchanged from the original theories to this reconstruction, as another has been renamed, while four others have been grouped together under new functions.
-'''Contralead''' - This function, although not found in Viennese Theory proper, is easily derivable through the Tonic Adjacent function, the Serviant Parallel function of [[16/15]], and the Antidominant function typified by the root of the [[Wikipedia:Neapolitan chord|Neapolitan chord]].  As such, this lowered second scale degree in Bass-Up tonality should be considered as more than just a simple chromatic alteration of the Supertonic.  Taking this idea into the realm of Microtonality, the Contralead is an interval that maps to both 1\7 and 2\24, and serves in part as a leading tone in the direction opposite that of the scale's direction of construction, but also has a Predominant function.
+'''Supervicinant''' - This is any note that maps to 1\7 above the Tonic, and in fact, intervals in this vicinity have both Tonic Adjacent and Serviant Parallel functions, beyond that, however, the precise behavior of notes in this range is determined by both mappings and concrete tuning ranges, see the Supervicinant and Subvicinant Subtypes section for more discussion of this function.
-'''Supertonic''' - This function is easily derivable through the Tonic Adjacent function, and either the Serviant Parallel function and or the "'''Didominant'''" function of [[9/8]], or, at least that's the case in Bass-Up tonality, where it is an interval that maps to both 1\7 and 4\24 and occurs above the Tonic as the second scale degree.  However, it should be noted that the lower boundary of this function is situated at roughly 119/108 above the Tonic, since notes located at smaller distances from the Tonic are liable to cause listeners to forget the ending pitch's relationship to the starting pitch- something which Supertonics don't do under any circumstances.
 '''Mediant''' - This is the note that maps to 2\7 from the Tonic in the scale's direction of construction, and is named due to being roughly halfway between the Tonic and the Dominant.  This is the first of the two diatonic scale degrees that are located relatively far from the Tonic along the Circle of Third Harmonics, and, as a consequence, not only has the most possibilities for realization and the ability to easily host chords built with wolf fifths, but also a tendency towards stagnation, leading to the historical designation as a "weak harmony".  Aside from these, the properties that are central to the Mediant function are all most easily derived through the Tonic Parallel function and the Serviant Adjacent function, and in addition, have both Preserviant and Predominant functions.  However, there are other functional aspects of a Mediant that are determined by whether the interval in question is considered consonant or dissonant, with [[5/4]] and [[6/5]] being examples of consonant Mediants, and [[81/64]] and [[32/27]] being examples of dissonant Mediants, though it should be noted that 81/64 also has the function of "'''Tetradominant'''" while 32/27 also has the function of "'''Triserviant'''".  Furthermore, since there's such a large range of Mediants, there are types of Mediant that don't have diatonic function.
-'''Antitonic''' - This is a special case, see the next section for more discussion of this function.
+'''Antitonic''' - This is a special case, see the Antitonic Subtypes section for more discussion of this function.
 '''Contramediant''' - Compared to the term "''Submediant''" from traditional music theory, the term "Contramediant" may have a slightly different frame of reference, as while a "Submediant" is halfway between the Tonic and a "Subdominant", the "Contramediant" is halfway between the Tonic and the Serviant.  The Contramediant is the note that maps to 5\7 from the Tonic in the scale's direction of construction, and is the second of two that are located relatively far from the Tonic along the Circle of Third Harmonics, and, as a consequence, is not only tied with the Mediant for having the most possibilities for realization, but also the ability to easily host chords built with wolf fifths, and lastly, a tendency towards stagnation, leading to the historical designation as a "weak harmony".  From a functional standpoint, the properties that are central to the Contramediant function are most easily derived through the Tonic Parallel function and the Dominant Adjacent function, and in addition, have both Preserviant and Predominant functions.  However, there are other functional aspects of a Contramediant that are determined by whether the interval in question is considered consonant or dissonant, with [[5/3]] and [[8/5]] being examples of consonant Contramediants, and [[27/16]] and [[128/81]] being examples of dissonant Contramediants, though it should be noted that 27/16 also has the function of "'''Tridominant'''" while 128/81 also has the function of "'''Tetraserviant'''".  Furthermore, since there's such a large range of Contramediants, there are types of Contramediant that don't have diatonic function.
-'''Subtonic''' - This function is easily derivable through the Tonic Adjacent function and either the Dominant Parallel function and or the "'''Diserviant'''" function of [[16/9]], with these intervals additionally having Predominant functions, or, at least that's the case in Bass-Up tonality, where it is an interval that maps to both 6\7 and 20\24 and occurs above the Tonic as the seventh scale degree.  However, it should be noted that the upper boundary of this function is situated at roughly 216/119 above the Tonic, since notes located at larger distances from the Tonic are liable to cause listeners to forget the ending pitch's relationship to the starting pitch- something which Subtonics don't do under any circumstances.
+'''Subvicinant''' - This is any note that maps to 1\7 below the Tonic, and in fact, intervals in this vicinity have both Tonic Adjacent and Dominant Parallel functions, beyond that, however, the precise behavior of notes in this range is determined by both mappings and concrete tuning ranges, see the Supervicinant and Subvicinant Subtypes section for more discussion of this function.
+== Supervicinant and Subvicinant Subtypes ==
+The Supervicinant and Subvicinant functions each have two subtypes that are common to traditional music theory, although leading tones have been specified according to their position, and have been given distinct functions.
+=== Specific Types of Supervicinant ===
+'''Supercollocant''' - This type of Supervicinant, although not found in Viennese Theory proper, additionally has the Antidominant function as typified by the root of the [[Wikipedia:Neapolitan chord|Neapolitan chord]] in Bass-Up tonality and the Antiserviant function in Treble-Down tonality.
+'''Supertonic''' - This type of Supervicinant is an interval that maps to both 1\7 and 4\24 in Bass-Up tonality and occurs above the Tonic as the second scale degree.  However, it should be noted that the lower boundary of this function is situated at roughly 119/108 above the Tonic, since notes located at smaller distances from the Tonic are liable to cause listeners to forget the ending pitch's relationship to the starting pitch- something which Supertonics don't do under any circumstances.  Conspicuously, one type of Supertonic is the "'''Bidominant'''", which is the function specifically of [[9/8]].
+=== Specific Types of Subvicinant ===
+'''Subtonic''' - This type of Subvicinant is an interval that maps to both 6\7 and 20\24 in Bass-Up tonality and occurs above the Tonic as the seventh scale degree.  However, it should be noted that the upper boundary of this function is situated at roughly 216/119 above the Tonic, since notes located at larger distances from the Tonic are liable to cause listeners to forget the ending pitch's relationship to the starting pitch- something which Subtonics don't do under any circumstances.  Conspicuously, one type of Supertonic is the "'''Biserviant'''", which is the function specifically of [[16/9]].
-'''Lead''' - This is the note typically referred to when people say "the leading tone", and, from a harmonic standpoint it is easily derivable through the Tonic Adjacent function, the Dominant Parallel function of [[15/8]], and the Antiserviant function.  This is an interval that maps to both 6\7 and 22\24, and serves as a leading tone in the scale's direction of construction.  Although triads built on this scale degree are regarded by some as simply incomplete Dominant Seventh chords, my own analysis, while acknowledging the functional similarities between the Lead and the Dominant, sees this interval as functionally distinct from the Dominant due to the Lead also being potentially related to the Mediant in the same way that the Dominant is related to the Tonic- a key functionality that is often exploited in [[Wikipedia:Vi–ii–V–I|circle progression]]s- and, the possibility of being set-up through quartertone-like motion from above (see below on Paradiatonic and Parachromatic Functions).
+'''Subcollocant''' - This type of Subvicinant is the note typically referred to when people say "the leading tone", and an interval that maps to both 6\7 and 22\24 in Bass-Up tonality.  Additionally, it has the Antiserviant function in Bass-Up tonality and the Antidominant function in Treble-Down tonality.  Although triads built on this scale degree are regarded by some as simply incomplete Dominant Seventh chords, my own analysis, while acknowledging the functional similarities between the Subcollocant and the Dominant in Bass-Up tonality, sees this interval as functionally distinct from the Dominant due to the Subcollocant also being potentially related to the Mediant in the same way that the Dominant is related to the Tonic- a key functionality that is often exploited in [[Wikipedia:Vi–ii–V–I|circle progression]]s.
-== Antitonic ==
+== Antitonic Subtypes ==
 Notes that occur around half an octave away from the Tonic, on account of harmonies built on notes in this area tending to oppose that of the Tonic, are referred to by the term "Antitonic" by myself and others.  It should be noted that the Antitonic is basically a first derivative function as it is derived from the Tonic through either perfect or imperfect Antipodism.  In addition, the term "Antitonic" acts as a generic term for any of a group of diatonic functions found in this region.  While some microtonal theorists insist that the Antitonic functionality is more fundamental than perhaps even the Dominant or Serviant, others, such as myself, disagree.