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

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 The three basic functions have their roots in [[LCJI]].  The functions themselves are labeled as follows:
-'''Tonic''' - This is the note that serves as the tonal center, and thus, the main resolution tone, and is the note for which scales are named (e.g. the key of C major is so-named because in this scale, C serves as the Tonic).  This functionality has its roots in the fundamental at the root of both the harmonic and subharmonic series, which for all intents and purposes, can be thought of as [[1/1]], and, in [[octave equivalence|octave equivalent]] systems, [[2/1]].  Beyond being simply one of the primary three functions in German Theory, it is the only function that is known to be universal when it comes to tonal music, with the various other functions being collectively defined as ''Nontonic'', thus, it shouldn't come as a great surprise that the Tonic exerts a very powerful influence on the context of functional harmony regardless of the nature of the tonal music system in question, even helping to define aspects of the other primary functions on the chord level as opposed to the root level.  In the realm of microtonality, the Tonic is not an interval that admits a lot of competition outside of modulation, and thus, deviations from a perfect 1/1 of up to 3.5 [[cent]]s away from the Tonic are considered here to be found in the Tonic's "event horizon", in which they are either absorbed into the bandwidth of the Tonic itself, altered through [[fudging]], or simply [[Tempering out|tempered out]].  To use a character metaphor for how the Tonic acts in functional harmony, the Tonic is the king of the Kingdom of Tonality- a very good king who not only exercises the highest authority in matters of governing the kingdom and does not tolerate challenges to his leadership, but also knows how be a top-notch confidante to his subjects both wherever and whenever possible.
+'''[[Tonic]]''' - To use a character metaphor for how the Tonic acts in functional harmony, the Tonic is the king of the Kingdom of Tonality- a very good king who not only exercises the highest authority in matters of governing the kingdom and does not tolerate challenges to his leadership, but also knows how be a top-notch confidante to his subjects both wherever and whenever possible.  For specifics on the functions of the Tonic, see the linked article.
 '''Dominant''' - As per the name, and as noted on the [[Wikipedia:Dominant (music)|Wikipedia article]], the Dominant is the second most important after the Tonic, and, to use a character metaphor for how the Dominant acts in functional harmony, the Dominant is both the Head Steward of the Tonic's castle, and the one that executes the Tonic's directives as a Manager of Civil Service in the Kingdom of Tonality.  However, in contrast to what is stated about the Dominant in the article, there are several caveats which must be addressed in the realm of microtonality.  Firstly, one must take stock of the fact that, aside from the Unison and Octave, each octave-reduced harmonic and corresponding subharmonic interval come together to generate their own axis which has a preferred direction of travel<ref>[https://www.youtube.com/watch?v=HBdWxSxxe1M Quartertone Harmony - Beyond the Circle of Fifths SD 480p]</ref> which is determined by a Tonality's direction of construction.  Secondly, one must take stock of the fact that when you take the notes that occur before the Tonic on each of these axes when moving in the preferred direction of travel and place them in a sequence, one finds that a clear hierarchy of functional strength based on the closeness of harmonic and subharmonic connection to the Tonic becomes apparent, with the [[3/2]] Perfect 5th away from the Tonic in the direction of tonality construction naturally emerging as the note with the strongest connection to the Tonic, though it should be noted that the relationships in this hierarchy are quite sensitive to detuning, and can even be scrambled by such detuning.  Thus, the term "Dominant"- in its most basic form as referred to in this article, and specifically at the root level- is restricted to where it only refers to such notes that occur roughly at a 3/2 interval away from the Tonic in the scale's direction of construction, with acceptable detuning levels being at around 3.5 cents from JI on either side.  On the chord level, not only is the root level definition of the Dominant function at play, but it should also be noted that the Dominant does not see the Tonic occurring in the proximal tertian structure of its chord- that is, as a third or fifth.
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 == Extra Functions of Prime Harmonics and Subharmonics ==
-It should be noted that the level of importance typically associated with the Dominant or Serviant goes instead to a different
+It should be noted that there are other layers of function besides those oriented around the [[3-limit]].  These are detailed here.
+'''Paradominant''' - This function typically appears along prime axes other than that of the 3-limit in which they take Dominant-like function.  Thus, for example, in Bass-Up Tonality, the note at 5/4 above the Tonic, being a direct prime harmonic of the Tonic, gets to serve this function in addition to its Mesodistomediant function as defined by the 3-limit, with the Paradominant function emerging mainly in a series of 5/4-based motions leading to the Tonic.  When considered alongside the actual Dominant function of 3/2, however, Paradominants take on the function of Predominant owing to the fact that the Dominant function of 3/2 is actually stronger than that of any predominant.
-"'''Paradominants'''" -
+'''Paraserviant''' - This function is the inverse of the Paradominant function
- these surrogate Serviants are called "'''Paraserviants'''"