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

The exact outcome and specific function of any given Antitonic depends on the interval between it and the Tonic in the scale's direction of construction, as well as by whether or not the interval in question is an augmented fourth or a diminished fifth:

*If the Antitonic is mapped to both 3\7 and 12\24, it tends to cause the Dominant to become a new Tonic unless followed up by a different note- one that is usually a Major 7th away from the Tonic.  Because of this tendency to "kiss up to" and tonicize the Dominant, this type of Antitonic can be dubbed a "'''Sycophant'''", with the prototypical Sycophant being 45/32.

*Conversely, if the Antitonic is mapped to both 4\7 and 12\24, it tends to contrast with the Tonic in a manner somewhat akin to that of a Dominant, but by sheer brute force and contrary harmonic nature- e.g. if the Tonic harmony is Minor in nature, the Antitonic harmony will be Major- or more rarely, Supermajor- in nature. Furthermore, in scales such as the Locrian scale, any type of Serviant harmony tends to resolve towards either this type of Antitonic, or some other type of substitute for a Dominant. Because of these Dominant-esque tendencies, this type of Antitonic can be dubbed a "'''Tyrant'''", with the prototypical Tyrant being 64/45.

In addition to the functions derived from both German theory and Viennese theory, as well as the Antitonic functions, I describe other functions here.  Do note that most of these these tend to only show up in systems where intervals such as these are distinct, such as higher [[EDO]]s.

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 32 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.

'''Subcommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 32 cents below the Tonic.  As with Supercommatic intervals, 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.

'''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 32 cents 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.

'''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from about 16 cents to about 32 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 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.