User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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One construct from Western Classical music with potential implications for Microtonalists is '''[[Wikipedia:Function (music)|harmonic function]]'''- especially as it pertains to the [[5L 2s|diatonic]] MOS scale and its various relatives. | One construct from Western Classical music with potential implications for Microtonalists is '''[[Wikipedia:Function (music)|harmonic function]]'''- especially as it pertains to the [[5L 2s|diatonic]] MOS scale and its various relatives. In Mainstream Music Theory there were once two prevailing schools of thought in regards to diatonic functional harmony- '''German Theory''' and '''Viennese Theory'''- however, in a conversation with [[User:Mousemambo|Mousemambo]] on Discord, it has been revealed to me that in modern practice, the old ideas of functional harmony have largely disintegrated due firstly to the conviction that after around 1900 CE, art music took a turn away from Common Practice Period foundations and those old analyses just don't work anymore as originally formulated, and secondly due to a suspicion that they never really existed beyond the pareidolia of minds trying to see patterns in noise. Mousemambo has also pointed out to me that modern writers have moved away from the convoluted depths of the two Germanic schools, now more often simply identifying scale degrees and the chords for which they are root as either Tonic; Dominant, which is basically anything leading to Tonic; and Predominant, which is basically anything leading to Dominant. However, upon listening to the ways in which Plagal cadences get used, and how the chords on the perfect 4th above the Tonic get used as a sort of "home away from home", it is obvious to me that the stance taken by modern writers is an oversimplification, and that there are more remnants of the ideas of the two schools in modern music than one would initially think. Furthermore, the genres of music I write call for a reconstruction of at least some of the ideals of the old Germanic schools from the ground up. Thus, ideas from both schools, as well as a number of other ideas, find a home in my microtonal theory and practice. If the reader will bear with me, I shall use narrative set-ups and character metaphors to describe how the various harmonic functions act in composition and the way they relate to one another, and, furthermore, I'll be looking at ways to extend this reconstruction of functional harmony into the microtonal realm. | ||
== Facets Derived from German Theory == | == Facets Derived from German Theory == | ||
Among the chief ideas that come from German Theory is that there are three basic, or primary functions, and that there are multiple operations that can be applied to these three basic functions in order to derive new functions. | Among the chief ideas that come from German Theory is that there are three basic, or primary functions, and that there are multiple operations that can be applied to these three basic functions in order to derive new functions. However, compared to those ideal functions, one of the three is in part original to my work. | ||
=== Basic Diatonic Functions === | === Basic Diatonic Functions === | ||
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'''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. 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. With all that said, it should be noted that the level of importance typically associated with the Dominant goes instead to a different note instead of a 3/2 Perfect 5th in scales where the 5th scale degree is too far away from 3/2, and that there are a variety of other interval constructions which have the tendency to create tension which requires the Tonic to resolve- these surrogate Dominants are called "'''Paradominants'''". On the chord level, not only is the root level definition of the Dominant function at play, but it should also be noted that no Dominant or Paradominant sees the Tonic occurring in the proximal structure of its chord- that is, as a third or fifth. | '''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. 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. With all that said, it should be noted that the level of importance typically associated with the Dominant goes instead to a different note instead of a 3/2 Perfect 5th in scales where the 5th scale degree is too far away from 3/2, and that there are a variety of other interval constructions which have the tendency to create tension which requires the Tonic to resolve- these surrogate Dominants are called "'''Paradominants'''". On the chord level, not only is the root level definition of the Dominant function at play, but it should also be noted that no Dominant or Paradominant sees the Tonic occurring in the proximal structure of its chord- that is, as a third or fifth. | ||
'''Serviant''' - Compared to the term "''Subdominant''" from | '''Serviant''' - Compared to the term "''Subdominant''" from music theory of old, the term "Serviant", specifically at the root level, is restricted to those notes that occur roughly at a [[4/3]] interval away from the Tonic in the scale's direction of construction since the Serviant function is essentially the inverse of the Dominant function, and acts as a sort of counterweight to the Dominant relative to the Tonic. To use a character metaphor for how the Serviant acts in functional harmony, the Serviant is a Servant who goes above and beyond the call of duty and acts as a confidante that observes things and reports back to the Dominant and Tonic about the way things are working both inside and outside the Tonic's castle due to its relationships to various Non-Tonic functions. Although one might think that the term "Subdominant" would be eligible for getting a similar treatment to the term "Dominant" here, the problems with such an option are threefold. Firstly, not all possible "Subdominant" harmonies have the same harmonic properties relative to the Tonic, as there is an extremely close connection between the Tonic and the 4/3 Perfect 4th. Secondly, in music built from the Treble downwards, the notes with these sorts of functions are actually located ''above'' the Dominant. Thirdly, in common parlance, "Subdominant" is often equated with "Predominant", however, while the Serviant does tend to resolve towards the Dominant, or else some other note that acts as a surrogate for the Dominant, the fact remains that it can also create plagal cadences, which break the modern Tonic-Dominant-Predominant paradigm and are better explained in part by the ideals of the two Germanic schools. With all that said, it should be noted that the level of importance typically associated with the Serviant goes instead to a different note instead of a 4/3 Perfect 4th in scales where the 4th scale degree is too far away from 4/3- these surrogate Serviants are called "'''Paraserviants'''". On the chord level, not only is the root level definition of the Serviant function at play, but it should also be noted that a Serviant or Paraserviant chord often sees the Tonic occurring in the proximal structure of its chord- that is, as either a third or fifth- which explains why Serviant chords are weaker than their Dominant counterparts in both Bass-Up and Treble-Down Tonalities. | ||
=== Basic Diatonic Function-Deriving Operations === | === Basic Diatonic Function-Deriving Operations === | ||