User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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'''Contralead''' - This function, although not found in Viennese Theory proper, is easily derivable through the Tonic Adjacent function, the Serviant Parallel function of [[16/15]], and the Antidominant function typified by the root of the [[Wikipedia:Neapolitan chord|Neapolitan chord]]. As such, this lowered second scale degree in Bass-Up tonality should be considered as more than just a simple chromatic alteration of the Supertonic. Taking this idea into the realm of Microtonality, the Contralead is an interval that maps to both 1\7 and 2\24, and serves in part as a leading tone in the direction opposite that of the scale's direction of construction, but also has a Predominant function. | '''Contralead''' - This function, although not found in Viennese Theory proper, is easily derivable through the Tonic Adjacent function, the Serviant Parallel function of [[16/15]], and the Antidominant function typified by the root of the [[Wikipedia:Neapolitan chord|Neapolitan chord]]. As such, this lowered second scale degree in Bass-Up tonality should be considered as more than just a simple chromatic alteration of the Supertonic. Taking this idea into the realm of Microtonality, the Contralead is an interval that maps to both 1\7 and 2\24, and serves in part as a leading tone in the direction opposite that of the scale's direction of construction, but also has a Predominant function. | ||
'''Supertonic''' - This function is easily derivable through the Tonic Adjacent function, the Serviant Parallel function | '''Supertonic''' - This function is easily derivable through the Tonic Adjacent function, and either the Serviant Parallel function and or the "'''Didominant'''" function of [[9/8]], or, at least that's the case in Bass-Up tonality, where it is an interval that maps to both 1\7 and 4\24 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. | ||
'''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 and the ability to easily host chords built with wolf fifths, 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, have both Preserviant and Predominant functions. However, there are other functional aspects of a Mediant that are determined by whether the interval in question is considered consonant or dissonant, with [[5/4]] and [[6/5]] being examples of consonant Mediants, and [[81/64]] and [[32/27]] being examples of dissonant Mediants. | '''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 and the ability to easily host chords built with wolf fifths, 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, have both Preserviant and Predominant functions. However, there are other functional aspects of a Mediant that are determined by whether the interval in question is considered consonant or dissonant, with [[5/4]] and [[6/5]] being examples of consonant Mediants, and [[81/64]] and [[32/27]] being examples of dissonant Mediants, though it should be noted that 81/64 also has the function of "'''Tetradominant'''" while 32/27 also has the function of "'''Triserviant'''". Furthermore, since there's such a large range of Mediants, there are types of Mediant that don't have diatonic function. | ||
'''Antitonic''' - This is a special case, see the next section for more discussion of this function. | '''Antitonic''' - This is a special case, see the next 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 the ability to easily host chords built with wolf fifths, and lastly, 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, have both Preserviant and Predominant functions. However, there are other functional aspects of a Contramediant that are determined by whether the interval in question is considered consonant or dissonant, with [[5/3]] and [[8/5]] being examples of consonant Contramediants, and [[27/16]] and [[128/81]] being examples of dissonant Contramediants. | '''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 the ability to easily host chords built with wolf fifths, and lastly, 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, have both Preserviant and Predominant functions. However, there are other functional aspects of a Contramediant that are determined by whether the interval in question is considered consonant or dissonant, with [[5/3]] and [[8/5]] being examples of consonant Contramediants, and [[27/16]] and [[128/81]] being examples of dissonant Contramediants, though it should be noted that 27/16 also has the function of "'''Tridominant'''" while 128/81 also has the function of "'''Tetraserviant'''". Furthermore, since there's such a large range of Contramediants, there are types of Contramediant that don't have diatonic function. | ||
'''Subtonic''' - This function is easily derivable through the Tonic Adjacent function | '''Subtonic''' - This function is easily derivable through the Tonic Adjacent function and either the Dominant Parallel function and or the "'''Diserviant'''" function of [[16/9]], with these intervals additionally having Predominant functions, or, at least that's the case in Bass-Up tonality, where it is an interval that maps to both 6\7 and 20\24 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. | ||
'''Lead''' - This is the note typically referred to when people say "the leading tone", and, from a harmonic standpoint it is easily derivable through the Tonic Adjacent function, the Dominant Parallel function of [[15/8]], and the Antiserviant function. This is an interval that maps to both 6\7 and 22\24, and serves as a leading tone in the scale's direction of construction. 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 Lead and the Dominant, sees this interval as functionally distinct from the Dominant due to the Lead 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- and, the possibility of being set-up through quartertone-like motion from above (see below on Paradiatonic and Parachromatic Functions). | '''Lead''' - This is the note typically referred to when people say "the leading tone", and, from a harmonic standpoint it is easily derivable through the Tonic Adjacent function, the Dominant Parallel function of [[15/8]], and the Antiserviant function. This is an interval that maps to both 6\7 and 22\24, and serves as a leading tone in the scale's direction of construction. 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 Lead and the Dominant, sees this interval as functionally distinct from the Dominant due to the Lead 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- and, the possibility of being set-up through quartertone-like motion from above (see below on Paradiatonic and Parachromatic Functions). | ||
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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... | 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 an interval that maps to both 1\5 and 5\24 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 an interval that maps to both 1\5 and 5\24 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. There are two different subtypes of this function that differ from each other based on how they are approached in interval stacking, the "'''Pseudodidominant'''", which arises from stacking two Pseudodominants, and the "'''Pseudotriserviant'''", which arises from stacking three Pseudoserviants. | ||
'''Intersubiant''' - This is an interval that maps to both 3\7 and 11\24 in the scale's direction of construction. Like both the Serviant and the Sycophant, intervals in this region tend to have a Predominant function, however, the way these intervals carry out this function is rather different from both as they neither act as a counterweight to the Dominant like a Serviant nor do they completely tonicize the Dominant like a Sycophant- at least to those who are more familiar with quartertones. Instead, there is a tendency for chords rooted on these intervals either to be preceded by a harmonic seventh chord built on the Tonic, to be followed by an augmented triad built on the Dominant, or to be preceded or followed by another chord with a root in the same quartertone field as itself. In Bass-Up tonality, this functionality has its roots in the eleventh harmonic, and indeed 11/8 is perhaps one of the best examples of an interval within this range, since, as its name implies, it has a decent Predominant function without the risks of tonicizing the Dominant that arise with Sycophant Antitonics due to it feeling almost like it's in its own universe when considered apart from the Tonic, while also having Preserviant functions. What's less expected, however, is that the Intersubiant also has Mocktyrant Functions. | '''Intersubiant''' - This is an interval that maps to both 3\7 and 11\24 in the scale's direction of construction. Like both the Serviant and the Sycophant, intervals in this region tend to have a Predominant function, however, the way these intervals carry out this function is rather different from both as they neither act as a counterweight to the Dominant like a Serviant nor do they completely tonicize the Dominant like a Sycophant- at least to those who are more familiar with quartertones. Instead, there is a tendency for chords rooted on these intervals either to be preceded by a harmonic seventh chord built on the Tonic, to be followed by an augmented triad built on the Dominant, or to be preceded or followed by another chord with a root in the same quartertone field as itself. In Bass-Up tonality, this functionality has its roots in the eleventh harmonic, and indeed 11/8 is perhaps one of the best examples of an interval within this range, since, as its name implies, it has a decent Predominant function without the risks of tonicizing the Dominant that arise with Sycophant Antitonics due to it feeling almost like it's in its own universe when considered apart from the Tonic, while also having Preserviant functions. What's less expected, however, is that the Intersubiant also has Mocktyrant Functions. | ||
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'''Interregnant''' - This is an interval that maps to both 4\7 and 13\24 in the scale's direction of construction. Accordingly, intervals in this region behave as a cross between a Tyrant Antitonic on one hand and a Dominant on the other in that they often contrast with the Tonic through some combination of harmonic connection and brute force contrast. In Bass-Up tonality, this functionality has its roots in the eleventh subharmonic, and indeed [[16/11]] is perhaps one of the best examples of an interval within this range, since, as its name implies, it has decent Preserviant and Predominant functions. However, it also has Mocksycophant Functions. What makes the Interregnant different from both the Dominant and the Tyrant is that it tends to be preceded or followed by another chord with a root in the same quartertone field. | '''Interregnant''' - This is an interval that maps to both 4\7 and 13\24 in the scale's direction of construction. Accordingly, intervals in this region behave as a cross between a Tyrant Antitonic on one hand and a Dominant on the other in that they often contrast with the Tonic through some combination of harmonic connection and brute force contrast. In Bass-Up tonality, this functionality has its roots in the eleventh subharmonic, and indeed [[16/11]] is perhaps one of the best examples of an interval within this range, since, as its name implies, it has decent Preserviant and Predominant functions. However, it also has Mocksycophant Functions. What makes the Interregnant different from both the Dominant and the Tyrant is that it tends to be preceded or followed by another chord with a root in the same quartertone field. | ||
'''Varicant''' - Just as a Mediant lies roughly in the middle of the 3/2 interval separating the Tonic and the Dominant above it, a Varicant lies roughly in the middle of the 4/3 interval separating the Dominant and the Tonic above it. Intervals in this region often don’t consistently act as either sixths or sevenths, or even act as a cross between a sixth and a seventh, only without potential for crowding in chords- effectively straddling the border between these two diatonic categories, hence the name "Varicant", from Latin "vāricō"<ref>[[Wiktionary: varico #Latin]]</ref>. This is an interval that maps to both 4\5 and 19\24 in the scale's direction of construction. In Bass-Up Tonality, this functionality is first encountered in the form of the [[7/4]] interval, though [[12/7]] is another notable interval included in this range. While many microtonalists think of 7/4 as being purely a type of seventh- and indeed, it most commonly acts as a sort of subminor seventh- I counterargue based on this same interval's relationships with 11/8 in particular that 7/4 is not merely a type of seventh, but rather, a type of a cross between a sixth and a seventh, with such a property explaining why [[14/11]] is generally considered to be a type of third. Furthermore, in contrast to the Subtonics of Bass-Up Tonality, Varicants are liable to acts as Predominants and Preserviants, but not as Dominant Parallels. | '''Varicant''' - Just as a Mediant lies roughly in the middle of the 3/2 interval separating the Tonic and the Dominant above it, a Varicant lies roughly in the middle of the 4/3 interval separating the Dominant and the Tonic above it. Intervals in this region often don’t consistently act as either sixths or sevenths, or even act as a cross between a sixth and a seventh, only without potential for crowding in chords- effectively straddling the border between these two diatonic categories, hence the name "Varicant", from Latin "vāricō"<ref>[[Wiktionary: varico #Latin]]</ref>. This is an interval that maps to both 4\5 and 19\24 in the scale's direction of construction. In Bass-Up Tonality, this functionality is first encountered in the form of the [[7/4]] interval, though [[12/7]] is another notable interval included in this range. While many microtonalists think of 7/4 as being purely a type of seventh- and indeed, it most commonly acts as a sort of subminor seventh- I counterargue based on this same interval's relationships with 11/8 in particular that 7/4 is not merely a type of seventh, but rather, a type of a cross between a sixth and a seventh, with such a property explaining why [[14/11]] is generally considered to be a type of third. Furthermore, in contrast to the Subtonics of Bass-Up Tonality, Varicants are liable to acts as Predominants and Preserviants, but not as Dominant Parallels. There are two different subtypes of this function that differ from each other based on how they are approached in interval stacking, the "'''Pseudotridominant'''", which arises from stacking three Pseudodominants, and the "'''Pseudodiserviant'''", which arises from stacking two Pseudoserviants. | ||
=== Derivative Paradiatonic Functions === | === Derivative Paradiatonic Functions === | ||