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Function (music)
In music, function (or harmonic function) is a term used to denote the relationship of a chord or a scale degree to a tonal centre. Two main theories of tonal functions exist today:
Both theories find part of their inspiration in the theories of Jean-Philippe Rameau, starting with his Traité d'harmonie (1722). Even if the concept of harmonic function was not so named before 1893, it can be shown to exist, explicitly or implicitly, in many theories of harmony before that date. Early usages of the term in music (not necessarily in the sense implied here, or only vaguely so) include those by Fétis (Traité complet de la théorie et de la pratique de l'harmonie, 1844), Durutte (Esthétique musicale, 1855), and Loquin (Notions élémentaires d'harmonie moderne, 1862).
The idea of function has been extended further and is sometimes used to translate Antique concepts, such as dynamis in Ancient Greece or qualitas in medieval Latin.
The concept of harmonic function originates in theories about just intonation. It was realized that three perfect major triads, distant from each other by a perfect fifth, produced the seven degrees of the major scale in one of the possible forms of just intonation: for instance, the triads F–A–C, C–E–G, and G–B–D (subdominant, tonic, and dominant respectively) produce the seven notes of the major scale. These three triads were soon considered the most important chords of the major tonality, with the tonic in the center, the dominant above, and the subdominant below.
This symmetric construction may have been one of the reasons the fourth degree of the scale, and the chord built on it, were named "subdominant", i.e. the "dominant under [the tonic]". It also is one of the origins of the dualist theories that describe not only the scale in just intonation as a symmetric construction, but also the minor tonality as an inversion of the major one. Dualist theories are documented from the 16th century onward.
The term "functional harmony" derives from Riemann and particularly from his Harmony Simplified. Riemann's direct inspiration was Moritz Hauptmann's dialectic description of tonality. Riemann identified three abstract functions: the tonic, the dominant (its upper fifth), and the subdominant (its lower fifth). He also considered the minor scale the inversion of the major scale, so that the dominant was the fifth above the tonic in major, but below the tonic in minor; the subdominant, similarly, was the fifth below the tonic (or the fourth above) in major, and the reverse in minor.
Despite their complexity, Riemann's ideas had huge impact, especially where German influence was strong. A good example are Hermann Grabner's textbooks. More recent German theorists have abandoned the most complex aspect of Riemann's theory, the dualist conception of major and minor, and consider the dominant the fifth degree above the tonic and the subdominant the fourth degree in both minor and major.
In Diether de la Motte's version of the theory, the three tonal functions are denoted by the letters T, D and S, for Tonic, Dominant and Subdominant respectively; the letters are uppercase for functions in major (T, D, S) and lowercase for functions in minor (t, d, s). Each function can in principle be fulfilled by three chords: the main chord corresponding to the function and the chords a third lower and a third higher, as indicated by additional letters. An additional letter P or p indicates that the function is fulfilled by the relative (German Parallel) of its main triad: for instance Tp for the minor relative of the major tonic (e.g., A minor for C major), tP for the major relative of the minor tonic (e.g. E♭ major for c minor), etc. The other triad a third apart from the main one may be denoted by an additional G or g for Gegenparallelklang or Gegenklang ("counterrelative"), for instance tG for the major counterrelative of the minor tonic (e.g. A♭ major for C minor).
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Function (music)
In music, function (or harmonic function) is a term used to denote the relationship of a chord or a scale degree to a tonal centre. Two main theories of tonal functions exist today:
Both theories find part of their inspiration in the theories of Jean-Philippe Rameau, starting with his Traité d'harmonie (1722). Even if the concept of harmonic function was not so named before 1893, it can be shown to exist, explicitly or implicitly, in many theories of harmony before that date. Early usages of the term in music (not necessarily in the sense implied here, or only vaguely so) include those by Fétis (Traité complet de la théorie et de la pratique de l'harmonie, 1844), Durutte (Esthétique musicale, 1855), and Loquin (Notions élémentaires d'harmonie moderne, 1862).
The idea of function has been extended further and is sometimes used to translate Antique concepts, such as dynamis in Ancient Greece or qualitas in medieval Latin.
The concept of harmonic function originates in theories about just intonation. It was realized that three perfect major triads, distant from each other by a perfect fifth, produced the seven degrees of the major scale in one of the possible forms of just intonation: for instance, the triads F–A–C, C–E–G, and G–B–D (subdominant, tonic, and dominant respectively) produce the seven notes of the major scale. These three triads were soon considered the most important chords of the major tonality, with the tonic in the center, the dominant above, and the subdominant below.
This symmetric construction may have been one of the reasons the fourth degree of the scale, and the chord built on it, were named "subdominant", i.e. the "dominant under [the tonic]". It also is one of the origins of the dualist theories that describe not only the scale in just intonation as a symmetric construction, but also the minor tonality as an inversion of the major one. Dualist theories are documented from the 16th century onward.
The term "functional harmony" derives from Riemann and particularly from his Harmony Simplified. Riemann's direct inspiration was Moritz Hauptmann's dialectic description of tonality. Riemann identified three abstract functions: the tonic, the dominant (its upper fifth), and the subdominant (its lower fifth). He also considered the minor scale the inversion of the major scale, so that the dominant was the fifth above the tonic in major, but below the tonic in minor; the subdominant, similarly, was the fifth below the tonic (or the fourth above) in major, and the reverse in minor.
Despite their complexity, Riemann's ideas had huge impact, especially where German influence was strong. A good example are Hermann Grabner's textbooks. More recent German theorists have abandoned the most complex aspect of Riemann's theory, the dualist conception of major and minor, and consider the dominant the fifth degree above the tonic and the subdominant the fourth degree in both minor and major.
In Diether de la Motte's version of the theory, the three tonal functions are denoted by the letters T, D and S, for Tonic, Dominant and Subdominant respectively; the letters are uppercase for functions in major (T, D, S) and lowercase for functions in minor (t, d, s). Each function can in principle be fulfilled by three chords: the main chord corresponding to the function and the chords a third lower and a third higher, as indicated by additional letters. An additional letter P or p indicates that the function is fulfilled by the relative (German Parallel) of its main triad: for instance Tp for the minor relative of the major tonic (e.g., A minor for C major), tP for the major relative of the minor tonic (e.g. E♭ major for c minor), etc. The other triad a third apart from the main one may be denoted by an additional G or g for Gegenparallelklang or Gegenklang ("counterrelative"), for instance tG for the major counterrelative of the minor tonic (e.g. A♭ major for C minor).