User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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The circumdomimant regions are the two main regions on either side of the Dominant proper, and since the uncanny valleys around the Dominant are not as deep as those around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities. Note that together with the Dominant itself, these functions are collectively called "'''Protodominants'''", as there are many systems where what would be the Dominant fails to get distinguished from either one or the other of the functions listed here. | The circumdomimant regions are the two main regions on either side of the Dominant proper, and since the uncanny valleys around the Dominant are not as deep as those around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities. Note that together with the Dominant itself, these functions are collectively called "'''Protodominants'''", as there are many systems where what would be the Dominant fails to get distinguished from either one or the other of the functions listed here. | ||
'''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond [[22/15]] to about 3.5 cents short of the 3/2 perfect fifth in the scale's direction of construction. Although often overlooked or even outright shunned by traditional theorists, the Geminodominant is a legitimate diatonic function in terms of this analysis- albeit one only existing in non-meantone environments in which it is easily derived from the Dominant through detempering, occurring in [[5-limit]] diatonic environments, and acting as a sort of "fraternal twin" to the Dominant, hence its name. Specifically, as typified by intervals like [[40/27]], Geminodominants are dissonant intervals that simultaneously act as alternatives to the Dominant in both chord progressions and chord construction, and often require resolution, though they also have a | '''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond [[22/15]] to about 3.5 cents short of the 3/2 perfect fifth in the scale's direction of construction. Although often overlooked or even outright shunned by traditional theorists, the Geminodominant is a legitimate diatonic function in terms of this analysis- albeit one only existing in non-meantone environments in which it is easily derived from the Dominant through detempering, occurring in [[5-limit]] diatonic environments, and acting as a sort of "fraternal twin" to the Dominant, hence its name. Specifically, as typified by intervals like [[40/27]], Geminodominants are dissonant intervals that simultaneously act as alternatives to the Dominant in both chord progressions and chord construction, and often require resolution, though they also have a Preservient function. The dissonance of this function relative to a chord root is useful in preventing tonicization of chords built on the traditional weak harmonies- the Mediant and the Contramediant- which also has the benefits of strengthening interrupted cadences and creating the sense of impending movement, but outside of these usages and well supported chords, this kind of thing is best avoided since things repel the similar but not identical. Apart from diatonic contexts, Geminodominants only rise to prominence in systems where what might otherwise function as a Dominant is found just short of the sweet spot range near the standard issue 3/2. | ||
'''Pseudodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 cents beyond the 3/2 perfect fifth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Dominant is found just beyond the sweet spot range near the standard issue 3/2. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Predominant function. | '''Pseudodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 cents beyond the 3/2 perfect fifth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Dominant is found just beyond the sweet spot range near the standard issue 3/2. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Predominant function. | ||
=== | === Circumservient Regions === | ||
The | The circumservient regions are the two main regions on either side of the Servient proper, and since the uncanny valleys around the Servient are not as deep as those around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities. Note that together with the Servient itself, these functions are collectively called "'''Protoservients'''", as there are many systems where what would be the Servient fails to get distinguished from either one or the other of the functions listed here. | ||
''' | '''Geminoservient''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond the 4/3 perfect fourth to about 3.5 cents short of [[15/11]] in the scale's direction of construction. Although often overlooked or even outright shunned by traditional theorists, the Geminoservient is a legitimate diatonic function in terms of this analysis- albeit one only existing in non-meantone environments in which it is easily derived from the Servient through detempering, occurring in 5-limit diatonic environments, and acting as a sort of "fraternal twin" to the Servient, hence its name. As typified by intervals like [[27/20]], Geminoservients are dissonant intervals that often act as a sort of Predominant and or as the inverses of Geminodominants. The dissonance of this function relative to a chord root is useful in preventing tonicization of chords built on the Mediant and the Contramediant, but outside of these usages and well supported chords, this kind of thing is best avoided. Apart from diatonic contexts, Geminoservients only rise to prominence in systems where what might otherwise function as a Servient is found just beyond the sweet spot range near the standard issue 4/3. | ||
''' | '''Pseudoservient''' - This is a note that occurs roughly at intervals ranging from about 25 cents to about 3.5 cents short of the 4/3 perfect fourth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Servient's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Servient is found just short the sweet spot range near the standard issue 4/3. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Preservient function. | ||
=== Governing Rules === | === Governing Rules === | ||
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However, in non-meantone settings, it is possible to have a chord which shares its root with the Tertiary Dominant and shares both its third and fifth with the Relative Minor. Since such an arrangement results in a wolf fifth, and since the wolf fifth is a dissonance requiring resolution, one could argue that such a chord has a function distinct from the more traditional options- specifically one which is involved in interrupted cadences, as well as in starting cadences that "wind down" such as VImin-IVmaj-Imaj or even VImin-Vmaj-Imaj. This particular function is what I call the ''Major Contramediant Tensive''. | However, in non-meantone settings, it is possible to have a chord which shares its root with the Tertiary Dominant and shares both its third and fifth with the Relative Minor. Since such an arrangement results in a wolf fifth, and since the wolf fifth is a dissonance requiring resolution, one could argue that such a chord has a function distinct from the more traditional options- specifically one which is involved in interrupted cadences, as well as in starting cadences that "wind down" such as VImin-IVmaj-Imaj or even VImin-Vmaj-Imaj. This particular function is what I call the ''Major Contramediant Tensive''. | ||
'''Primary Adpositive Purity''' - This rule is that for every chord root located one step away from either the Tonic, Dominant or | '''Primary Adpositive Purity''' - This rule is that for every chord root located one step away from either the Tonic, Dominant or Servient along the Circle of Fifths, there is a demand for the fifth of the chord in question to be within 3.5 cents of a just 3/2, though in the case of a chord that has a root located at two steps away from the Tonic along the along the Circle of Fifths, the fifth of the chord can be deliberately subjected to the process of Displacement as mentioned before and not run afoul of this restriction. However, chord roots that are located three or more steps away from the Tonic along the circle of fifths are not subject to the aforementioned restriction due to their distance. This means that the Tonic, Dominant, Servient, Supertonic and Subtonic chords all demand a perfect fifth as the fifth of the chord, whether you are building the Tonality upwards or downwards, but wolf fifths can occur easily as the fifth of chords which are located three or more steps away from the Tonic. | ||
== Beyond Diatonic and Chromatic Functional Harmony == | == Beyond Diatonic and Chromatic Functional Harmony == | ||