User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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One of the things that Quartertone Harmony has found and mentioned<ref>[https://www.youtube.com/watch?v=3N_l5ciE14g Quartertone Harmony - The Truth About Quartertone Melodies]</ref> is that when dealing with quartertones, there seems to be something about a given 12-tone scale in 24edo which assures that notes in that same field will sound like they go together. However, in systems such as 159edo, you begin to see that things are slightly more complicated, as this distinctive atmosphere or quality turns out to be around 20 cents at widest and seems to surround and be generated by notes related to the Tonic by Pythagorean intervals that aren't all that far away from the Tonic, hence the term '''proximal Pythagorean aura''' to refer to it. Notably, the proximal Pythagorean aura is at its thickest at around six or seven steps away from the Tonic in either direction along the circle of fifths, and extends along the circle of fifths on either side of these areas from two steps away from the Tonic to eleven steps away from the Tonic. The presence of this aura explains things related to the uncanny valleys around the Dominant and Serviant- namely why these uncanny valleys are not as deep or as wide as those around the Tonic, and why simple intervals with single factors of prime 5 seem to be at least somewhat "in key" relative to the Tonic. It should be noted that the Tonic, the Dominant, and the Serviant work together with this aura to define safe regions for field shifts that are guaranteed to not come across as jarring. Intervals outside of this aura, such as most paradiatonic intervals, must abide by certain rules in order to not come across as jarring. | One of the things that Quartertone Harmony has found and mentioned<ref>[https://www.youtube.com/watch?v=3N_l5ciE14g Quartertone Harmony - The Truth About Quartertone Melodies]</ref> is that when dealing with quartertones, there seems to be something about a given 12-tone scale in 24edo which assures that notes in that same field will sound like they go together. However, in systems such as 159edo, you begin to see that things are slightly more complicated, as this distinctive atmosphere or quality turns out to be around 20 cents at widest and seems to surround and be generated by notes related to the Tonic by Pythagorean intervals that aren't all that far away from the Tonic, hence the term '''proximal Pythagorean aura''' to refer to it. Notably, the proximal Pythagorean aura is at its thickest at around six or seven steps away from the Tonic in either direction along the circle of fifths, and extends along the circle of fifths on either side of these areas from two steps away from the Tonic to eleven steps away from the Tonic. The presence of this aura explains things related to the uncanny valleys around the Dominant and Serviant- namely why these uncanny valleys are not as deep or as wide as those around the Tonic, and why simple intervals with single factors of prime 5 seem to be at least somewhat "in key" relative to the Tonic. It should be noted that the Tonic, the Dominant, and the Serviant work together with this aura to define safe regions for field shifts that are guaranteed to not come across as jarring. Intervals outside of this aura, such as most paradiatonic intervals, must abide by certain rules in order to not come across as jarring. | ||
== Composite Functions == | == Composite Functions == | ||
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'''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. | '''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. | ||
== Extra Functions of Prime Harmonics and Subharmonics == | |||
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 due to being closer to the fundamental. | |||
'''Paraserviant''' - This function is essentially the inverse of the Paradominant function, and acts as a sort of counterweight to the Paradominant relative to the Tonic. Like the Paradominant function, it typically appears along prime axes other than that of the 3-limit in which they take Serviant-like function. Thus, for example, in Bass-Up tonality, the note at 8/5 above the Tonic, being a direct prime subharmonic of the Tonic, gets to serve this function in addition to its Mesodistocontramediant function as defined by the 3-limit. When considered alongside the actual Serviant function of 4/3, however, Paraserviants take on the function of Preserviant since the Serviant function of 4/3 is stronger. | |||
== Differences from Traditional Neo-Riemannian Theory == | == Differences from Traditional Neo-Riemannian Theory == | ||