User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions
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Among the chief ideas that come from German Theory is that there are three basic, or primary functions, and that there are multiple operations that can be applied to these three basic functions in order to derive new functions. However, compared to those ideal functions, one of the three is in part original to my work. | Among the chief ideas that come from German Theory is that there are three basic, or primary functions, and that there are multiple operations that can be applied to these three basic functions in order to derive new functions. However, compared to those ideal functions, one of the three is in part original to my work. | ||
[[File:Diatonic Function Map (Version 4).png|thumb| | [[File:Diatonic Function Map (Version 4).png|thumb|Diagram of diatonic and paradiatonic function locations as of an older edition of this article- note the use of the now obsolete terms "Interregnant" and "Intersubiant" for what are now the Imponent and Subient functions respectively. Apart from these, and the new spelling standardization of the term "Servient", there have only been minor changes, and a new diagram should be forthcoming.]] | ||
=== Basic Diatonic Functions === | === Basic Diatonic Functions === | ||
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'''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, Preservient, 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 "'''Pseudobidominant'''", which arises from stacking two Pseudodominants, and the "'''Pseudotriservient'''", which arises from stacking three Pseudoservients. | '''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, Preservient, 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 "'''Pseudobidominant'''", which arises from stacking two Pseudodominants, and the "'''Pseudotriservient'''", which arises from stacking three Pseudoservients. | ||
'''Subient''' - This is an interval that maps to both 3\7 and 11\24 in the scale's direction of construction and comprises the intervals ranging from around 3.5 cents short of [[15/11]] to around 3.5 cents beyond [[11/8]]. Like both the Servient and the Sycophant, intervals in this region have a Predominant function, however, this predominant function is weaker than that of the surrounding interval regions since they neither act as a counterweight to the Dominant like a Servient nor do they completely tonicize the Dominant like a Sycophant- at least to those who are more familiar with quartertones. What is even less expected is that these same intervals also have Preservient and Mocktyrant functions. The name of this function comes from Latin "subeō"<ref>[[Wiktionary: subeo #Latin]]</ref>, specifically from the senses ranging from "approach" to "follow" and even "undergo", as all of these senses describe what the Subient actually does musically. Since the Subient is not found in the Tonic's quartertone field, there is a tendency for Subient chords to be preceded and or followed by other chords with roots in the same quartertone field, though one could also reasonably approach it from the Tonic, the Servient, some kind of Contramediant, some kind of Supervicinant, or, in some tuning systems, certain kinds of Mediant. In Bass-Up tonality, this functionality has its roots in the eleventh harmonic. | '''Subient''' - This is an interval that maps to both 3\7 and 11\24 in the scale's direction of construction and comprises the intervals ranging from around 3.5 cents short of [[15/11]] to around 3.5 cents beyond [[11/8]]. Like both the Servient and the Sycophant, intervals in this region have a Predominant function, however, this predominant function is weaker than that of the surrounding interval regions since they neither act as a counterweight to the Dominant like a Servient nor do they completely tonicize the Dominant like a Sycophant- at least to those who are more familiar with quartertones. What is even less expected is that these same intervals also have Preservient and Mocktyrant functions. The name of this function comes from Latin "subeō"<ref>[[Wiktionary: subeo #Latin]]</ref>, specifically from the senses ranging from "approach" to "follow" and even "undergo", as all of these senses describe what the Subient actually does musically. Since the Subient is not found in the Tonic's quartertone field, there is a tendency for Subient chords to be preceded and or followed by other chords with roots in the same quartertone field, though one could also reasonably approach it from the Tonic, the Servient, some kind of Contramediant, some kind of Supervicinant, or, in some tuning systems, certain kinds of Mediant. In Bass-Up tonality, this functionality has its roots in the eleventh harmonic. This function used to be called the "Intersubiant" on an ad hoc basis, though that term has since been rendered obsolete. | ||
'''Imponent''' - This is an interval that maps to both 4\7 and 13\24 in the scale's direction of construction and comprises the intervals ranging from around 3.5 cents short of [[16/11]] to around 3.5 cents beyond [[22/15]]. 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, though it unexpectedly has decent Predominant and Mocksycophant functions. Like the Subient, the Imponent is not found in the Tonic's quartertone field and is either very distant from the Tonic along the circle of fifths or is completely missed by said circle of fifths, thus, there is a tendency for Imponent chords to be preceded and or followed by other chords with roots in the same quartertone field. As if all that weren't enough, the Imponent can be used in the formation of chords, but because of [[delta-rational]] and other considerations, tertian chords framed with this type of interval usually have a markedly different structure imposed on them. The name of this function comes from Latin "impōnō"<ref>[[Wiktionary: impono #Latin]]</ref>, specifically from the senses ranging from "impose upon" to "inflict" and even "establish", as all of these senses describe what the Imponent actually does musically. Conspicuously, the distance between the Imponent and the Subient is only about a Minor Second- or, at the very most, a Supraminor Second- so as a result, the Imponent can be both a set-up and a follow-up to the Subient. In Bass-Up tonality, the Imponent functionality has its roots in the eleventh subharmonic. | '''Imponent''' - This is an interval that maps to both 4\7 and 13\24 in the scale's direction of construction and comprises the intervals ranging from around 3.5 cents short of [[16/11]] to around 3.5 cents beyond [[22/15]]. 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, though it unexpectedly has decent Predominant and Mocksycophant functions. Like the Subient, the Imponent is not found in the Tonic's quartertone field and is either very distant from the Tonic along the circle of fifths or is completely missed by said circle of fifths, thus, there is a tendency for Imponent chords to be preceded and or followed by other chords with roots in the same quartertone field. As if all that weren't enough, the Imponent can be used in the formation of chords, but because of [[delta-rational]] and other considerations, tertian chords framed with this type of interval usually have a markedly different structure imposed on them. The name of this function comes from Latin "impōnō"<ref>[[Wiktionary: impono #Latin]]</ref>, specifically from the senses ranging from "impose upon" to "inflict" and even "establish", as all of these senses describe what the Imponent actually does musically. Conspicuously, the distance between the Imponent and the Subient is only about a Minor Second- or, at the very most, a Supraminor Second- so as a result, the Imponent can be both a set-up and a follow-up to the Subient. In Bass-Up tonality, the Imponent functionality has its roots in the eleventh subharmonic. This function used to be called the "Interregnant" on an ad hoc basis, though that term has since been rendered obsolete. | ||
'''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 act as Predominants, Preservients, and Serviant Parallels, as well as display 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 "'''Pseudotridominant'''", which arises from stacking three Pseudodominants, and the "'''Pseudobiservient'''", which arises from stacking two Pseudoservients. | '''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 act as Predominants, Preservients, and Serviant Parallels, as well as display 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 "'''Pseudotridominant'''", which arises from stacking three Pseudodominants, and the "'''Pseudobiservient'''", which arises from stacking two Pseudoservients. | ||
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'''Paradominant''' - This function typically appears along prime axes other than that of the 3-limit in which they take Dominant-like function. Thus, for example, in Bass-Up Tonality, the note at 5/4 above the Tonic, being a direct prime harmonic of the Tonic, gets to serve this function in addition to its Mesodistomediant function as defined by the 3-limit, with the Paradominant function emerging mainly in a series of 5/4-based motions leading to the Tonic. When considered alongside the actual Dominant function of 3/2, however, Paradominants take on the function of Predominant owing to the fact that the Dominant function of 3/2 is actually stronger than that of any predominant due to being closer to the fundamental. | '''Paradominant''' - This function typically appears along prime axes other than that of the 3-limit in which they take Dominant-like function. Thus, for example, in Bass-Up Tonality, the note at 5/4 above the Tonic, being a direct prime harmonic of the Tonic, gets to serve this function in addition to its Mesodistomediant function as defined by the 3-limit, with the Paradominant function emerging mainly in a series of 5/4-based motions leading to the Tonic. When considered alongside the actual Dominant function of 3/2, however, Paradominants take on the function of Predominant owing to the fact that the Dominant function of 3/2 is actually stronger than that of any predominant due to being closer to the fundamental. | ||
''' | '''Paraservient''' - This function is essentially the inverse of the Paradominant function, and acts as a sort of counterweight to the Paradominant relative to the Tonic. Like the Paradominant function, it typically appears along prime axes other than that of the 3-limit in which they take Serviant-like function. Thus, for example, in Bass-Up tonality, the note at 8/5 above the Tonic, being a direct prime subharmonic of the Tonic, gets to serve this function in addition to its Mesodistocontramediant function as defined by the 3-limit. When considered alongside the actual Serviant function of 4/3, however, Paraservients take on the function of Preservient since the Serviant function of 4/3 is stronger. | ||
== References == | == References == | ||