User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions

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 === Circumtonic Regions ===
-The Circumtonic regions are the two main regions on either side of the Tonic, outside the Tonic's "event horizon".  These intervals are invariably inside the Tonic's uncanny valleys, so they're often avoided.
+The Circumtonic regions are the two main regions on either side of the Tonic, outside the Tonic's "event horizon".  These intervals are invariably inside the Tonic's uncanny valleys, so they're usually avoided outside of modulation.
 '''Supercommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 20 cents above the Tonic.  These intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance, or for a slightly less resolved version of a Unison or Octave.
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 '''Acuodominant''' - This function is a compositing of Dominant detempering and Misodominant (see below on Basic Parachromatic Functions).
-'''Geminodominant''' - This is a note that occurs roughly at intervals ranging from 187/128 away from the Tonic to about 16 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.  Apart from this, 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.  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.
+'''Geminodominant''' - This is a note that occurs roughly at intervals ranging from 187/128 away from the Tonic to about 16 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.  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.
 === Circumserviant Regions ===
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 The circumserviant regions are the two main regions on either side of the Serviant proper, and there are two functions located in these regions, one of which is an actual diatonic function.  Note that antitonic and paradiatonic functions falling in this region are not covered in this section.
-'''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from 3.5 cents beyond the 4/3 perfect fourth to 256/187 away from the Tonic 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 Dominant, 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.  Apart from this, 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.  The dissonance of this function relative to a chord root is useful in preventing tonicization of chords built on the Supertonic, Subtonic, the Mediant and the Contramediant, but outside of these usages and well supported chords, this kind of thing is best avoided.
+'''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from 3.5 cents beyond the 4/3 perfect fourth to 256/187 away from the Tonic 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 Dominant, 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 the Supertonic, Subtonic, 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, 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.
 '''Gravoserviant''' - This function is a compositing of Serviant detempering and Misoserviant (see below on Basic Parachromatic Functions).