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I've been in the process of developing 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 at least back to the work of [[Ivan Wyschnegradsky]].
I've been in the process of developing 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 at least back to the work of [[Ivan Wyschnegradsky]].


Specifically, the collection of ideas that are now coming together to form the basis of MOS-shadow theory can be traced back to the 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 takes 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.
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 takes 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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In January of 2022, Quartertone Harmony posted a video in which he grouped together a series of functions he referd to in the video as the "shadow scale"<ref>[https://www.youtube.com/watch?v=P6WJryxB_0Y Quartertone Harmony - Harmonic Functions of Quartertones SD 480p]</ref>, which I will refer to here as the '''paradiatonic scale''', and this in turn led to the separation of Paradiatonic and Parachromatic harmonic functions for me.  This whole concept of a "shadow scale", in addition to everything else discuss in this section, paves the way for the my idea of [[MOS-Shadow theory]], but, aside from how it applies to Diatonic-scale based functional harmony, MOS-Shadow theory is another whole discussion for another time.
In January of 2022, Quartertone Harmony posted a video in which he grouped together a series of functions he referd to in the video as the "shadow scale"<ref>[https://www.youtube.com/watch?v=P6WJryxB_0Y Quartertone Harmony - Harmonic Functions of Quartertones SD 480p]</ref>, which I will refer to here as the '''paradiatonic scale''', and this in turn led to the separation of Paradiatonic and Parachromatic harmonic functions for me.  This whole concept of a "shadow scale", in addition to everything else discuss in this section, paves the way for the my idea of [[MOS-Shadow theory]], but, aside from how it applies to Diatonic-scale based functional harmony, MOS-Shadow theory is another whole discussion for another time.


=== The Paradiatonic Scale and Basic Paradiatonic Functions ===
=== The Paradiatonic Scale ===


The Paradiatonic scale from a given tonic acts as a sort of "second shelf" of that tonality, and consists of the following scale degrees as analyzed relative to Viennese Theory's scale steps:
The Paradiatonic scale from a given tonic acts as a sort of "second shelf" of that tonality, and consists of the following scale degrees as analyzed relative to Viennese Theory's scale steps:


I, tII/dbIII, dIII, tIV, dV, dVI, tVI/dbVII, tVII
tII/dbIII, dIII, tIV, dV, dVI, tVI/dbVII, tVII


Of these, four of them- specifically, the tII/dbIII, tIV, dV and tVI/dbVII- can be considered basic, while the other three are first derivatives.  As with the three basic diatonic functions, the four most basic paradiatonic functions have their roots in LCJI.  In the order listed, the tII/dbIII, tIV, dV and tVI/dbVII functions are the following...
While the Diatonic scale itself has seven notes, the Paradiatonic scale has seven other notes, furthermore, the tunings of each note in the Paradiatonic scale not only depend upon the exact tuning of the Diatonic scale used as a basis, but also vary considerably when it comes to the notes of the Paradiatonic that occur between the main Diatonic interval category ranges.
 
=== Basic Paradiatonic Functions ===
 
Out of the various functions found in the Paradiatonic scale, four of them- specifically, the tII/dbIII, tIV, dV and tVI/dbVII- can be considered basic, while the other three are first derivatives.  As with the three basic diatonic functions, the four most basic paradiatonic functions have their roots in LCJI.  In the order listed, the tII/dbIII, tIV, dV and tVI/dbVII functions are the following...


'''Contravaricant''' - Named in contrast to the Varicant function, this is a note that occurs roughly at intervals between 256/225 and 75/64 away from the Tonic in the scale's direction of construction, lying roughly in the middle of the 4/3 interval separating the Tonic and the Serviant above it.  Intervals in the Contravaricant region often don't consistently act as either seconds or thirds, or even act as a cross between a second and a third, only without potential for crowding in chords.  In Bass-Up tonality, this functionality is first encountered in the form of [[8/7]], though [[7/6]] is another notable interval included in this range, with intervals in this range having Predominant, Preserviant, and Dominant Parallel functions, as well as an overlap between Tonic Adjacent and Tonic Parallel functions.
'''Contravaricant''' - Named in contrast to the Varicant function, this is a note that occurs roughly at intervals between 256/225 and 75/64 away from the Tonic in the scale's direction of construction, lying roughly in the middle of the 4/3 interval separating the Tonic and the Serviant above it.  Intervals in the Contravaricant region often don't consistently act as either seconds or thirds, or even act as a cross between a second and a third, only without potential for crowding in chords.  In Bass-Up tonality, this functionality is first encountered in the form of [[8/7]], though [[7/6]] is another notable interval included in this range, with intervals in this range having Predominant, Preserviant, and Dominant Parallel functions, as well as an overlap between Tonic Adjacent and Tonic Parallel functions.
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