User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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'''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 25 cents to about 3.5 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 since things repel the similar but not identical. 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. | '''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 25 cents to about 3.5 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 since things repel the similar but not identical. 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. | ||
'''Pseudodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 cents beyond the 3/2 perfect fifth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Dominant is found just beyond the sweet spot range near the standard issue 3/2. | '''Pseudodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 cents beyond the 3/2 perfect fifth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Dominant is found just beyond the sweet spot range near the standard issue 3/2. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Predominant function. | ||
=== Circumserviant Regions === | === Circumserviant Regions === | ||
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'''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 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 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. | '''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 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 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. | ||
'''Pseudoserviant''' - This is a note that occurs roughly at intervals ranging from about 25 cents to about 3.5 cents short of the 4/3 perfect fourth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Dominant is found just short the sweet spot range near the standard issue 3/2. | '''Pseudoserviant''' - This is a note that occurs roughly at intervals ranging from about 25 cents to about 3.5 cents short of the 4/3 perfect fourth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Dominant is found just short the sweet spot range near the standard issue 3/2. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Preserviant function. | ||
=== Governing Rules === | === Governing Rules === | ||
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== Diatonic, Paradiatonic, and the Aura of the Tonic's Chain of Fifths == | == Diatonic, Paradiatonic, and the Aura of the Tonic's Chain of Fifths == | ||
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 aura turns out to be around five steps wide at the thickest and centered around the notes that are related to the Tonic by Pythagorean tuning. Notably, this region 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, | 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 aura turns out to be around five steps wide at the thickest and centered around the notes that are related to the Tonic by Pythagorean tuning. Notably, this region 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". 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 == | ||