Xenharmonic Wiki

User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions

← Older editNewer edit →
VisualWikitext
Aura (talk | contribs)
autopatrolled
5,920 edits
No edit summary
Aura (talk | contribs)
autopatrolled
5,920 edits
No edit summary
Line 57: Line 57:
=== Specific Types of Supervicinant ===
=== Specific Types of Supervicinant ===


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


'''Supercollocant''' - This type 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.
'''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]].


'''Superabrogant''' - This type 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 direction is liable to come across as jarring.


'''Supertonic''' - This type 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]].


=== Specific Types of Subvicinant ===
=== Specific Types of Subvicinant ===


The three subtypes of Subvicinant are as follows...
The four subtypes of Subvicinant are as follows...
 
'''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]].
 
'''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.


'''Subtonic''' - This type 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]].


'''Subabrogant''' - This type 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 type 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.
'''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 ==
Line 83: Line 87:
The five subtypes of Mediant are as follows...
The five subtypes of Mediant are as follows...


'''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 type 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 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]].
Line 91: Line 95:
'''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 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]].


'''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 type 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]].


=== Specific Types of Contramediant ===
=== Specific Types of Contramediant ===
Line 97: Line 101:
The five subtypes of Contramediant are as follows...
The five subtypes of Contramediant are as follows...


'''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 type 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 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]].
Line 105: Line 109:
'''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 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]].


'''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 type 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]].  


== Antitonic Subtypes ==
== Antitonic Subtypes ==
Retrieved from "https://en.xen.wiki/w/User:Aura/Aura%27s_Ideas_on_Functional_Harmony_(Part_1)"