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

'''Mediant''' - This is the note that maps to 2\7 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 both the most possibilities for realization and the ability to easily host chords built with wolf fifths.  In terms of any sort of octave-reduced harmonic-subharmonic interval axis featuring harmonic motion by intervals in this region, one of the main features that characterizes this region is a tendency towards stagnation, leading to the historical characterization of these sorts of harmonies as "weak harmonies".  Aside from this tendency towards stagnation, the properties that are central to the Mediant function are all most easily derived through the Tonic Parallel function and the Serviant Adjacent function, and in addition, have both Preserviant and Predominant functions.  However, there are other functional aspects of a Mediant that are determined by whether the interval in question is considered consonant or dissonant, with [[5/4]] and [[6/5]] being examples of consonant Mediants, and [[81/64]] and [[32/27]] being examples of dissonant Mediants.

'''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 the note that maps to 5\7 from the Tonic in the scale's direction of construction, and is the second of two scale degrees both the most possibilities for realization and the ability to easily host chords built with wolf fifths.  Furthermore, it also displays a tendency towards stagnation akin to that of the Mediant, leading to harmonies in this region being historically designated as "weak harmonies".  From a functional standpoint, the properties that are central to the Contramediant function are most easily derived through the Tonic Parallel function and the Dominant Adjacent function, and in addition, have both Preserviant and Predominant functions.  However, there are other functional aspects of a Contramediant that are determined by whether the interval in question is considered consonant or dissonant, with [[5/3]] and [[8/5]] being examples of consonant Contramediants, and [[27/16]] and [[128/81]] being examples of dissonant Contramediants.

'''Subtonic''' - This function is easily derivable through the Tonic Adjacent function, the Dominant Parallel function, and the Diserviant function of [[16/9]], with these intervals additionally having Predominant functions, or, at least that's the case in Bass-Up tonality, where it is an interval that maps to both 6\7 and 20\24 and occurs above the Tonic as the seventh scale degree.

'''Lead''' - This is the note typically referred to when people say "the leading tone", and, from a harmonic standpoint it is easily derivable through the Tonic Adjacent function, the Dominant Parallel function of [[15/8]], and the Antiserviant function.  This is an interval that maps to both 6\7 and 22\24, and 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 Lead also being potentially 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- and, the possibility of being set-up through quartertone-like motion from above (see below on Paradiatonic and Parachromatic Functions).

Notes that occur around half an octave away from the Tonic, on account of harmonies built on notes in this area tending to oppose that of the Tonic, are referred to by the term "Antitonic" by myself and others.  It should be noted that the Antitonic is basically a first derivative function as it is derived from the Tonic through either perfect or imperfect Antipodism.  In addition, the term "Antitonic" acts as a generic term for any of a group of diatonic functions found in this region.  While some microtonal theorists insist that the Antitonic functionality is more fundamental than perhaps even the Dominant or Serviant, others, such as myself, disagree.

The circumdomimant regions are the two main regions on either side of the Dominant proper, and since the uncanny valley around the Dominant is around half the size of the one around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities.  Note that antitonic and paradiatonic functions falling in this region are not covered in this section.

'''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 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.

The circumserviant regions are the two main regions on either side of the Serviant proper, and since the uncanny valley around the Serviant is around half the size of the one around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities.  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 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.

'''Gravoserviant''' - This function is a compositing of Serviant Detempering and Misoserviant (see below on Basic Parachromatic Functions).

 

'''Acuotyrant''' - Although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless operates more on the side of brute force when it contrasts with the Tonic.

'''Gravosycophant''' - Although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless often runs a high risk of tonicizing either the Dominant or the Geminodominant.

In addition to all the aforementioned Diatonic and Chromatic functions, as well as the detemperings of diatonic functions, there is an additional set of categories for dealing with the notes in between the various Diatonic scale degrees.