Diatonic function

In tonal music theory, a function (often called harmonic function, tonal function or diatonic function, or also chord area) is a term denoting the relationship of a chord to the tonal center. The concept of harmonic function has never been clearly defined, but it appears to say something of the tonal significance of chords (or of their role) in tonal music. It rests on the recognition of essential hierarchies between the degrees of the tonal scale and the harmonies that they support, and of possible equivalences between some of these hierarchic values.

Two main theories of tonal functions exist today, both dealing with the relation of the chords to their tonic:

Both theories find part of their inspiration in the theories of Jean-Philippe Rameau, starting with his Traité d'harmonie of 1722. Even if the concept of harmonic function was not so named before 1893, it could 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), Loquin (Notions élémentaires d'harmonie moderne, 1862), etc.

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 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 under.

This symmetric construction may have been one of the reasons why 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 which described 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 onwards.

The term functional harmony derives from Hugo Riemann and, more particularly, from his Harmony Simplified. Riemann's direct inspiration was Moriz Hauptmann dialectic description of tonality. Riemann described three abstract functions, the tonic, the dominant (its fifth) and the subdominant (its fourth). He considered in addition that the minor scale was the inversion of the major one, 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.

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