Tonic: Difference between revisions

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== 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.

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 ==

@@ Line 18: / Line 18: @@
 == 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.
-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 ==