User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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'''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. | '''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. | ||
'''Supertonic''' - This function is easily derivable through the Tonic Adjacent function, the Serviant Parallel function, and 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. | '''Supertonic''' - This function is easily derivable through the Tonic Adjacent function, the Serviant Parallel function, and 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. | '''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. | ||
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'''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. | '''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. | ||
'''Subtonic''' - This function is easily derivable through the Tonic Adjacent function, the Dominant Parallel function, and 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. | '''Subtonic''' - This function is easily derivable through the Tonic Adjacent function, the Dominant Parallel function, and 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. | ||
'''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). | '''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). | ||
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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. | ||
''' | '''Superabrogant''' - This is a note that occurs roughly at intervals between 14/13 and 119/108 above the Tonic as the second scale degree. As per this function's name, the bulk of intervals in this range are like Contraleads 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 either Leads or Dislocants, and the occurrance of two successive instances of these sorts of intervals in the same direction is liable to come across as jarring. Still, chords built on a note with this function have traits reminiscent of a Neapolitan chord though with the catch that the Superabrogant also has the Misoserviant Parallel and Antimisodominant functions. The [[12/11]] neutral second is a rather typical example of an interval with this function. | ||
''' | '''Subabrogant''' - This is a note that occurs roughly at intervals between 216/119 and 13/7 above the Tonic as the seventh scale degree. Naturally, this interval functions as a sort of Dominant Parallel, though there are significant differences from both a Subtonic and a Lead. For starters, the Subabrogant also has the Misodominant Parallel and Antimisoserviant functions, and furthermore as Subabrogant has many of the same properties as a Superabrogant except for being located below the Tonic as opposed to being located above the Tonic. The [[11/6]] neutral seventh is a rather typical example of an interval with this function. | ||
== Composite Functions == | == Composite Functions == | ||