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The four subtypes of Supervicinant are as follows...
The four subtypes of Supervicinant are as follows...


'''Supercollocant''' - This subtype of Supervicinant, although not found in Viennese Theory proper, is an interval that maps to both 1\7 and 2\24 in Bass-Up tonality.  Additionally, it has the Antidominant function as typified by the root of the [[Wikipedia:Neapolitan chord|Neapolitan chord]] in Bass-Up tonality and the Antiserviant function in Treble-Down tonality.  In actuality, two subtypes of Supercollocant exist- the "'''Proximosupercollocant'''" and the "'''Distosupercollocant'''", which are distinct from each other only in finer tuning systems where the latter is usually more consonant.  An example of a Proximosupercollocant is [[256/243]] while an example of a Distosupercollocant is [[16/15]].
'''Supercollocant''' - This subtype of Supervicinant, although not found in Viennese Theory proper, is an interval that usually maps to both 1\7 and 2\24 in Bass-Up tonality.  Additionally, it has the Antidominant function as typified by the root of the [[Wikipedia:Neapolitan chord|Neapolitan chord]] in Bass-Up tonality and the Antiserviant function in Treble-Down tonality.  In actuality, two subtypes of Supercollocant exist- the "'''Proximosupercollocant'''", which always maps to both 1\7 and 2\24 in Bass-Up tonality, and the "'''Distosupercollocant'''", which maps to 1\7 and either 2\24 or 3\24 depending on a variety of factors, and is distinct from both Proximosupercollocant and Superabrogant only in finer tuning systems where it is usually more consonant, and thus, weaker.  An example of a Proximosupercollocant is [[256/243]] while an example of a Distosupercollocant is [[16/15]].
 
'''Superabrogant''' - This subtype of Supervicinant is not a traditional diatonic function at all since it is an interval that maps to both 1\7 and 3\24 in Bass-Up tonality.  As per this function's name, the intervals in this range are like Supercollocants in that they may cause listeners to forget the ending pitch's relationship to the starting pitch in voice-leading.  However, they are noticeably too wide for them to convincingly pass off as being totally semitone-like since they feel as if they're rather disconnected from the Tonic, and furthermore, the occurrence of two successive instances of these sorts of intervals in the same direction is liable to come across as jarring.


'''Superabrogant''' - This subtype of Supervicinant is not a traditional diatonic function at all since it is an interval that maps to both 1\7 and 3\24 in Bass-Up tonality.  As per this function's name, the intervals in this range are like Supercollocants in that they may cause listeners to forget the ending pitch's relationship to the starting pitch in voice-leading.  However, they are noticeably too wide for them to convincingly pass off as being totally semitone-like since they feel as if they're rather disconnected from the Tonic, and furthermore, the occurrence of two successive instances of these sorts of intervals in the same melodic line in the same direction is liable to come across as jarring.


'''Superaequient''' - This subtype of Supervicinant is an interval that maps to 1\7 and either 3\24 or 4\24 depending on a variety of factors.  It is so named for the [[equable heptatonic]] region above the Tonic, which comprises the bulk of its range, and for its capacity to straddle the line between the Supertonic and Superabrogant functions in voice-leading.  Conspicuously, it is only distinct from Supertonic and Superabrogant functions only in finer tuning systems, with the approximation ranges for [[11/0]] and [[10/9]] being located at its borders.


'''Supertonic''' - This subtype of Supervicinant is an interval that maps to both 1\7 and 4\24 in Bass-Up tonality and occurs above the Tonic as the second scale degree.  However, it should be noted that the lower boundary of this function is situated at roughly 119/108 above the Tonic, since notes located at smaller distances from the Tonic are liable to cause listeners to forget the ending pitch's relationship to the starting pitch- something which Supertonics don't do under any circumstances.  Conspicuously, one type of Supertonic is the "'''Bidominant'''", which is the function specifically of [[9/8]].
'''Supertonic''' - This subtype of Supervicinant is an interval that maps to both 1\7 and 4\24 in Bass-Up tonality and occurs above the Tonic as the second scale degree.  However, it should be noted that the lower boundary of this function is situated at roughly 119/108 above the Tonic, since notes located at smaller distances from the Tonic are liable to cause listeners to forget the ending pitch's relationship to the starting pitch- something which Supertonics don't do under any circumstances.  Conspicuously, one type of Supertonic is the "'''Bidominant'''", which is the function specifically of [[9/8]].
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'''Subtonic''' - This subtype of Subvicinant is an interval that maps to both 6\7 and 20\24 in Bass-Up tonality and occurs above the Tonic as the seventh scale degree.  However, it should be noted that the upper boundary of this function is situated at roughly 216/119 above the Tonic, since notes located at larger distances from the Tonic are liable to cause listeners to forget the ending pitch's relationship to the starting pitch- something which Subtonics don't do under any circumstances.  Conspicuously, one type of Supertonic is the "'''Biserviant'''", which is the function specifically of [[16/9]].
'''Subtonic''' - This subtype of Subvicinant is an interval that maps to both 6\7 and 20\24 in Bass-Up tonality and occurs above the Tonic as the seventh scale degree.  However, it should be noted that the upper boundary of this function is situated at roughly 216/119 above the Tonic, since notes located at larger distances from the Tonic are liable to cause listeners to forget the ending pitch's relationship to the starting pitch- something which Subtonics don't do under any circumstances.  Conspicuously, one type of Supertonic is the "'''Biserviant'''", which is the function specifically of [[16/9]].


'''Subaequient''' - This subtype of Subvicinant is an interval that maps to 6\7 and either 20\24 or 21\24 depending on a variety of factors.  It is so named for the equable heptatonic region below the Tonic, which comprises the bulk of its range, and for its capacity to straddle the line between the Subtonic and Subabrogant functions in voice-leading.  Conspicuously, it is only distinct from Subtonic and Subabrogant functions only in finer tuning systems, with the approximation ranges for [[9/5]] and [[20/11]] being located at its borders.


'''Subabrogant''' - This subtype of Subrvicinant is not a traditional diatonic function at all since it is an interval that maps to both 6\7 and 21\24 in Bass-Up tonality.  As per this function's name, the intervals in this range are like Subcollocants in that they may cause listeners to forget the ending pitch's relationship to the starting pitch in voice-leading.  However, they, like Superabrogants, feel as if they're rather disconnected from the Tonic, and furthermore, the occurrence of two successive instances of these sorts of intervals in the same melodic line in the same direction is liable to come across as jarring.


'''Subabrogant''' - This subtype of Subrvicinant is not a traditional diatonic function at all since it is an interval that maps to both 6\7 and 21\24 in Bass-Up tonality.  As per this function's name, the intervals in this range are like Subcollocants in that they may cause listeners to forget the ending pitch's relationship to the starting pitch in voice-leading.  However, they, like Superabrogants, feel as if they're rather disconnected from the Tonic, and furthermore, the occurrence of two successive instances of these sorts of intervals in the same direction is liable to come across as jarring.
'''Subcollocant''' - This subtype of Subvicinant is the note typically referred to when people say "the leading tone", and an interval that usually maps to both 6\7 and 22\24 in Bass-Up tonality.  Additionally, it has the Antiserviant function in Bass-Up tonality and the Antidominant function in Treble-Down tonality.  Although triads built on this scale degree are regarded by some as simply incomplete Dominant Seventh chords, my own analysis, while acknowledging the functional similarities between the Subcollocant and the Dominant in Bass-Up tonality, sees this interval as functionally distinct from the Dominant due to the Subcollocant also being potentially related to the Mediant in the same way that the Dominant is related to the Tonic- a key functionality that is often exploited in [[Wikipedia:Vi–ii–V–I|circle progression]]s.  In actuality, two subtypes of Subcollocant exist- the "'''Proximosubcollocant'''", which always maps to both 6\7 and 22\24 in Bass-Up tonality, and the "'''Distosubcollocant'''", which maps to 6\7 and either 21\24 or 22\24 depending on a variety of factors, and is distinct from both Proximosubcollocant and Subabrogant only in finer tuning systems where it is usually more consonant, and thus, weaker.  An example of a Proximosubcollocant is [[243/128]] while an example of a Distosubcollocant is [[15/8]].
 
'''Subcollocant''' - This subtype of Subvicinant is the note typically referred to when people say "the leading tone", and an interval that maps to both 6\7 and 22\24 in Bass-Up tonality.  Additionally, it has the Antiserviant function in Bass-Up tonality and the Antidominant function in Treble-Down tonality.  Although triads built on this scale degree are regarded by some as simply incomplete Dominant Seventh chords, my own analysis, while acknowledging the functional similarities between the Subcollocant and the Dominant in Bass-Up tonality, sees this interval as functionally distinct from the Dominant due to the Subcollocant also being potentially related to the Mediant in the same way that the Dominant is related to the Tonic- a key functionality that is often exploited in [[Wikipedia:Vi–ii–V–I|circle progression]]s.  In actuality, two subtypes of Subcollocant exist- the "'''Proximosubcollocant'''" and the "'''Distosubcollocant'''", which are distinct from each other only in finer tuning systems where the latter is usually more consonant.  An example of a Proximosubcollocant is [[243/128]] while an example of a Distosubcollocant is [[15/8]].


== Mediant and Contramediant Subtypes ==
== Mediant and Contramediant Subtypes ==


There are five basic types of Mediant, although only three of them are distinct in [[24edo]]- you'd need to go to [[41edo]] or [[53edo]] to see all five.  Similarly, there are five basic types of Contraediant, with only three of them being distinct in [[24edo]], so you'd need to go to [[41edo]] or [[53edo]] to see all five.
There are five basic types of Mediant, although only three of them are distinct in [[24edo]]- you'd need to go to [[41edo]] or [[53edo]] to see all five.  Similarly, there are five basic types of Contramediant, with only three of them being distinct in [[24edo]], so you'd need to go to [[41edo]] or [[53edo]] to see all five.


=== Specific Types of Mediant ===
=== Specific Types of Mediant ===
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'''Proximomediant''' - This type of Mediant is mapped to 2\7 and 6\24 and is so named due to being located on the end of the Mediant range closest to the Tonic.  Conspicuously, it is one of the possible the types of Mediant seen in Minor keys and is only distinct from the Mesoproximomediant in finer tuning systems where it is usually more dissonant.  One subtype of Proximomediant is the "'''Triserviant'''", which is the function specifically of [[32/27]].
'''Proximomediant''' - This type of Mediant is mapped to 2\7 and 6\24 and is so named due to being located on the end of the Mediant range closest to the Tonic.  Conspicuously, it is one of the possible the types of Mediant seen in Minor keys and is only distinct from the Mesoproximomediant in finer tuning systems where it is usually more dissonant.  One subtype of Proximomediant is the "'''Triserviant'''", which is the function specifically of [[32/27]].


'''Mesoproximomediant''' - This type of Mediant is mapped to both 2\7 and 6\24 and is so named due to being located between the proximal end of the Mediant range and the midline between the Tonic and the Dominant.  Conspicuously, it is one of the possible the types of Mediant seen in Minor keys and is only distinct from the Proximomediant in finer tuning systems where it is usually more consonant.  A primary example of an interval with this type of function is the interval [[6/5]].
'''Mesoproximomediant''' - This type of Mediant is mapped to both 2\7 and either 6\24 or 7\24 depending on a variety of factors.  It is so named due to being located between the proximal end of the Mediant range and the midline between the Tonic and the Dominant.  Conspicuously, it is one of the possible the types of Mediant seen in Minor keys and is only distinct from the Proximomediant and Mesomediant in finer tuning systems where it's notable for containing the approximation range for [[6/5]] at its lower border and for being the [[fourth complement]] of the Superaequient, hence why it's not merely a simple compositing of the adjacent functions.


'''Mesomediant''' - This type of Mediant is mapped to both 2\7 and 7\24 and is so named due to being located along the midline between the Tonic and the Dominant.  This type of Mediant is arguably the most dissonant, and is not a traditional diatonic function at all, and in fact, it doesn't serve well at phrase endings- rather, its Tonic Parallel function is only appropriate during the middle of musical phrases.  Intervals with this type of function include [[11/9]] and [[27/22]].
'''Mesomediant''' - This type of Mediant is mapped to both 2\7 and 7\24 and is so named due to being located along the midline between the Tonic and the Dominant.  This type of Mediant is arguably the most dissonant, and is not a traditional diatonic function at all, and in fact, it doesn't serve well at phrase endings- rather, its Tonic Parallel function is only appropriate during the middle of musical phrases.  Intervals with this type of function include [[11/9]] and [[27/22]].


'''Mesodistomediant''' - This type of Mediant is mapped to both 2\7 and 8\24 and is so named due to being located between the distal end of the Mediant range and the midline between the Tonic and the Dominant.  Conspicuously, it is one of the possible the types of Mediant seen in Major keys and is only distinct from the Distomediant in finer tuning systems where it is usually more consonant.  A primary example of an interval with this type of function is the interval [[5/4]].
'''Mesodistomediant''' - This type of Mediant is mapped to both 2\7 and either 7\24 or 8\24 depending on a variety of factors.  It is so named due to being located between the distal end of the Mediant range and the midline between the Tonic and the Dominant.  Conspicuously, it is one of the possible the types of Mediant seen in Major keys and is only distinct from the Mesomediant and Distomediant in finer tuning systems where it's notable for containing the approximation range for [[5/4]] at its upper border and for being the fourth complement of the Distosupercollocant, hence why it's not merely a simple compositing of the adjacent functions.


'''Distomediant''' - This type of Mediant is mapped to both 2\7 and 8\24 and is so named due to being located on the end of the Mediant range furthest from the Tonic.  Conspicuously, it is one of the possible the types of Mediant seen in Major keys and is only distinct from the Mesodistomediant in finer tuning systems where it is usually more dissonant.  One subtype of Distomediant is the "'''Quadridominant'''", which is the function specifically of [[81/64]].
'''Distomediant''' - This type of Mediant is mapped to both 2\7 and 8\24 and is so named due to being located on the end of the Mediant range furthest from the Tonic.  Conspicuously, it is one of the possible the types of Mediant seen in Major keys and is only distinct from the Mesodistomediant in finer tuning systems where it is usually more dissonant.  One subtype of Distomediant is the "'''Quadridominant'''", which is the function specifically of [[81/64]].
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'''Proximocontramediant''' - This type of Contramediant is mapped to 5\7 and 18\24 and is so named due to being located on the end of the Contramediant range closest to the Tonic.  Conspicuously, it is one of the possible the types of Contraediant seen in Major keys and is only distinct from the Mesoproximocontramediant in finer tuning systems where it is usually more dissonant.  One subtype of Proximocontramediant is the "'''Tridominant'''", which is the function specifically of [[27/16]].
'''Proximocontramediant''' - This type of Contramediant is mapped to 5\7 and 18\24 and is so named due to being located on the end of the Contramediant range closest to the Tonic.  Conspicuously, it is one of the possible the types of Contraediant seen in Major keys and is only distinct from the Mesoproximocontramediant in finer tuning systems where it is usually more dissonant.  One subtype of Proximocontramediant is the "'''Tridominant'''", which is the function specifically of [[27/16]].


'''Mesoproximocontramediant''' - This type of Contramediant is mapped to both 5\7 and 18\24 and is so named due to being located between the proximal end of the Mediant range and the midline between the Tonic and the Serviant.  Conspicuously, it is one of the possible the types of Contramediant seen in Major keys and is only distinct from the Proximocontramediant in finer tuning systems where it is usually more consonant.  A primary example of an interval with this type of function is the interval [[5/3]].
'''Mesoproximocontramediant''' - This type of Contramediant is mapped to 5\7 and either 17\24 or 18\24 depending on a variety of factors.  It is so named due to being located between the proximal end of the Contramediant range and the midline between the Tonic and the Serviant.  Conspicuously, it is one of the possible the types of Contramediant seen in Major keys and is only distinct from the Proximocontramediant and Mesocontramediant in finer tuning systems where it's notable for containing the approximation range for [[5/3]] at its upper border, hence why it's not merely a simple compositing of the adjacent functions.


'''Mesocontramediant''' - This type of Contramediant is mapped to both 5\7 and 17\24 and is so named due to being located along the midline between the Tonic and the Serviant.  This type of Contramediant is arguably the most dissonant, and is not a traditional diatonic function at all, and in fact, it doesn't serve well at phrase endings- rather, its Tonic Parallel function is only appropriate during the middle of musical phrases.  Intervals with this type of function include [[18/11]] and [[44/27]].
'''Mesocontramediant''' - This type of Contramediant is mapped to both 5\7 and 17\24 and is so named due to being located along the midline between the Tonic and the Serviant.  This type of Contramediant is arguably the most dissonant, and is not a traditional diatonic function at all, and in fact, it doesn't serve well at phrase endings- rather, its Tonic Parallel function is only appropriate during the middle of musical phrases.  Intervals with this type of function include [[18/11]] and [[44/27]].


'''Mesodistocontramediant''' - This type of Contramediant is mapped to both 5\7 and 16\24 and is so named due to being located between the distal end of the Contramediant range and the midline between the Tonic and the Serviant.  Conspicuously, it is one of the possible the types of Contramediant seen in Minor keys and is only distinct from the Distocontramediant in finer tuning systems where it is usually more consonant.  A primary example of an interval with this type of function is the interval [[8/5]].
'''Mesodistocontramediant''' - This type of Contramediant is mapped to both 5\7 and either 16\24 or 17\24 depending on a variety of factors.  It is so named due to being located between the distal end of the Contramediant range and the midline between the Tonic and the Serviant.  Conspicuously, it is one of the possible the types of Contramediant seen in Minor keys and is only distinct from the Mesocontramediant and Distocontramediant in finer tuning systems where it's notable for containing the approximation range for [[8/5]] at its lower border, hence why it's not merely a simple compositing of the adjacent functions.


'''Distocontramediant''' - This type of Contramediant is mapped to both 5\7 and 16\24 and is so named due to being located on the end of the Contramediant range furthest from the Tonic.  Conspicuously, it is one of the possible the types of Contramediant seen in Minor keys and is only distinct from the Mesodistocontramediant in finer tuning systems where it is usually more dissonant.  One subtype of Distomediant is the "'''Quadriserviant'''", which is the function specifically of [[128/81]].  
'''Distocontramediant''' - This type of Contramediant is mapped to both 5\7 and 16\24 and is so named due to being located on the end of the Contramediant range furthest from the Tonic.  Conspicuously, it is one of the possible the types of Contramediant seen in Minor keys and is only distinct from the Mesodistocontramediant in finer tuning systems where it is usually more dissonant.  One subtype of Distomediant is the "'''Quadriserviant'''", which is the function specifically of [[128/81]].  
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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 ==
== Additional Composite Functions ==


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<todo>
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'''Supermaculant''' - This function is a compositing of Supergradient and Superdislocant, and thus is like the chromatic version of the Contrableed.  
'''Supermaculant''' - This function is a compositing of Supergradient and Superdislocant, and thus is like the chromatic version of the Contrableed.  


'''Bilancant''' - This function is a compositing of Lead and Subabrogant functions, however, the tendency to resolve to the Tonic or to the Subtonic are about equal due to Tonic having greater gravity than the Subtonic.  The term ultimately comes from "bilancāns"- a Latin-based calque of similar verb forms from Romance languages meaning "balancing" which consists of Latin "bilanx"<ref>[[Wiktionary: bilanx #Latin]]</ref> with the Latin "-āns"<ref>[[Wiktionary: -ans #Latin]]</ref> suffix attached.
'''Subbilancant''' - This function is a compositing of Subcollocant and Subabrogant functions, however, the tendency to resolve to the Tonic or to the Subtonic are about equal due to Tonic having greater gravity than the Subtonic.  The term ultimately comes from "bilancāns"- a Latin-based calque of similar verb forms from Romance languages meaning "balancing" which consists of Latin "bilanx"<ref>[[Wiktionary: bilanx #Latin]]</ref> with the Latin "-āns"<ref>[[Wiktionary: -ans #Latin]]</ref> suffix attached.


'''Contrabilancant''' - This function is a compositing of Contralead and Superabrogant functions, however, the tendency to resolve to the Tonic or to the Supertonic are about equal due to Tonic having greater gravity than the Supertonic.
'''Superbilancant''' - This function is a compositing of Supercollocant and Superabrogant functions, however, the tendency to resolve to the Tonic or to the Supertonic are about equal due to Tonic having greater gravity than the Supertonic.


'''Coduplicant''' - This function is a compositing of Superabrogant and Supertonic functions.  It is so named because, along with both the Superabrogant, and the Supertonic, it sits in the middle between the Tonic and the Mediant, and because it is the fifth complement of the Duplicant.
'''Coduplicant''' - This function is a compositing of Superabrogant and Supertonic functions.  It is so named because, along with both the Superabrogant, and the Supertonic, it sits in the middle between the Tonic and the Mediant, and because it is the fifth complement of the Duplicant.
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