User:Aura/Aura's Ideas on Functional Harmony (Part 1) - Revision history

Aura: /* The Realm of the Paradiatonic and the Parachormatic */

2026-03-02T20:11:37Z

The Realm of the Paradiatonic and the Parachormatic

← Older revision		Revision as of 20:11, 2 March 2026
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	Out of the various functions found in the Paradiatonic scales, 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 scales, 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 with ~~minor~~ potential for crowding in chords depending on the exact tuning. 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 with slight potential for crowding in chords depending on the exact tuning. 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. This function used to be called the "Intersubiant" on an ad hoc basis, though that term has since been rendered obsolete.		'''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.
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	'''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.		'''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 with ~~minor~~ potential for crowding in chords depending on the exact tuning- 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 with slight potential for crowding in chords depending on the exact tuning- 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.

	=== Derivative Paradiatonic Functions ===		=== Derivative Paradiatonic Functions ===

Aura at 19:33, 2 March 2026

2026-03-02T19:33:01Z

← Older revision		Revision as of 19:33, 2 March 2026
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	Out of the various functions found in the Paradiatonic scales, 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 scales, 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, 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 with minor potential for crowding in chords depending on the exact tuning. 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. This function used to be called the "Intersubiant" on an ad hoc basis, though that term has since been rendered obsolete.		'''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.
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	'''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.		'''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 with minor potential for crowding in chords depending on the exact tuning- 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.

	=== Derivative Paradiatonic Functions ===		=== Derivative Paradiatonic Functions ===

Aura at 17:52, 6 September 2025

2025-09-06T17:52:58Z

← Older revision		Revision as of 17:52, 6 September 2025
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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\|~~Current diagram~~ of diatonic and paradiatonic function locations as of ~~the current~~ edition of this article.]]		[[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.

	'''~~Paraserviant~~''' - 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, ~~Paraserviants~~ take on the function of ~~Preserviant~~ since the Serviant function of 4/3 is stronger.		'''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 ==

Aura: /* Additional Composite Functions */

2025-09-06T17:36:47Z

Additional Composite Functions

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	'''Supermaculant''' - This function is a compositing of Supergradient and Superdislocant, and thus is like the chromatic version of the Supersanguinant.		'''Supermaculant''' - This function is a compositing of Supergradient and Superdislocant, and thus is like the chromatic version of the Supersanguinant.

	'''Acuotyrant''' - This function is a compositing of Prototyrant and ~~Interregnant~~ in Bass-Up Tonality, and although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless operates more on the side of brute force when it contrasts with the Tonic.		'''Acuotyrant''' - This function is a compositing of Prototyrant and Imponent in Bass-Up Tonality, and although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless operates more on the side of brute force when it contrasts with the Tonic.

	'''Gravosycophant''' - This function is a compositing of Protosycophant and ~~Intersubiant~~ in Bass-Up Tonality, and although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless often runs a high risk of tonicizing the Geminodominant.		'''Gravosycophant''' - This function is a compositing of Protosycophant and Subient in Bass-Up Tonality, and although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless often runs a high risk of tonicizing the Geminodominant.

	'''Gravotyrant''' this function is a compositing of Prototyrant and ~~Interregnant~~ in Treble-Down Tonality, and although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless operates more on the side of brute force when it contrasts with the Tonic.		'''Gravotyrant''' this function is a compositing of Prototyrant and Imponent in Treble-Down Tonality, and although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless operates more on the side of brute force when it contrasts with the Tonic.

	'''Acuosycophant''' - This function is a compositing of Protosycophant and ~~Intersubiant~~ in Treble-Down Tonality, and although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless often runs a high risk of tonicizing the Geminodominant.		'''Acuosycophant''' - This function is a compositing of Protosycophant and Subient in Treble-Down Tonality, and although an interval like this generally fails to truly oppose the harmonies of the Tonic, it nevertheless often runs a high risk of tonicizing the Geminodominant.

	== Extra Functions of Prime Harmonics and Subharmonics ==		== Extra Functions of Prime Harmonics and Subharmonics ==

Aura: /* The Realm of the Paradiatonic and the Parachormatic */

2025-09-06T17:35:20Z

The Realm of the Paradiatonic and the Parachormatic

Aura: /* Circumtonic Regions */

2025-09-06T17:05:43Z

Circumtonic Regions

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	The Circumtonic regions are the two main regions on either side of the Tonic, outside the Tonic's "event horizon". These intervals are invariably inside the Tonic's uncanny valleys, and the uncanny valleys around the Tonic, unlike those around the other two functions, are very deep, and as a result, wolf intervals around the Tonic are tolerable in ornamentation but not melody or harmony. Thus, these intervals cannot be directly approached from the Tonic, even melodically, and so they're usually avoided outside of modulation.		The Circumtonic regions are the two main regions on either side of the Tonic, outside the Tonic's "event horizon". These intervals are invariably inside the Tonic's uncanny valleys, and the uncanny valleys around the Tonic, unlike those around the other two functions, are very deep, and as a result, wolf intervals around the Tonic are tolerable in ornamentation but not melody or harmony. Thus, these intervals cannot be directly approached from the Tonic, even melodically, and so they're usually avoided outside of modulation.

	'''Supercommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 25 cents above the Tonic. These intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance, or for a slightly less resolved version of a Unison or Octave.		'''Supercommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 35 cents above the Tonic. These intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance, or for a slightly less resolved version of a Unison or Octave.

	'''Subcommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 25 cents below the Tonic. As with Supercommatic intervals, these intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance.		'''Subcommatic''' - This is a note that occurs at intervals from about 3.5 cents to roughly 35 cents below the Tonic. As with Supercommatic intervals, these intervals are little more than stepping stones in modulation, and extra intervals that can be used together with the Tonic for a sense of dissonance.

	=== Circumdominant Regions ===		=== Circumdominant Regions ===

Aura: /* Wolf Fifths, Wolf Fourths and the Uncanny Valleys of Harmony */

2025-09-06T16:57:36Z

Wolf Fifths, Wolf Fourths and the Uncanny Valleys of Harmony

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	The circumdomimant regions are the two main regions on either side of the Dominant proper, and since the uncanny valleys around the Dominant are not as deep as those around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities. Note that together with the Dominant itself, these functions are collectively called "'''Protodominants'''", as there are many systems where what would be the Dominant fails to get distinguished from either one or the other of the functions listed here.		The circumdomimant regions are the two main regions on either side of the Dominant proper, and since the uncanny valleys around the Dominant are not as deep as those around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities. Note that together with the Dominant itself, these functions are collectively called "'''Protodominants'''", as there are many systems where what would be the Dominant fails to get distinguished from either one or the other of the functions listed here.

	'''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond [[22/15]] to about 3.5 cents short of the 3/2 perfect fifth in the scale's direction of construction. Although often overlooked or even outright shunned by traditional theorists, the Geminodominant is a legitimate diatonic function in terms of this analysis- albeit one only existing in non-meantone environments in which it is easily derived from the Dominant through detempering, occurring in [[5-limit]] diatonic environments, and acting as a sort of "fraternal twin" to the Dominant, hence its name. Specifically, as typified by intervals like [[40/27]], Geminodominants are dissonant intervals that simultaneously act as alternatives to the Dominant in both chord progressions and chord construction, and often require resolution, though they also have a ~~Preserviant~~ function. The dissonance of this function relative to a chord root is useful in preventing tonicization of chords built on the traditional weak harmonies- the Mediant and the Contramediant- which also has the benefits of strengthening interrupted cadences and creating the sense of impending movement, but outside of these usages and well supported chords, this kind of thing is best avoided since things repel the similar but not identical. Apart from diatonic contexts, Geminodominants only rise to prominence in systems where what might otherwise function as a Dominant is found just short of the sweet spot range near the standard issue 3/2.		'''Geminodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond [[22/15]] to about 3.5 cents short of the 3/2 perfect fifth in the scale's direction of construction. Although often overlooked or even outright shunned by traditional theorists, the Geminodominant is a legitimate diatonic function in terms of this analysis- albeit one only existing in non-meantone environments in which it is easily derived from the Dominant through detempering, occurring in [[5-limit]] diatonic environments, and acting as a sort of "fraternal twin" to the Dominant, hence its name. Specifically, as typified by intervals like [[40/27]], Geminodominants are dissonant intervals that simultaneously act as alternatives to the Dominant in both chord progressions and chord construction, and often require resolution, though they also have a Preservient function. The dissonance of this function relative to a chord root is useful in preventing tonicization of chords built on the traditional weak harmonies- the Mediant and the Contramediant- which also has the benefits of strengthening interrupted cadences and creating the sense of impending movement, but outside of these usages and well supported chords, this kind of thing is best avoided since things repel the similar but not identical. Apart from diatonic contexts, Geminodominants only rise to prominence in systems where what might otherwise function as a Dominant is found just short of the sweet spot range near the standard issue 3/2.

	'''Pseudodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 cents beyond the 3/2 perfect fifth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Dominant is found just beyond the sweet spot range near the standard issue 3/2. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Predominant function.		'''Pseudodominant''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents to about 25 cents beyond the 3/2 perfect fifth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Dominant's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Dominant is found just beyond the sweet spot range near the standard issue 3/2. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Predominant function.

	=== ~~Circumserviant~~ Regions ===		=== Circumservient Regions ===

	The ~~circumserviant~~ regions are the two main regions on either side of the ~~Serviant~~ proper, and since the uncanny valleys around the ~~Dominant~~ are not as deep as those around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities. Note that together with the ~~Serviant~~ itself, these functions are collectively called "'''~~Protoserviants~~'''", as there are many systems where what would be the ~~Serviant~~ fails to get distinguished from either one or the other of the functions listed here.		The circumservient regions are the two main regions on either side of the Servient proper, and since the uncanny valleys around the Servient are not as deep as those around the Tonic, there is more room for actual first derivative diatonic functionality, as well as other functionalities. Note that together with the Servient itself, these functions are collectively called "'''Protoservients'''", as there are many systems where what would be the Servient fails to get distinguished from either one or the other of the functions listed here.

	'''~~Geminoserviant~~''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond the 4/3 perfect fourth to about 3.5 cents short of [[15/11]] in the scale's direction of construction. Although often overlooked or even outright shunned by traditional theorists, the ~~Geminodominant~~ is a legitimate diatonic function in terms of this analysis- albeit one only existing in non-meantone environments in which it is easily derived from the ~~Serviant~~ through detempering, occurring in 5-limit diatonic environments, and acting as a sort of "fraternal twin" to the ~~Serviant~~, hence its name. As typified by intervals like [[27/20]], ~~Geminoserviants~~ are dissonant intervals that often act as a sort of Predominant and or as the inverses of Geminodominants. The dissonance of this function relative to a chord root is useful in preventing tonicization of chords built on the Mediant and the Contramediant, but outside of these usages and well supported chords, this kind of thing is best avoided. Apart from diatonic contexts, ~~Geminoserviants~~ only rise to prominence in systems where what might otherwise function as a ~~Serviant~~ is found just beyond the sweet spot range near the standard issue 4/3.		'''Geminoservient''' - This is a note that occurs roughly at intervals ranging from about 3.5 cents beyond the 4/3 perfect fourth to about 3.5 cents short of [[15/11]] in the scale's direction of construction. Although often overlooked or even outright shunned by traditional theorists, the Geminoservient is a legitimate diatonic function in terms of this analysis- albeit one only existing in non-meantone environments in which it is easily derived from the Servient through detempering, occurring in 5-limit diatonic environments, and acting as a sort of "fraternal twin" to the Servient, hence its name. As typified by intervals like [[27/20]], Geminoservients are dissonant intervals that often act as a sort of Predominant and or as the inverses of Geminodominants. The dissonance of this function relative to a chord root is useful in preventing tonicization of chords built on the Mediant and the Contramediant, but outside of these usages and well supported chords, this kind of thing is best avoided. Apart from diatonic contexts, Geminoservients only rise to prominence in systems where what might otherwise function as a Servient is found just beyond the sweet spot range near the standard issue 4/3.

	'''~~Pseudoserviant~~''' - This is a note that occurs roughly at intervals ranging from about 25 cents to about 3.5 cents short of the 4/3 perfect fourth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the ~~Serviant~~'s uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a ~~Serviant~~ is found just short the sweet spot range near the standard issue 4/3. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a ~~Preserviant~~ function.		'''Pseudoservient''' - This is a note that occurs roughly at intervals ranging from about 25 cents to about 3.5 cents short of the 4/3 perfect fourth in the scale's direction of construction. Because none of these intervals arise naturally in a [[5-limit]] diatonic scale, and because they fall within one of the Servient's uncanny valleys, it is rare to see this functionality outside of systems where what might otherwise function as a Servient is found just short the sweet spot range near the standard issue 4/3. However, these intervals naturally arise in the Circle of Thirteenth Harmonics, in which case they have a Preservient function.

	=== Governing Rules ===		=== Governing Rules ===
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	However, in non-meantone settings, it is possible to have a chord which shares its root with the Tertiary Dominant and shares both its third and fifth with the Relative Minor. Since such an arrangement results in a wolf fifth, and since the wolf fifth is a dissonance requiring resolution, one could argue that such a chord has a function distinct from the more traditional options- specifically one which is involved in interrupted cadences, as well as in starting cadences that "wind down" such as VImin-IVmaj-Imaj or even VImin-Vmaj-Imaj. This particular function is what I call the ''Major Contramediant Tensive''.		However, in non-meantone settings, it is possible to have a chord which shares its root with the Tertiary Dominant and shares both its third and fifth with the Relative Minor. Since such an arrangement results in a wolf fifth, and since the wolf fifth is a dissonance requiring resolution, one could argue that such a chord has a function distinct from the more traditional options- specifically one which is involved in interrupted cadences, as well as in starting cadences that "wind down" such as VImin-IVmaj-Imaj or even VImin-Vmaj-Imaj. This particular function is what I call the ''Major Contramediant Tensive''.

	'''Primary Adpositive Purity''' - This rule is that for every chord root located one step away from either the Tonic, Dominant or ~~Serviant~~ along the Circle of Fifths, there is a demand for the fifth of the chord in question to be within 3.5 cents of a just 3/2, though in the case of a chord that has a root located at two steps away from the Tonic along the along the Circle of Fifths, the fifth of the chord can be deliberately subjected to the process of Displacement as mentioned before and not run afoul of this restriction. However, chord roots that are located three or more steps away from the Tonic along the circle of fifths are not subject to the aforementioned restriction due to their distance. This means that the Tonic, Dominant, ~~Serviant~~, Supertonic and Subtonic chords all demand a perfect fifth as the fifth of the chord, whether you are building the Tonality upwards or downwards, but wolf fifths can occur easily as the fifth of chords which are located three or more steps away from the Tonic.		'''Primary Adpositive Purity''' - This rule is that for every chord root located one step away from either the Tonic, Dominant or Servient along the Circle of Fifths, there is a demand for the fifth of the chord in question to be within 3.5 cents of a just 3/2, though in the case of a chord that has a root located at two steps away from the Tonic along the along the Circle of Fifths, the fifth of the chord can be deliberately subjected to the process of Displacement as mentioned before and not run afoul of this restriction. However, chord roots that are located three or more steps away from the Tonic along the circle of fifths are not subject to the aforementioned restriction due to their distance. This means that the Tonic, Dominant, Servient, Supertonic and Subtonic chords all demand a perfect fifth as the fifth of the chord, whether you are building the Tonality upwards or downwards, but wolf fifths can occur easily as the fifth of chords which are located three or more steps away from the Tonic.

	== Beyond Diatonic and Chromatic Functional Harmony ==		== Beyond Diatonic and Chromatic Functional Harmony ==

Aura: /* Basic Chromatic Function-Deriving Operations */

2025-09-06T16:48:55Z

Basic Chromatic Function-Deriving Operations

← Older revision		Revision as of 16:48, 6 September 2025
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	=== Basic Chromatic Function-Deriving Operations ===		=== Basic Chromatic Function-Deriving Operations ===

	The way I see it, there ~~are~~ at least one known operation which can be used to derive additional Chromatic functions from various Diatonic functions.		The way I see it, there is at least one known operation which can be used to derive additional Chromatic functions from various Diatonic functions.

	'''Displacement''' - This process results in a note that is near the Dominant or Serviant taking on similar functions to said notes rather than the opposite function, or, when applied to the Tonic, results in a Nontonic function that tends to want to lead away from the Tonic rather than towards it. This process is distinct from Detempering in that the notes created by this process are located at further distances from the note to which this process is applied.		'''Displacement''' - This process results in a note that is near the Dominant or Serviant taking on similar functions to said notes rather than the opposite function, or, when applied to the Tonic, results in a Nontonic function that tends to want to lead away from the Tonic rather than towards it. This process is distinct from Detempering in that the notes created by this process are located at further distances from the note to which this process is applied.

Aura: /* Antitonic Subtypes */

2025-09-06T16:47:45Z

Antitonic Subtypes

← Older revision		Revision as of 16:47, 6 September 2025
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	== Antitonic Subtypes ==		== Antitonic Subtypes ==

	Notes that occur around half an octave away from the Tonic, on account of harmonies built on notes in this area tending to oppose that of the Tonic, are referred to by the term "Antitonic" by myself and others. It should be noted that the Antitonic is basically a first derivative function as it is derived from the Tonic through either perfect or imperfect Antipodism. In addition, the term "Antitonic" acts as a generic term for any of a group of diatonic functions found in this region. While some microtonal theorists insist that the Antitonic functionality is more fundamental than perhaps even the Dominant or ~~Serviant~~, others, such as myself, disagree.		Notes that occur around half an octave away from the Tonic, on account of harmonies built on notes in this area tending to oppose that of the Tonic, are referred to by the term "Antitonic" by myself and others. It should be noted that the Antitonic is basically a first derivative function as it is derived from the Tonic through either perfect or imperfect Antipodism. In addition, the term "Antitonic" acts as a generic term for any of a group of diatonic functions found in this region. While some microtonal theorists insist that the Antitonic functionality is more fundamental than perhaps even the Dominant or Servient, others, such as myself, disagree.

	=== Specific Types of Antitonic ===		=== Specific Types of Antitonic ===
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	The exact outcome and specific function of any given Antitonic depends on whether or not the interval in question is an augmented fourth or a diminished fifth.		The exact outcome and specific function of any given Antitonic depends on whether or not the interval in question is an augmented fourth or a diminished fifth.

	'''Sycophant''' - This type of Antitonic is mapped to both 3\7 and 12\24, and is named as such on account of it having a tendency to "kiss up to" and tonicize the Dominant- that is, to cause the Dominant to become a new Tonic- unless followed up by a different note such as some type of Mediant. A prototypical example of this type of Antitonic is 45/32.		'''Sycophant''' - This type of Antitonic is mapped to both 3\7 and 12\24, and is named as such on account of it having a tendency to "kiss up to" and tonicize the Dominant- that is, to cause the Dominant to become a new Tonic- unless followed up by a different note such as some type of Mediant. A prototypical example of this type of Antitonic is [[45/32]].

	'''Tyrant''' - This type of Antitonic is mapped to both 4\7 and 12\24, and it tends to contrast with the Tonic in a manner somewhat akin to that of a Dominant, but by sheer brute force and contrary harmonic nature, and indeed these brute force Dominant-esque tendencies are the source of the name "Tyrant". For example, if the Tonic harmony is Minor in nature, the Antitonic harmony will be Major- or more rarely, Supermajor- in nature. Furthermore, in scales such as the Locrian scale, any type of Serviant harmony tends to resolve towards some other type of substitute for a Dominant, often bypassing this type of Antitonic, though on rare occasions, a Tyrant will act as a leading tone to the ~~Serviant~~. A prototypical example of this type of Antitonic is 64/45.		'''Tyrant''' - This type of Antitonic is mapped to both 4\7 and 12\24, and it tends to contrast with the Tonic in a manner somewhat akin to that of a Dominant, but by sheer brute force and contrary harmonic nature, and indeed these brute force Dominant-esque tendencies are the source of the name "Tyrant". For example, if the Tonic harmony is Minor in nature, the Antitonic harmony will be Major- or more rarely, Supermajor- in nature. Furthermore, in scales such as the Locrian scale, any type of Serviant harmony tends to resolve towards some other type of substitute for a Dominant, often bypassing this type of Antitonic, though on rare occasions, a Tyrant will act as a leading tone to the Servient. A prototypical example of this type of Antitonic is [[64/45]].

	== Chromatic Functions ==		== Chromatic Functions ==

Aura: More terminology correction

2025-09-06T16:45:40Z

More terminology correction

Show changes