User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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=== Circumdominant Regions === | === Circumdominant Regions === | ||
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. | 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 25 cents 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 Preserviant 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. | '''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 25 cents 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 Preserviant 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. | ||
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=== Circumserviant Regions === | === Circumserviant Regions === | ||
The circumserviant regions are the two main regions on either side of the Serviant 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. | The circumserviant regions are the two main regions on either side of the Serviant 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 Serviant itself, these functions are collectively called "'''Protoserviants'''", as there are many systems where what would be the Serviant fails to get distinguished from either one or the other of the functions listed here. | ||
'''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 cents beyond the 4/3 perfect fourth 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 Serviant through detempering, occurring in 5-limit diatonic environments, and acting as a sort of "fraternal twin" to the Serviant, hence its name. As typified by intervals like [[27/20]], Geminoserviants 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 Mediant and the Contramediant, but outside of these usages and well supported chords, this kind of thing is best avoided. Apart from diatonic contexts, Geminoserviants only rise to prominence in systems where what might otherwise function as a Serviant is found just beyond the sweet spot range near the standard issue 4/3. | '''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 cents beyond the 4/3 perfect fourth 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 Serviant through detempering, occurring in 5-limit diatonic environments, and acting as a sort of "fraternal twin" to the Serviant, hence its name. As typified by intervals like [[27/20]], Geminoserviants 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 Mediant and the Contramediant, but outside of these usages and well supported chords, this kind of thing is best avoided. Apart from diatonic contexts, Geminoserviants only rise to prominence in systems where what might otherwise function as a Serviant is found just beyond the sweet spot range near the standard issue 4/3. | ||