User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
No edit summary |
No edit summary |
||
| Line 35: | Line 35: | ||
== Facets Derived from Viennese Theory == | == Facets Derived from Viennese Theory == | ||
Among the chief ideas that come from Viennese Theory is the idea that each degree has its own function relative to the Tonic. However, while in Viennese Theory proper, the degrees are strictly defined only relative to the cycle of fifths, I, for the realm of Microtonality, not only take stacks of 3/2 to form a key navigational axis called the "'''Diatonic Axis'''", but also additionally take things like Bass-Up | Among the chief ideas that come from Viennese Theory is the idea that each degree has its own function relative to the Tonic. However, while in Viennese Theory proper, the degrees are strictly defined only relative to the cycle of fifths, I, for the realm of Microtonality, not only take stacks of 3/2 to form a key navigational axis called the "'''Diatonic Axis'''", but also additionally take things like Bass-Up tonality (that is, tonal music built from the low pitches upwards) and Treble-Down tonality (that is, tonal music built from the high pitches downwards) into consideration. On top of that, I also contend that virtually all of the functions described by Viennese Theory find their roots in specific combinations of the different operations described above on the basic functions from German Theory. | ||
=== Derivative Diatonic Functions === | === Derivative Diatonic Functions === | ||
| Line 43: | Line 43: | ||
'''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. | '''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. | ||
'''Mediant''' - This is the note that maps to 2\7 from the Tonic in the scale's direction of construction | '''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, Mediants have both Preserviant and Predominant functions. Furthermore, since there's such a large range of Mediants, there are a multitude of subtypes, see the Mediant Subtypes section for more discussion of this function. | ||
'''Antitonic''' - This is a special case, see the Antitonic Subtypes 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 | '''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, Contramediants have both Preserviant and Predominant functions. Furthermore, since there's such a large range of Contramediants, there are a multitude of subtypes, see the Contramediant Subtypes section for more discussion of this function. | ||
'''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. | '''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. | ||
| Line 53: | Line 53: | ||
== Supervicinant and Subvicinant Subtypes == | == 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 | 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 === | === Specific Types of Supervicinant === | ||
'''Supercollocant''' - This type of Supervicinant, although not found in Viennese Theory proper, | '''Supercollocant''' - This type of Supervicinant, although not found in Viennese Theory proper, is an interval that maps to both 1\7 and 2\24 in Bass-Up tonality. Additionally, it 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. | ||
'''Superabrogant''' - This type of Supervicinant is not a traditional diatonic function at all since it is an interval that maps to both 1\7 and 3\24 in Bass-Up tonality. As per this function's name, the intervals in this range are like Supercollocants in that they may cause listeners to forget the ending pitch's relationship to the starting pitch in voice-leading. However, they are noticeably too wide for them to convincingly pass off as being totally semitone-like since they feel as if they're rather disconnected from the Tonic, and furthermore, the occurrence of two successive instances of these sorts of intervals in the same direction is liable to come across as jarring. | |||
'''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]]. | '''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]]. | ||
| Line 64: | Line 66: | ||
'''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]]. | '''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]]. | ||
''Subabrogant''' - This type of Subrvicinant is not a traditional diatonic function at all since it is an interval that maps to both 6\7 and 21\24 in Bass-Up tonality. As per this function's name, the intervals in this range are like Subcollocants in that they may cause listeners to forget the ending pitch's relationship to the starting pitch in voice-leading. However, they, like Superabrogants, feel as if they're rather disconnected from the Tonic, and furthermore, the occurrence of two successive instances of these sorts of intervals in the same direction is liable to come across as jarring. | |||
'''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. | '''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. | ||
== Mediant Subtypes == | |||
<todo> | |||
It is worth noting | |||
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. | |||
== Contramediant Subtypes == | |||
<todo> | |||
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'''". | |||
== Antitonic Subtypes == | == Antitonic Subtypes == | ||
| Line 213: | Line 229: | ||
While some neutralized scale degrees- such as the Neutral third and Neutral sixth- have many of the same diatonic functions as the adjacent Major and Minor scale degrees, this is not the case for neutral seconds and neutral sevenths due to the Major and Minor versions of these scale degrees having noticeably different functions. | While some neutralized scale degrees- such as the Neutral third and Neutral sixth- have many of the same diatonic functions as the adjacent Major and Minor scale degrees, this is not the case for neutral seconds and neutral sevenths due to the Major and Minor versions of these scale degrees having noticeably different functions. | ||
== Diatonic, Paradiatonic, and the Tonic's Proximal Pythagorean Aura == | == Diatonic, Paradiatonic, and the Tonic's Proximal Pythagorean Aura == | ||