Tonic - Revision history

Aura: /* Relationship to other tonal centers */Clarified a statement about how tonics function

2025-04-10T20:14:27Z

Relationship to other tonal centers: Clarified a statement about how tonics function

← Older revision		Revision as of 20:14, 10 April 2025
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	== Relationship to other tonal centers ==		== Relationship to other tonal centers ==

	Like any other tonal center, the tonic has a way of successfully contextualizing the collection of notes ~~around it~~ across long distances in time around itself, provided that each note in the collection meets certain criteria that enable such contextualization. Consequently, in pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece, and it contextualizes the other tonal centers by means of its being located at critical positions within the piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.		Like any other tonal center, the tonic has a way of successfully contextualizing the surrounding collection of notes across long distances in time around itself, provided that each note in the collection meets certain criteria that enable such contextualization. Consequently, in pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece, and it contextualizes the other tonal centers by means of its being located at critical positions within the piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.

	== As an initiating event, anchor, or resolution tone ==		== As an initiating event, anchor, or resolution tone ==

Aura: Corrected some terminology and added a more recent insight as to the function of a tonal center

2025-01-31T23:30:42Z

Corrected some terminology and added a more recent insight as to the function of a tonal center

← Older revision		Revision as of 23:30, 31 January 2025
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	== Relationship to other tonal centers ==		== Relationship to other tonal centers ==

	In pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.		Like any other tonal center, the tonic has a way of successfully contextualizing the collection of notes around it across long distances in time around itself, provided that each note in the collection meets certain criteria that enable such contextualization. Consequently, in pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece, and it contextualizes the other tonal centers by means of its being located at critical positions within the piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.

	== As an initiating event, anchor, or resolution tone ==		== As an initiating event, anchor, or resolution tone ==

	In many Medieval, Neo-Medieval and [[Wikipedia:Common practice period\|Common Practice]] pieces, the ~~Tonic~~ is often the tone used for resolution in musical phrases, and, as a logical extension of this, can be considered the principal goal tone of a piece. This is especially known for being established through an [[Wikipedia:Cadence#Authentic%20cadence\|Authentic cadence]]. In addition, it should be noted that other chords in diatonic harmony, namely the mediant and submediant, often have tonic-like function in the sense of being resolution tones, with the caveat that they are ultimately nontonic functions, and hence, such resolutions are considered to be either interrupted or deceptive cadences. In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a piece— a function which continues to be widespread in Western Classical music. As a consequence of its role as both a common initiating event and the main resolution tone, the tonic often serves as the single most important anchor for both melodies and harmonies in a tonal piece, and as a consequence, it is likely to occur very frequently, even if it is not the most commonly occurring functional element of a piece.		In many Medieval, Neo-Medieval and [[Wikipedia:Common practice period\|Common Practice]] pieces, the tonic is often the tone used for resolution in musical phrases, and, as a logical extension of this, can be considered the principal goal tone of a piece. This is especially known for being established through an [[Wikipedia:Cadence#Authentic%20cadence\|Authentic cadence]]. In addition, it should be noted that other chords in diatonic harmony, namely the mediant and submediant, often have tonic-like function in the sense of being resolution tones, with the caveat that they are ultimately nontonic functions, and hence, such resolutions are considered to be either interrupted or deceptive cadences. In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a piece— a function which continues to be widespread in Western Classical music. As a consequence of its role as both a common initiating event and the main resolution tone, the tonic often serves as the single most important anchor for both melodies and harmonies in a tonal piece, and as a consequence, it is likely to occur very frequently, even if it is not the most commonly occurring functional element of a piece.

	== Relationship to other functions ==		== Relationship to other functions ==
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	Since the tonic is the generator of other tones through either the [[harmonic series]] or the [[subharmonic series]], it is thus the origin and the definer of all other functions and can be considered the [[1/1]], and, in [[Octave #Octave equivalence\|octave equivalent]] systems, [[2/1]]. In such systems, the first [[3-limit]] nontonic pitches in both the harmonic series and the subharmonic series give rise to the dominant and subdominant (or, alternatively, superdominant) harmonies, with the exact role of each 3-limit pitch being determined by whether you build your tonality from the low pitches to the high pitches, or from the high pitches to the low pitches—that is, your tonality's chosen direction of construction. From there, the next 3-limit pitches in both the harmonic series and the subharmonic series give rise to the [[Wikipedia:Supertonic\|supertonic]] and [[Wikipedia:Subtonic\|subtonic]]—with the exact functions of each of these also being determined by your chosen tonality's direction of construction—and the next three limit pitches after that in both the harmonic series and the subharmonic series give rise to variations of the [[Wikipedia:Mediant\|mediant]] and [[Wikipedia:Submediant\|submediant]] (or, alternatively, the supermediant) depending on your tonality's direction of construction.		Since the tonic is the generator of other tones through either the [[harmonic series]] or the [[subharmonic series]], it is thus the origin and the definer of all other functions and can be considered the [[1/1]], and, in [[Octave #Octave equivalence\|octave equivalent]] systems, [[2/1]]. In such systems, the first [[3-limit]] nontonic pitches in both the harmonic series and the subharmonic series give rise to the dominant and subdominant (or, alternatively, superdominant) harmonies, with the exact role of each 3-limit pitch being determined by whether you build your tonality from the low pitches to the high pitches, or from the high pitches to the low pitches—that is, your tonality's chosen direction of construction. From there, the next 3-limit pitches in both the harmonic series and the subharmonic series give rise to the [[Wikipedia:Supertonic\|supertonic]] and [[Wikipedia:Subtonic\|subtonic]]—with the exact functions of each of these also being determined by your chosen tonality's direction of construction—and the next three limit pitches after that in both the harmonic series and the subharmonic series give rise to variations of the [[Wikipedia:Mediant\|mediant]] and [[Wikipedia:Submediant\|submediant]] (or, alternatively, the supermediant) depending on your tonality's direction of construction.

	In the [[5-limit]], the first pair of nontonic pitches in both the harmonic series and the subharmonic series give rise to the simplest variations of the mediant and ~~contramediant~~, while the first combinations of 3-limit and 5-limit give rise to a set of leading tones— the exact role of each individual pitch is again determined by your chosen tonality's direction of construction. Between the 3-limit and the 5-limit, all [[Diatonic functional harmony\|diatonic functions]] are generated.		In the [[5-limit]], the first pair of nontonic pitches in both the harmonic series and the subharmonic series give rise to the simplest variations of the mediant and either the submediant or supermediant, while the first combinations of 3-limit and 5-limit give rise to a set of leading tones— the exact role of each individual pitch is again determined by your chosen tonality's direction of construction. Between the 3-limit and the 5-limit, all [[Diatonic functional harmony\|diatonic functions]] are generated.

	Of course, this same pattern of generation extends to the [[7-limit]], the [[11-limit]], the [[13-limit]], and so on, resulting in [[Paradiatonic functional harmony\|pardiatonic functions]]. As a result of all this giving rise to other functions, the tonic neutralizes the tension between the dominant and the subdominant (or superdominant) as well as their respective [[Wikipedia:Parallel and counter parallel\|"parallels" and "counter parallels"]].		Of course, this same pattern of generation extends to the [[7-limit]], the [[11-limit]], the [[13-limit]], and so on, resulting in [[Paradiatonic functional harmony\|pardiatonic functions]]. As a result of all this giving rise to other functions, the tonic neutralizes the tension between the dominant and the subdominant (or superdominant) as well as their respective [[Wikipedia:Parallel and counter parallel\|"parallels" and "counter parallels"]].

Aura at 15:06, 30 August 2023

2023-08-30T15:06:58Z

← Older revision		Revision as of 15:06, 30 August 2023
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	== As an initiating event, anchor, or resolution tone ==		== As an initiating event, anchor, or resolution tone ==

	In many Medieval, Neo-Medieval and [[Wikipedia:Common practice period\|Common Practice]] pieces, the Tonic is often the tone used for resolution in musical phrases, and, as a logical extension of this, can be considered the principal goal tone of a piece. This is especially known for being established through an [[Wikipedia:Cadence#Authentic%20cadence\|Authentic cadence]]. In addition, it should be noted that other chords in diatonic harmony, namely the mediant and submediant, often have tonic-like function in the sense of being resolution tones, with the caveat that they are ultimately nontonic functions, and hence, such resolutions are considered to be either interrupted or deceptive cadences. In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a piece— a function which continues to be widespread in Western Classical music. As a consequence of its role as both a common initiating event and the main resolution tone, the tonic often serves as the single most important anchor for both melodies and harmonies in a tonal piece, and as a consequence, it is likely to occur very frequently, even if it is not the most commonly occurring functional element of a piece.		In many Medieval, Neo-Medieval and [[Wikipedia:Common practice period\|Common Practice]] pieces, the Tonic is often the tone used for resolution in musical phrases, and, as a logical extension of this, can be considered the principal goal tone of a piece. This is especially known for being established through an [[Wikipedia:Cadence#Authentic%20cadence\|Authentic cadence]]. In addition, it should be noted that other chords in diatonic harmony, namely the mediant and submediant, often have tonic-like function in the sense of being resolution tones, with the caveat that they are ultimately nontonic functions, and hence, such resolutions are considered to be either interrupted or deceptive cadences. In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a piece— a function which continues to be widespread in Western Classical music. As a consequence of its role as both a common initiating event and the main resolution tone, the tonic often serves as the single most important anchor for both melodies and harmonies in a tonal piece, and as a consequence, it is likely to occur very frequently, even if it is not the most commonly occurring functional element of a piece.

	== Relationship to other functions ==		== Relationship to other functions ==

Aura at 15:06, 30 August 2023

2023-08-30T15:06:37Z

← Older revision		Revision as of 15:06, 30 August 2023
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	In pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.		In pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.

	== As an initiating event ~~and the main~~ resolution tone ~~of a piece~~ ==		== As an initiating event, anchor, or resolution tone ==

	In many Medieval, Neo-Medieval and [[Wikipedia:Common practice period\|Common Practice]] pieces, the Tonic is often the tone used for resolution in musical phrases, and, as a logical extension of this, can be considered the principal goal tone of a piece. This is especially known for being established through an [[Wikipedia:Cadence#Authentic%20cadence\|Authentic cadence]]. In addition, it should be noted that other chords in diatonic harmony, namely the mediant and submediant, often have tonic-like function in the sense of being resolution tones, with the caveat that they are ultimately nontonic functions, and hence, such resolutions are considered to be either interrupted or deceptive cadences. In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a piece— a function which continues to be widespread in Western Classical music.		In many Medieval, Neo-Medieval and [[Wikipedia:Common practice period\|Common Practice]] pieces, the Tonic is often the tone used for resolution in musical phrases, and, as a logical extension of this, can be considered the principal goal tone of a piece. This is especially known for being established through an [[Wikipedia:Cadence#Authentic%20cadence\|Authentic cadence]]. In addition, it should be noted that other chords in diatonic harmony, namely the mediant and submediant, often have tonic-like function in the sense of being resolution tones, with the caveat that they are ultimately nontonic functions, and hence, such resolutions are considered to be either interrupted or deceptive cadences. In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a piece— a function which continues to be widespread in Western Classical music. As a consequence of its role as both a common initiating event and the main resolution tone, the tonic often serves as the single most important anchor for both melodies and harmonies in a tonal piece, and as a consequence, it is likely to occur very frequently, even if it is not the most commonly occurring functional element of a piece.

	~~== As a melodic and or harmonic anchor ==~~

	As a consequence of its role as both a common initiating event and the main resolution tone, the tonic often serves as the single most important anchor for both melodies and harmonies in a tonal piece, and as a consequence, it is likely to occur very frequently, even if it is not the most commonly occurring functional element of a piece.

	== Relationship to other functions ==		== Relationship to other functions ==

Aura at 15:04, 30 August 2023

2023-08-30T15:04:42Z

← Older revision		Revision as of 15:04, 30 August 2023
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	In pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.		In pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.

	== As the main resolution tone ==		== As an initiating event and the main resolution tone of a piece ==

	In many Medieval, Neo-Medieval and [[Wikipedia:Common practice period\|Common Practice]] pieces, the Tonic is often the tone used for resolution in musical phrases, and, as a logical extension of this, can be considered the principal goal tone of a piece. This is especially known for being established through an [[Wikipedia:Cadence#Authentic%20cadence\|Authentic cadence]]. In addition, it should be noted that other chords in diatonic harmony, namely the mediant and submediant, often have tonic-like function in the sense of being resolution tones, with the caveat that they are ultimately nontonic functions, and hence, such resolutions are considered to be either interrupted or deceptive cadences.		In many Medieval, Neo-Medieval and [[Wikipedia:Common practice period\|Common Practice]] pieces, the Tonic is often the tone used for resolution in musical phrases, and, as a logical extension of this, can be considered the principal goal tone of a piece. This is especially known for being established through an [[Wikipedia:Cadence#Authentic%20cadence\|Authentic cadence]]. In addition, it should be noted that other chords in diatonic harmony, namely the mediant and submediant, often have tonic-like function in the sense of being resolution tones, with the caveat that they are ultimately nontonic functions, and hence, such resolutions are considered to be either interrupted or deceptive cadences. In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a piece— a function which continues to be widespread in Western Classical music.

	== As ~~an initiating event in~~ a ~~piece~~ ==		== As a melodic and or harmonic anchor ==

	~~In Common Practice music~~, most ~~pieces began~~ in ~~the tonic key~~, and ~~thus~~, the ~~tonic can be considered~~ a ~~very common initiating event for a piece— a function which continues to be widespread in Western Classical music~~.		As a consequence of its role as both a common initiating event and the main resolution tone, the tonic often serves as the single most important anchor for both melodies and harmonies in a tonal piece, and as a consequence, it is likely to occur very frequently, even if it is not the most commonly occurring functional element of a piece.

	== Relationship to other functions ==		== Relationship to other functions ==

Aura at 14:55, 30 August 2023

2023-08-30T14:55:39Z

← Older revision		Revision as of 14:55, 30 August 2023
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	{{Wikipedia\|Tonic (music)}}		{{Wikipedia\|Tonic (music)}}
	The '''tonic''' is the first note of a [[scale]] or [[mode]], and typically serves as one, or often more, of the following— the primary ''tonal center'', the main resolution tone, one of the most common initiating events of a piece, the generator of other tones either harmonically or subharmonically, and or a discourager against the usage of other microtonally nearby pitches.		The '''tonic''' is the first note of a [[scale]] or [[mode]], and typically serves as one, or often more, of the following— the primary ''tonal center'', the main resolution tone, one of the most common initiating events of a piece, the most important melodic and or harmonic anchor in tonal music, the generator of other tones either harmonically or subharmonically, and or a discourager against the usage of other microtonally nearby pitches.

	Given all this, it is the only function that is known to be universal when it comes to tonal music, with the various other functions being collectively defined as ''nontonic'', thus, it should not come as a great surprise that the tonic exerts a very powerful influence on the context of functional harmony regardless of the nature of the tonal music system in question, even helping to define aspects of the other primary functions on the chord level as opposed to the root level.		Given all this, it is the only function that is known to be universal when it comes to tonal music, with the various other functions being collectively defined as ''nontonic'', thus, it should not come as a great surprise that the tonic exerts a very powerful influence on the context of functional harmony regardless of the nature of the tonal music system in question, even helping to define aspects of the other primary functions on the chord level as opposed to the root level.

Aura at 14:25, 30 August 2023

2023-08-30T14:25:04Z

← Older revision		Revision as of 14:25, 30 August 2023
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	== As an initiating event in a piece ==		== As an initiating event in a piece ==

	In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a ~~piece—a~~ function which continues to be widespread in Western Classical music.		In Common Practice music, most pieces began in the tonic key, and thus, the tonic can be considered a very common initiating event for a piece— a function which continues to be widespread in Western Classical music.

	== Relationship to other functions ==		== Relationship to other functions ==

Aura at 14:24, 30 August 2023

2023-08-30T14:24:19Z

← Older revision		Revision as of 14:24, 30 August 2023
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	{{Wikipedia\|Tonic (music)}}		{{Wikipedia\|Tonic (music)}}
	The '''tonic''' is the first note of a [[scale]] or [[mode]], and typically serves as one, or often more, of the ~~following—the~~ primary ''tonal center'', the main resolution tone, one of the most common initiating events of a piece, the generator of other tones either harmonically or subharmonically, and or a discourager against the usage of other microtonally nearby pitches.		The '''tonic''' is the first note of a [[scale]] or [[mode]], and typically serves as one, or often more, of the following— the primary ''tonal center'', the main resolution tone, one of the most common initiating events of a piece, the generator of other tones either harmonically or subharmonically, and or a discourager against the usage of other microtonally nearby pitches.

	Given all this, it is the only function that is known to be universal when it comes to tonal music, with the various other functions being collectively defined as ''nontonic'', thus, it should not come as a great surprise that the tonic exerts a very powerful influence on the context of functional harmony regardless of the nature of the tonal music system in question, even helping to define aspects of the other primary functions on the chord level as opposed to the root level.		Given all this, it is the only function that is known to be universal when it comes to tonal music, with the various other functions being collectively defined as ''nontonic'', thus, it should not come as a great surprise that the tonic exerts a very powerful influence on the context of functional harmony regardless of the nature of the tonal music system in question, even helping to define aspects of the other primary functions on the chord level as opposed to the root level.
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	== Repelling the competition ==		== Repelling the competition ==

	As first put succinctly [[Flora Canou]]<ref>''[[User:FloraC/Analysis on the 13-limit just intonation space: episode ii #Chapter V. Things Repel the Similar but Not Identical\| Analysis on the 13-limit just intonation space: episode ii]]''. Flora Canou. Xenharmonic Wiki.</ref>, in the realm of microtonality, things repel the similar but not identical, and futhermore, a strong tonic admits no competition. As a consequence, the presence of a strong tonic acts as a ~~very~~ powerful discouragement against the usage of other microtonally nearby pitches outside of modulation or deliberate [[Consonance and dissonance\|dissonance]], as well as shimmer and chorus effects. While this effect is not unique to the tonic, being shared by both the dominant and subdominant (or superdominant), it is most consistently and strongly present around the tonic itself, and, furthermore, is one of the main drivers behind the need to [[temper out]] and or [[fudge]] either [[small comma\|small]] or [[unnoticeable comma\|unnoticeable]] commas.		As first put succinctly [[Flora Canou]]<ref>''[[User:FloraC/Analysis on the 13-limit just intonation space: episode ii #Chapter V. Things Repel the Similar but Not Identical\| Analysis on the 13-limit just intonation space: episode ii]]''. Flora Canou. Xenharmonic Wiki.</ref>, in the realm of microtonality, things repel the similar but not identical, and futhermore, a strong tonic admits no competition. As a consequence, the presence of a strong tonic acts as a powerful discouragement against the usage of other microtonally nearby pitches outside of modulation or deliberate [[Consonance and dissonance\|dissonance]], as well as shimmer and chorus effects. While this effect is not unique to the tonic, being shared by both the dominant and subdominant (or superdominant), it is most consistently and strongly present around the tonic itself, and, furthermore, is one of the main drivers behind the need to [[temper out]] and or [[fudge]] either [[small comma\|small]] or [[unnoticeable comma\|unnoticeable]] commas.

	== See also ==		== See also ==

Aura at 14:15, 30 August 2023

2023-08-30T14:15:35Z

← Older revision		Revision as of 14:15, 30 August 2023
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	== Relationship to other tonal centers ==		== Relationship to other tonal centers ==

	In pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor,~~_BWV~~ 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.		In pieces that have more than one tonal center throughout their length, as with many Western Classical pieces, the tonic is the most important of the various tonal centers that appear in that piece. For that reason, it is considered the home note, and, as a consequence, is often referenced in the name of certain works, for example, Bach's [[Wikipedia: Fugue in G_minor, BWV 578\|Fugue in G Minor, BWV 578]], otherwise known as the "Little Fugue", in which G is the Tonic.

	== As the main resolution tone ==		== As the main resolution tone ==
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	== Relationship to other functions ==		== Relationship to other functions ==

	Since the tonic is the generator of other tones through either the [[harmonic series]] or the [[subharmonic series]], it is thus the origin and the definer of all other functions and can be considered the [[1/1]], and, in [[Octave #Octave equivalence\|octave equivalent]] systems, [[2/1]]. In such systems, the first [[3-limit]] nontonic pitches in both the harmonic series and the subharmonic series give rise to the dominant and subdominant (or, alternatively, superdominant) harmonies, with the exact role of each 3-limit pitch being determined by whether you build your tonality from the low pitches to the high pitches, or from the high pitches to the low pitches—that is, your tonality's chosen direction of construction.		Since the tonic is the generator of other tones through either the [[harmonic series]] or the [[subharmonic series]], it is thus the origin and the definer of all other functions and can be considered the [[1/1]], and, in [[Octave #Octave equivalence\|octave equivalent]] systems, [[2/1]]. In such systems, the first [[3-limit]] nontonic pitches in both the harmonic series and the subharmonic series give rise to the dominant and subdominant (or, alternatively, superdominant) harmonies, with the exact role of each 3-limit pitch being determined by whether you build your tonality from the low pitches to the high pitches, or from the high pitches to the low pitches—that is, your tonality's chosen direction of construction. From there, the next 3-limit pitches in both the harmonic series and the subharmonic series give rise to the [[Wikipedia:Supertonic\|supertonic]] and [[Wikipedia:Subtonic\|subtonic]]—with the exact functions of each of these also being determined by your chosen tonality's direction of construction—and the next three limit pitches after that in both the harmonic series and the subharmonic series give rise to variations of the [[Wikipedia:Mediant\|mediant]] and [[Wikipedia:Submediant\|submediant]] (or, alternatively, the supermediant) depending on your tonality's direction of construction.

	~~From there,~~ the ~~next 3~~-limit pitches in both the harmonic series and the subharmonic series give rise to the ~~[[Wikipedia:Supertonic\|supertonic]]~~ and ~~[[Wikipedia:Subtonic\|subtonic]]—with~~ the exact ~~functions~~ of each ~~of these also being~~ determined by your chosen tonality's direction of ~~construction—and~~ the ~~next three~~ limit ~~pitches after that in both the harmonic series~~ and the ~~subharmonic series give rise to variations of the~~ [[~~Wikipedia:Mediant~~\|~~mediant]] and [[Wikipedia:Submediant\|submediant~~]] ~~(or, alternatively, the supermediant) depending on your tonality's direction of construction~~.		In the [[5-limit]], the first pair of nontonic pitches in both the harmonic series and the subharmonic series give rise to the simplest variations of the mediant and contramediant, while the first combinations of 3-limit and 5-limit give rise to a set of leading tones— the exact role of each individual pitch is again determined by your chosen tonality's direction of construction. Between the 3-limit and the 5-limit, all [[Diatonic functional harmony\|diatonic functions]] are generated.

	In the [[5-limit]], the first pair of nontonic pitches in both the harmonic series and the subharmonic series give rise to the simplest variations of the mediant and contramediant, while the first combinations of 3-limit and 5-limit give rise to a set of leading tones—the exact role of each individual pitch is again determined by your chosen tonality's direction of construction. Of course, this same pattern of generation extends to the [[7-limit]], the [[11-limit]], the [[13-limit]], and so on, resulting in [[Paradiatonic functional harmony\|pardiatonic functions]]. As a result of all this giving rise to other functions, the tonic neutralizes the tension between the dominant and the subdominant (or superdominant) as well as their respective [[Wikipedia:Parallel and counter parallel\|"parallels" and "counter parallels"]].		Of course, this same pattern of generation extends to the [[7-limit]], the [[11-limit]], the [[13-limit]], and so on, resulting in [[Paradiatonic functional harmony\|pardiatonic functions]]. As a result of all this giving rise to other functions, the tonic neutralizes the tension between the dominant and the subdominant (or superdominant) as well as their respective [[Wikipedia:Parallel and counter parallel\|"parallels" and "counter parallels"]].

	== Repelling the competition ==		== Repelling the competition ==

Aura at 14:09, 30 August 2023

2023-08-30T14:09:25Z

← Older revision		Revision as of 14:09, 30 August 2023
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	== Relationship to other functions ==		== Relationship to other functions ==

	Since the tonic is the generator of other tones through either the [[harmonic series]] or the [[subharmonic series]], it is thus the origin and the definer of all other functions~~. For example~~, in [[Octave #Octave equivalence\|octave equivalent]] systems, the first [[3-limit]] nontonic pitches in both the harmonic series and the subharmonic series give rise to the dominant and subdominant (or, alternatively, superdominant) harmonies, with the exact role of each 3-limit pitch being determined by whether you build your tonality from the low pitches to the high pitches, or from the high pitches to the low pitches—that is, your tonality's chosen direction of construction.		Since the tonic is the generator of other tones through either the [[harmonic series]] or the [[subharmonic series]], it is thus the origin and the definer of all other functions and can be considered the [[1/1]], and, in [[Octave #Octave equivalence\|octave equivalent]] systems, [[2/1]]. In such systems, the first [[3-limit]] nontonic pitches in both the harmonic series and the subharmonic series give rise to the dominant and subdominant (or, alternatively, superdominant) harmonies, with the exact role of each 3-limit pitch being determined by whether you build your tonality from the low pitches to the high pitches, or from the high pitches to the low pitches—that is, your tonality's chosen direction of construction.

	From there, the next 3-limit pitches in both the harmonic series and the subharmonic series give rise to the [[Wikipedia:Supertonic\|supertonic]] and [[Wikipedia:Subtonic\|subtonic]]—with the exact functions of each of these also being determined by your chosen tonality's direction of construction—and the next three limit pitches after that in both the harmonic series and the subharmonic series give rise to variations of the [[Wikipedia:Mediant\|mediant]] and [[Wikipedia:Submediant\|submediant]] (or, alternatively, the supermediant) depending on your tonality's direction of construction.		From there, the next 3-limit pitches in both the harmonic series and the subharmonic series give rise to the [[Wikipedia:Supertonic\|supertonic]] and [[Wikipedia:Subtonic\|subtonic]]—with the exact functions of each of these also being determined by your chosen tonality's direction of construction—and the next three limit pitches after that in both the harmonic series and the subharmonic series give rise to variations of the [[Wikipedia:Mediant\|mediant]] and [[Wikipedia:Submediant\|submediant]] (or, alternatively, the supermediant) depending on your tonality's direction of construction.

	In the [[5-limit]], the first pair of nontonic pitches in both the harmonic series and the subharmonic series give rise to the simplest variations of the mediant and contramediant, while the first combinations of 3-limit and 5-limit give rise to a set of leading tones—the exact role of each individual pitch is again determined by your chosen tonality's direction of construction. Of course, this same pattern of generation extends to the [[7-limit]], the [[11-limit]], the [[13-limit]], and so on. As a result of all this giving rise to other functions, the tonic neutralizes the tension between the dominant and the subdominant (or superdominant) as well as their respective [[Wikipedia:Parallel and counter parallel\|"parallels" and "counter parallels"]].		In the [[5-limit]], the first pair of nontonic pitches in both the harmonic series and the subharmonic series give rise to the simplest variations of the mediant and contramediant, while the first combinations of 3-limit and 5-limit give rise to a set of leading tones—the exact role of each individual pitch is again determined by your chosen tonality's direction of construction. Of course, this same pattern of generation extends to the [[7-limit]], the [[11-limit]], the [[13-limit]], and so on, resulting in [[Paradiatonic functional harmony\|pardiatonic functions]]. As a result of all this giving rise to other functions, the tonic neutralizes the tension between the dominant and the subdominant (or superdominant) as well as their respective [[Wikipedia:Parallel and counter parallel\|"parallels" and "counter parallels"]].

	== Repelling the competition ==		== Repelling the competition ==