User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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The exact outcome and specific function of any given Antitonic depends on the interval between it and the Tonic in the scale's direction of construction, as well as by whether or not the interval in question is an augmented fourth or a diminished fifth: | The exact outcome and specific function of any given Antitonic depends on the interval between it and the Tonic in the scale's direction of construction, as well as by whether or not the interval in question is an augmented fourth or a diminished fifth: | ||
*If the Antitonic is | |||
*Conversely, if the Antitonic is | *If the Antitonic is mapped to both 3\7 and 12\24, it tends to cause the Dominant to become a new Tonic unless followed up by a different note- one that is usually a Major 7th away from the Tonic. Because of this tendency to "kiss up to" and tonicize the Dominant, this type of Antitonic can be dubbed a "'''Sycophant'''", with the prototypical Sycophant being 45/32. | ||
*Conversely, if the Antitonic is mapped to both 4\7 and 12\24, it tends to contrast with the Tonic in a manner somewhat akin to that of a Dominant, but by sheer brute force and contrary harmonic nature- e.g. if the Tonic harmony is Minor in nature, the Antitonic harmony will be Major- or more rarely, Supermajor- in nature. Furthermore, in scales such as the Locrian scale, any type of Serviant harmony tends to resolve towards either this type of Antitonic, or some other type of substitute for a Dominant. Because of these Dominant-esque tendencies, this type of Antitonic can be dubbed a "'''Tyrant'''", with the prototypical Tyrant being 64/45. | |||
== Chromatic Functions == | == Chromatic Functions == | ||
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=== Circumdominant Regions === | === Circumdominant Regions === | ||
The circumdomimant regions are the two main regions on either side of the Dominant proper, and since the uncanny valley around the Dominant is around half the size of the one around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities | The circumdomimant regions are the two main regions on either side of the Dominant proper, and since the uncanny valley around the Dominant is around half the size of the one around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities. | ||
'''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 32 cents to about 16 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. 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 32 cents to about 16 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. 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. | ||
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'''Geminoserviant''' - This is a note that occurs roughly at intervals ranging from about 16 cents to about 32 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 the Supertonic, Subtonic, the 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 16 cents to about 32 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 the Supertonic, Subtonic, the 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. | ||
== Paradiatonic and Parachromatic Functions == | == Paradiatonic and Parachromatic Functions == | ||
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== Composite Functions == | == Composite Functions == | ||
As per Flora's later analysis<ref>''Analysis on the 13-limit just intonation space: episode ii''. FloraC. Xenharmonic Wiki. </ref>, it turns out that notes on the boundaries of functional regions have multiple functions due to occurring at the boundary between different functions. | As per Flora's later analysis<ref>''Analysis on the 13-limit just intonation space: episode ii''. FloraC. Xenharmonic Wiki. </ref>, it turns out that notes on the boundaries of functional regions have multiple functions due to occurring at the boundary between different functions, the process by which this happens is known as '''Compositing'''. | ||
'''Acuodominant''' - This function is a compositing of Dominant Detempering and Misodominant. | |||
'''Gravoserviant''' - This function is a compositing of Serviant Detempering and Misoserviant. | |||
These are composite functions immediately surrounding the Antitonic region | |||
''' | '''Acuotyrant''' - Although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless operates more on the side of brute force when it contrasts with the Tonic. | ||
'''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. | |||
*If the Antitonic is between 7/5 and 600 cents away from the Tonic and functions as a diminished fifth, it demonstrates a mixture of both Sycophant-like and Tyrant-like properties, but because it is found just below the range of a typical Tyrant in Bass-Up Tonality, it is called a '''Gravotyrant''' in this kind of tonal system. A classic example of such an interval is 1024/729. | |||
*If the Antitonic is between 600 cents and 10/7 away from the Tonic and functions as an augmented fourth, it demonstrates a mixture of both Sycophant-like and Tyrant-like properties, but because it is found just above the range of a typical Sycophant in Bass-Up Tonality, it is called an '''Acuosycophant''' in this kind of tonal system. A classic example of such an interval is 729/512. | |||
== Differences from Traditional Neo-Riemannian Theory == | == Differences from Traditional Neo-Riemannian Theory == | ||