Xenharmonic Wiki

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

← Older editNewer edit →
VisualWikitext
Aura (talk | contribs)
autopatrolled, emailconfirmed
6,012 edits
Begin the process of changing terminology- this will take several edits
Aura (talk | contribs)
autopatrolled, emailconfirmed
6,012 edits
More terminology correction
Line 29: Line 29:
The way I see it, there are seven known operations which can be used to derive additional diatonic functions from the three basic functions listed above.
The way I see it, there are seven known operations which can be used to derive additional diatonic functions from the three basic functions listed above.


'''Stacking''' - The notes that are arrived at through stacking multiple instances of either 3/2 or 4/3 (or their tempered counterparts) are dubbed according to the number of instances stacked, and the nature of the notes separated by the interval being stacked.  Thus, stacking two instances of the Dominant or the Serviant results in the creation of the "Bidominant" or "Biserviant" respectively.  This concept comes from the German language's way of referring to the chord built on the second scale degree of the Diatonic scale as the "Doppeldominante", which literally means "Double Dominant".
'''Stacking''' - The notes that are arrived at through stacking multiple instances of either 3/2 or 4/3 (or their tempered counterparts) are dubbed according to the number of instances stacked, and the nature of the notes separated by the interval being stacked.  Thus, stacking two instances of the Dominant or the Servient results in the creation of the "Bidominant" or "Biservient" respectively.  This concept comes from the German language's way of referring to the chord built on the second scale degree of the Diatonic scale as the "Doppeldominante", which literally means "Double Dominant".


'''Parallelism''' - Notes located in the same primary [[tetrachord]] as either the Tonic, the Dominant, or the Serviant but that don't crowd them tend to take on similar functions to said notes, with the caveat that functions derived from the Tonic in this fashion are still technically Nontonic functions.  This process is one of two that create what in traditional music theory are referred to as [[Wikipedia:Parallel and counter parallel|"''parallels''" and "''counter parallels''"]].  It should be noted that the ability of an interval to relate to the Tonic through Parallelism, as well as the surrounding of more dissonant intervals by consonant intervals in the same region displaying such relationships to the Tonic, results in a tendency towards harmonic stagnation.
'''Parallelism''' - Notes located in the same primary [[tetrachord]] as either the Tonic, the Dominant, or the Servient but that don't crowd them tend to take on similar functions to said notes, with the caveat that functions derived from the Tonic in this fashion are still technically Nontonic functions.  This process is one of two that create what in traditional music theory are referred to as [[Wikipedia:Parallel and counter parallel|"''parallels''" and "''counter parallels''"]].  It should be noted that the ability of an interval to relate to the Tonic through Parallelism, as well as the surrounding of more dissonant intervals by consonant intervals in the same region displaying such relationships to the Tonic, results in a tendency towards harmonic stagnation.


'''Adjacency''' - Notes within a suitable voice leading distance from either the Dominant or Serviant tend to have the opposite function relative to the Tonic- this process even extends to the relationship between the Dominant and Serviant themselves.  On the other hand, notes within this same kind of distance from the Tonic often tend to have their functions colored more by their relationships to both the Dominant and Serviant.  This process is one of two that create what in traditional music theory are referred to as "''parallels''" and "''counter parallels''", however, unlike Parallelism proper, this process can establish these kinds of relationships outside the primary tetrachord.
'''Adjacency''' - Notes within a suitable voice leading distance from either the Dominant or Servient tend to have the opposite function relative to the Tonic- this process even extends to the relationship between the Dominant and Servient themselves.  On the other hand, notes within this same kind of distance from the Tonic often tend to have their functions colored more by their relationships to both the Dominant and Servient.  This process is one of two that create what in traditional music theory are referred to as "''parallels''" and "''counter parallels''", however, unlike Parallelism proper, this process can establish these kinds of relationships outside the primary tetrachord.


'''Antipodism''' - Notes that are either opposite in pitch hue or nearly so due to being approximately half an octave away from the starting point are harmonically opposed to the starting point.  Non-tonic notes related through this process tend to have the opposite function relative to the Tonic.  For the notes related to the Tonic by this process, see Antitonic below.
'''Antipodism''' - Notes that are either opposite in pitch hue or nearly so due to being approximately half an octave away from the starting point are harmonically opposed to the starting point.  Non-tonic notes related through this process tend to have the opposite function relative to the Tonic.  For the notes related to the Tonic by this process, see Antitonic below.


'''Preparation''' - Notes that "prepare the way" for either a Dominant or a Serviant through any of the above operations, or through some other mechanism, relate to said notes by this process.  Functions which have this kind of role relative to some other function are denoted with a "pre-" prefix here.
'''Preparation''' - Notes that "prepare the way" for either a Dominant or a Servient through any of the above operations, or through some other mechanism, relate to said notes by this process.  Functions which have this kind of role relative to some other function are denoted with a "pre-" prefix here.


'''Detempering''' - When the comma or subchroma that separates a note from one of the three primary functions is not tempered out, it results in the appearance of notes with either similar functions to the Dominant or Serviant, or, in the case of this function being applied to the Tonic, a Nontonic function similar to one of the Chromatic functions.  Often, though not always, these notes fall within the uncanny valleys of the three primary functions.
'''Detempering''' - When the comma or subchroma that separates a note from one of the three primary functions is not tempered out, it results in the appearance of notes with either similar functions to the Dominant or Servient, or, in the case of this function being applied to the Tonic, a Nontonic function similar to one of the Chromatic functions.  Often, though not always, these notes fall within the uncanny valleys of the three primary functions.


'''Neutralization''' - When one hybridizes Major and Minor Diatonic scale degrees of the same class or even tempers them together, one is using this process.
'''Neutralization''' - When one hybridizes Major and Minor Diatonic scale degrees of the same class or even tempers them together, one is using this process.
Line 53: Line 53:
'''Supervicinant''' - This is any note that maps to 1\7 above the Tonic, and in fact, intervals in this vicinity have both Tonic Adjacent and Serviant Parallel functions, beyond that, however, the precise behavior of notes in this range is determined by both mappings and concrete tuning ranges, see the Supervicinant and Subvicinant Subtypes section for more discussion of this function.
'''Supervicinant''' - This is any note that maps to 1\7 above the Tonic, and in fact, intervals in this vicinity have both Tonic Adjacent and Serviant Parallel functions, beyond that, however, the precise behavior of notes in this range is determined by both mappings and concrete tuning ranges, see the Supervicinant and Subvicinant Subtypes section for more discussion of this function.


'''Mediant''' - This is the note that maps to 2\7 from the Tonic in the scale's direction of construction and is named due to being roughly halfway between the Tonic and the Dominant.  This is the first of the two diatonic scale degrees that are located relatively far from the Tonic along the Circle of Third Harmonics, and, as a consequence, not only has the most possibilities for realization, but also a tendency towards stagnation, leading to the historical designation as a "weak harmony".  Aside from these, the properties that are central to the Mediant function are all most easily derived through the Tonic Parallel function and the Serviant Adjacent function, and in addition, Mediants have both Preserviant and Predominant functions.  Furthermore, since there's such a large range of Mediants, there are a multitude of subtypes, see the Mediant Subtypes section for more discussion of this function.
'''Mediant''' - This is the note that maps to 2\7 from the Tonic in the scale's direction of construction and is named due to being roughly halfway between the Tonic and the Dominant.  This is the first of the two diatonic scale degrees that are located relatively far from the Tonic along the Circle of Third Harmonics, and, as a consequence, not only has the most possibilities for realization, but also a tendency towards stagnation, leading to the historical designation as a "weak harmony".  Aside from these, the properties that are central to the Mediant function are all most easily derived through the Tonic Parallel function and the Servient Adjacent function, and in addition, Mediants have both Preservient and Predominant functions.  Furthermore, since there's such a large range of Mediants, there are a multitude of subtypes, see the Mediant Subtypes section for more discussion of this function.


'''Antitonic''' - This is a special case, see the Antitonic Subtypes section for more discussion of this function.
'''Antitonic''' - This is a special case, see the Antitonic Subtypes section for more discussion of this function.


'''Contramediant''' - Compared to the term "''Submediant''" from traditional music theory, the term "Contramediant" may have a slightly different frame of reference, as while a "Submediant" is halfway between the Tonic and a "Subdominant", the "Contramediant" is halfway between the Tonic and the Serviant.  The Contramediant is the note that maps to 5\7 from the Tonic in the scale's direction of construction, and is the second of two that are located relatively far from the Tonic along the Circle of Third Harmonics, and, as a consequence, is not only tied with the Mediant for having the most possibilities for realization, but also has a tendency towards stagnation, leading to the historical designation as a "weak harmony".  From a functional standpoint, the properties that are central to the Contramediant function are most easily derived through the Tonic Parallel function and the Dominant Adjacent function, and in addition, Contramediants have both Preserviant and Predominant functions.  Furthermore, since there's such a large range of Contramediants, there are a multitude of subtypes, see the Contramediant Subtypes section for more discussion of this function.
'''Contramediant''' - Compared to the term "''Submediant''" from traditional music theory, the term "Contramediant" may have a slightly different frame of reference, as while a "Submediant" is halfway between the Tonic and a "Subdominant", the "Contramediant" is halfway between the Tonic and the Serviant.  The Contramediant is the note that maps to 5\7 from the Tonic in the scale's direction of construction, and is the second of two that are located relatively far from the Tonic along the Circle of Third Harmonics, and, as a consequence, is not only tied with the Mediant for having the most possibilities for realization, but also has a tendency towards stagnation, leading to the historical designation as a "weak harmony".  From a functional standpoint, the properties that are central to the Contramediant function are most easily derived through the Tonic Parallel function and the Dominant Adjacent function, and in addition, Contramediants have both Preservient and Predominant functions.  Furthermore, since there's such a large range of Contramediants, there are a multitude of subtypes, see the Contramediant Subtypes section for more discussion of this function.


'''Subvicinant''' - This is any note that maps to 1\7 below the Tonic, and in fact, intervals in this vicinity have both Tonic Adjacent and Dominant Parallel functions, beyond that, however, the precise behavior of notes in this range is determined by both mappings and concrete tuning ranges, see the Supervicinant and Subvicinant Subtypes section for more discussion of this function.
'''Subvicinant''' - This is any note that maps to 1\7 below the Tonic, and in fact, intervals in this vicinity have both Tonic Adjacent and Dominant Parallel functions, beyond that, however, the precise behavior of notes in this range is determined by both mappings and concrete tuning ranges, see the Supervicinant and Subvicinant Subtypes section for more discussion of this function.
Line 69: Line 69:
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 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]].
'''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 Antiservient 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 melodic line 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.
Line 81: Line 81:
The four 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]].
'''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 "'''Biservient'''", 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 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.
'''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 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.
Line 97: Line 97:
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 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 "'''Triservient'''", which is the function specifically of [[32/27]].


'''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.
'''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.
Line 113: Line 113:
'''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 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.
'''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 Servient.  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 Servient.  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 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.
'''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 Servient.  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 "'''Quadriservient'''", 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)"