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

'''Primary Adpositive Purity''' - This rule is that for every chord root located one step away from either the Tonic, Dominant or Serviant 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.  This means that the Tonic, Dominant, Serviant, Supertonic and Subtonic chords all demand a perfect fifth as the fifth of the chord, whether you are building the Tonality upwards or downwards.  One of the obvious applications of this is that chords built with wolf fifths must have roots located three or more steps away from the Tonic along the Circle of Fifths, and that when two notes within a given Diatonic system are separated by a wolf fifth, they both must likewise be located three or more steps away from the Tonic along the Circle of Fifths.

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.

The way I see it, paradiatonic quartertones are analogous to diatonic semitones in that they are denoted as seconds, albeit inframinor seconds by default, while parachromatic quartertones are analogous to chromatic semitones in that they are denoted as primes, albiet as ultraprimes by default.  However, the distinction goes further than that- a parachromatic quartertone and a paradiatonic quartertone add up to a diatonic semitone, while two parachromatic quartertones add up to a chromatic semitone.  Given both these definitions for "paradiatonic" and "parachromatic", and given that a diatonic semitone and a chromatic semitone add up to a whole tone when paired correctly, it can be deduced that a whole tone can be assembled from three parachromatic quartertones and one paradiatonic quartertone.  Because there are sometimes multiple correct options for assembling parachromatic and paradiatonic intervals to make a 9/8 whole tone, I ended up choosing the simplest configuration of paradiatonic and parachromatic intervals to assemble in order to create a 9/8 whole tone- a configuration that only requires one type of parachromatic quartertone and one type of paradiatonic quartertone.  As a result of multiple factors, I ended up choosing the combination of three 33/32 parachromatic quartertones and one [[4096/3993]] paradiatonic quartertone as the JI basis for this in regards to both Diatonic theory and [[Alpharabian tuning]], and, through interactions with others in the Xenharmonic community, I was later influenced by others on Discord to take [[MOS]]-based structural considerations into account.  This eventually resulted in the first formal definition of a "'''parachroma'''" (an interval that can be easily tempered to equal half of a MOS-chroma), and later, the "'''parastep'''" (the interval that remains after subtracting as many parachromas from a Major MOS-step as possible without resulting in a negative interval).  Finally, drawing from the concept of "parachromas" as applied to MOS-based contexts, I was able to finally give a formal definition of terms like "paramajor" (the result of adding a parachroma to either a MOS generator or its period-inverse) and "paraminor" (the result of subtracting a parachroma from a MOS generator or its period-inverse), which I had previously come up with on an informal basis.

In January of 2022, Quartertone Harmony posted a video in which he grouped together a series of functions he refered to in the video as the "shadow scale"<ref>[https://www.youtube.com/watch?v=P6WJryxB_0Y Quartertone Harmony - Harmonic Functions of Quartertones SD 480p]</ref>, which I will refer to here as a '''paradiatonic scale''' since there are technically two of these, and this in turn led to the separation of Paradiatonic and Parachromatic harmonic functions for me.  This whole concept of a "shadow scale", in addition to everything else discuss in this section, paves the way for my idea of [[MOS-Shadow theory]], but, aside from how it applies to Diatonic-scale based functional harmony, MOS-Shadow theory is another whole discussion for another time.

'''Misoserviant''' - This is a note that occurs roughly at intervals between 32/25 and 21/16 away from the Tonic in the scale's direction of construction.  This region is characterized by intervals that don’t consistently act as either thirds or fourths, or even act as a cross between a third and a fourth, as well as by intervals that act as parachromatic alterations of either the Mediant or the Serviant.  Although originally named the "Varicoserviant" region- the name coming from "Varicant" and "Serviant", with a linking "-o-" in place of the "-ant" of "Varicant"- the fact that intervals in this region are also generally more dissonant, leading to their avoidance in chords outside of deliberate dissonances, has lead to a name change for the region as a whole.  The new name of this region comes from "miso-" and "Serviant".  Chords of this type have Preserviant, Preintersubiant and Preinterregnant functions as well as Mockserviant and Premediant functions.

== Diatonic, Paradiatonic, and the Tonic's Proximal Pythagorean Aura ==