User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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=== Circumtonic Regions === | === Circumtonic Regions === | ||
The Circumtonic regions are the two main regions on either side of the Tonic, outside the Tonic's "event horizon". These intervals are invariably inside the Tonic's uncanny valleys, and | The Circumtonic regions are the two main regions on either side of the Tonic, outside the Tonic's "event horizon". These intervals are invariably inside the Tonic's uncanny valleys, and as per Flora's later analysis<ref>''Analysis on the 13-limit just intonation space: episode ii''. Flora Canou. Xenharmonic Wiki. </ref>, things repel the similar but not identical. Thus, these intervals cannot be directly approached, even melodically, and so they're usually avoided outside of modulation. | ||
'''Supercommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 30 cents above the Tonic. These intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance, or for a slightly less resolved version of a Unison or Octave. | '''Supercommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 30 cents above the Tonic. These intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance, or for a slightly less resolved version of a Unison or Octave. | ||
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I've been in the process of developing this since well before I officially joined the Microtonal community, in fact, it all started for me with my discovery of the nature of the eleventh harmonic as a quartertone, however, while it is only thanks to a YouTuber who goes by "Quartertone Harmony" <ref>[https://www.youtube.com/channel/UCeDhhWQYqGRPy5ES8gTtIAQ Quartertone Harmony - YouTube]</ref> that I've been able to fill in significant gaps in my theory, the reality is that the idea of extending Diatonic functional harmony to cover intervals between the standard scale degrees, can trace at least some of its roots back to the work of [[Ivan Wyschnegradsky]]. | I've been in the process of developing this since well before I officially joined the Microtonal community, in fact, it all started for me with my discovery of the nature of the eleventh harmonic as a quartertone, however, while it is only thanks to a YouTuber who goes by "Quartertone Harmony" <ref>[https://www.youtube.com/channel/UCeDhhWQYqGRPy5ES8gTtIAQ Quartertone Harmony - YouTube]</ref> that I've been able to fill in significant gaps in my theory, the reality is that the idea of extending Diatonic functional harmony to cover intervals between the standard scale degrees, can trace at least some of its roots back to the work of [[Ivan Wyschnegradsky]]. | ||
Specifically, idea of extending Diatonic functional harmony to cover intervals between the standard scale degrees- an idea that has at least some roots in Wyschnegradsky's concept of [[Wikipedia: Major fourth and minor fifth|"Major Fourth" and "Minor Fifth"]]. However, I wanted to use LCJI as a basis for defining these intervals and thus decided to take [[11/8]] as being the just version of Wyschnegradsky's "Major Fourth", and while I drew up sketches based loosely on [[24edo]] for early versions of this concept, I also realized that that two instances of [[33/32]] added up to an interval smaller than [[2187/2048]] but which had a similar function. Furthermore, since two instances of 11/8 resulted in an interval in the vicinity of a Major seventh, I decided to | Specifically, idea of extending Diatonic functional harmony to cover intervals between the standard scale degrees- an idea that has at least some roots in Wyschnegradsky's concept of [[Wikipedia: Major fourth and minor fifth|"Major Fourth" and "Minor Fifth"]]. However, I wanted to use LCJI as a basis for defining these intervals and thus decided to take [[11/8]] as being the just version of Wyschnegradsky's "Major Fourth", and while I drew up sketches based loosely on [[24edo]] for early versions of this concept, I also realized that that two instances of [[33/32]] added up to an interval smaller than [[2187/2048]] but which had a similar function. Furthermore, since two instances of 11/8 resulted in an interval in the vicinity of a Major seventh, I decided to take stacks of 11/8 to form a second navigational axis which works together with the Diatonic Axis in order to define the microtonal functions positioned roughly halfway between the German and Viennese Diatonic functions, though there are a few other microtonal functions as well that are not immediately covered by this second axis. | ||
[[File:Diatonic_Function_Map.png|thumb|Initial diagram of paradiatonic function locations I made around the time of officially joining the Xenharmonic community. Note that a number of the functions listed on this page are missing, while the Contralead, the Semicontralead, the Intersubiant, the Interregnant, the Misoserviant and the Misodominant initially had different names.]] | [[File:Diatonic_Function_Map.png|thumb|Initial diagram of paradiatonic function locations I made around the time of officially joining the Xenharmonic community. Note that a number of the functions listed on this page are missing, while the Contralead, the Semicontralead, the Intersubiant, the Interregnant, the Misoserviant and the Misodominant initially had different names.]] | ||
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'''Semicontralead''' - This is a note that occurs roughly at intervals between 14/13 and 567/512 above the Tonic as the second scale degree. Naturally, this interval functions as a sort of cross between a Contralead and a Supertonic, and indeed chords built on this can function as some sort of cross between a Neapolitan chord and a Supertonic chord. However, there are ways in which the Semicontralead is distinct from both- notably, the Semicontralead also has the Misoserviant Parallel and Antimisodominant functions. The [[12/11]] neutral second is a rather typical example of an interval with this function. | '''Semicontralead''' - This is a note that occurs roughly at intervals between 14/13 and 567/512 above the Tonic as the second scale degree. Naturally, this interval functions as a sort of cross between a Contralead and a Supertonic, and indeed chords built on this can function as some sort of cross between a Neapolitan chord and a Supertonic chord. However, there are ways in which the Semicontralead is distinct from both- notably, the Semicontralead also has the Misoserviant Parallel and Antimisodominant functions. The [[12/11]] neutral second is a rather typical example of an interval with this function. | ||
'''Semilead''' - This is a note that occurs roughly at intervals between 1024/567 and 13/7 above the Tonic as the seventh scale degree. Naturally, this interval functions as a sort of Dominant Parallel, though there are significant differences from both a Subtonic and a Lead. For starters, the Semilead also has the Misodominant Parallel and Antimisoserviant functions, and furthermore, in Bass-Up Tonality, a Semilead is also likely to either resolve downwards to a Subtonic, or, upwards to | '''Semilead''' - This is a note that occurs roughly at intervals between 1024/567 and 13/7 above the Tonic as the seventh scale degree. Naturally, this interval functions as a sort of Dominant Parallel, though there are significant differences from both a Subtonic and a Lead. For starters, the Semilead also has the Misodominant Parallel and Antimisoserviant functions, and furthermore, in Bass-Up Tonality, a Semilead is also likely to either resolve downwards to a Subtonic, or, upwards to the Lead. The [[11/6]] neutral seventh is a rather typical example of an interval with this function. | ||
== Composite Functions == | == Composite Functions == | ||
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<todo> | <todo> | ||
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'''. As for the actual composite functions themselves, there are quite a few of them. | |||
'''Subdietic''' - This function is a compositing of Subcommatic and Subgradient, and as Subcommatic is part of its nature, it is effectively repelled harmonically. | |||
'''Superdietic''' - This function is a compositing of Subcommatic and Subgradient, and as Supercommatic is part of its nature, it is effectively repelled harmonically. | |||
'''Acuodominant''' - This function is a compositing of Dominant Detempering and Misodominant. | '''Acuodominant''' - This function is a compositing of Dominant Detempering and Misodominant. | ||