User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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=== Basic Operations === | === Basic Operations === | ||
The way I see it, there are at least | The way I see it, there are at least four known operations which can be used to derive additional functions from the three basic functions listed above. | ||
''' | '''Stacking''' - The notes that are arrived at through stacking multiple instances of either 3/2 or 4/3 (or their tempered counterparts) are dubbed according to the number of instances stacked, and the nature of the notes separated by the interval being stacked. Thus, stacking two instances of the Dominant or the Serviant results in the creation of the "Double Dominant" or "Double Serviant" respectively. This concept comes from the German language's way of referring to the chord built on the second scale degree of the Diatonic scale as the "Doppeldominante", which literally means "Double Dominant". | ||
''' | '''Parallelism''' - Notes located in the same primary [[tetrachord]] as either the Tonic, the Dominant, or the Serviant take on similar functions to said notes, with the caveat that functions derived from the Tonic in this fashion are still technically nontonic functions. This process is one of two that create what in traditional music theory are referred to as [[Wikipedia:Parallel and counter parallel|"''parallels''" and "''counter parallels''"]]. | ||
'''Adjacency''' - Notes within a suitable voice leading distance from either the Dominant or Serviant tend to have the opposite function relative to the Tonic- this process even extends to the relationship between the Dominant and Serviant themselves. This process is one of two that create what in traditional music theory are referred to as "''parallels''" and "''counter parallels''", however, unlike Parallelism proper, this process can establish these kinds of relationships outside the primary tetrachord. | |||
'''Antipodism''' - Notes that are either opposite in tone color or nearly so due to being approximately half an octave away from the starting point are harmonically opposed to the starting point. Non-tonic notes related through this process tend to have the opposite function relative to the Tonic. For the notes related to the Tonic by this process see Antitonic below. | |||
== 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 Tonality (that is, music built from the Bass upwards) and Treble-Down Tonality (that is, music built from the Treble downwards) into consideration. On top of that, I also contend that | 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, music built from the Bass upwards) and Treble-Down Tonality (that is, music built from the Treble 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. | ||
=== Scale Degree Functions === | === Scale Degree Functions === | ||
In addition to the | In addition to the aforementioned Basic Diatonic Functions, Aura contends that the following scale degree functions also exist: | ||
'''Contralead''' - | '''Contralead''' - This function, although not found in Viennese Theory proper, is easily derivable through a combination of the Tonic Adjacent function, the Subdominant 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 occurs at intervals between [[25/24]] and [[14/13]] away from the Tonic, and serves in part as a leading tone in the direction opposite that of the scale's direction of construction. | ||
'''Supertonic''' - This function is easily derivable through a combination of the Subdominant Parallel function of [[10/9]] and Double Dominant function of [[9/8]], or at least that's the case in Bass-Up Tonality, and especially in [[meantone]] contexts where the two intervals are equated. However, I would argue that due to both the close proximity of 10/9 and 9/8 even in non-meantone settings and the shared Predominant functionalities of both scale degrees, these two functions often overlap to some degree or other. Accordingly, this is the note that occurs roughly at intervals between [[567/512]] and [[256/225]] above the Tonic as the second scale degree. | '''Supertonic''' - This function is easily derivable through a combination of the Tonic Adjacent function, the Subdominant Parallel function of [[10/9]] and Double Dominant function of [[9/8]], or at least that's the case in Bass-Up Tonality, and especially in [[meantone]] contexts where the two intervals are equated. However, I would argue that due to both the close proximity of 10/9 and 9/8 even in non-meantone settings and the shared Predominant functionalities of both scale degrees, these two functions often overlap to some degree or other. Accordingly, this is the note that occurs roughly at intervals between [[567/512]] and [[256/225]] above the Tonic as the second scale degree. | ||
'''Mediant''' - This is the note that occurs roughly at intervals between [[75/64]] and [[32/25]] away 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 with the most possibilities for realization, though it is most often within 20 cents of either [[6/5]] or [[5/4]] due to these two LCJI intervals coming the closest to the halfway point between the Tonic and the Dominant. From a functional standpoint, the Mediant | '''Mediant''' - This is the note that occurs roughly at intervals between [[75/64]] and [[32/25]] away 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 with the most possibilities for realization, though it is most often within 20 cents of either [[6/5]] or [[5/4]] due to these two LCJI intervals coming the closest to the halfway point between the Tonic and the Dominant. From a functional standpoint, the Mediant function is most easily derived through a combination of the Tonic Parallel function and the Serviant Adjacent 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 a note that occurs roughly at intervals between [[25/16]] and [[128/75]] away from the Tonic in the scale's direction of construction, and is the second of two scale degrees with the most possibilities for the realization. From a functional standpoint, the Contramediant | '''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 a note that occurs roughly at intervals between [[25/16]] and [[128/75]] away from the Tonic in the scale's direction of construction, and is the second of two scale degrees with the most possibilities for the realization. From a functional standpoint, the Contramediant function is most easily derived through a combination of the Tonic Parallel function and the Dominant Adjacent function. | ||
'''Subtonic''' - This function is easily derivable through a combination of the Dominant Parallel function of [[9/5]] and Double Serviant function of [[16/9]], or at least that's the case in Bass-Up Tonality, and especially in meantone contexts where the two intervals are equated. As with the Supertonic, however, I would argue that due to both the close proximity of 9/5 and 16/9 even in non-meantone settings, these two functions often overlap to some degree or other. This is the note that occurs roughly at intervals between [[225/128]] and [[1024/567]] above the Tonic as the seventh scale degree. | '''Subtonic''' - This function is easily derivable through a combination of the Dominant Parallel function of [[9/5]] and Double Serviant function of [[16/9]], or at least that's the case in Bass-Up Tonality, and especially in meantone contexts where the two intervals are equated. As with the Supertonic, however, I would argue that due to both the close proximity of 9/5 and 16/9 even in non-meantone settings, these two functions often overlap to some degree or other. This is the note that occurs roughly at intervals between [[225/128]] and [[1024/567]] above the Tonic as the seventh scale degree. | ||
'''Lead''' - This is the note typically referred to when people say "the leading tone". This is a note that occurs at intervals between [[13/7]] and [[48/25]] away from the Tonic, which serves as a leading tone in the scale's direction of construction | '''Lead''' - This is the note typically referred to when people say "the leading tone", and, from a harmonic standpoint it is easily derivable through a combination of the Tonic Adjacent function, the Dominant Parallel function of [[15/8]], and the Antiserviant function. This is a note that occurs at intervals between [[13/7]] and [[48/25]] away from the Tonic, which 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 the Lead also being 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 == | ||