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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 term was proposed mainly by Hugo Riemann in 1893, but the concept had been used before under different names. While Riemann described three harmonic functions, tonic, dominant and subdominant, to which all chords of the tonal scale could be related in varying guises, later theorists considered that the names of the scale degrees (and their representations by Roman numerals) denoted as many different functions, seven in the case of a seven-note scale.
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Each degree of the seven-tone diatonic scale has a name that relates to its function. The major scale and all three forms of the minor scale share these terms.
The concept of harmonic function rests on the recognition of essential hierarchies between the degrees of the tonal scale, (i.e. in the context of a given tonality) and of possible equivalencies between some of these hierarchic values.
Harmonic function essentially results from the judgment that certain chords and tonal combinations sound and behave alike, even though these individuals might not be analyzed into equivalent harmonic classes," "Harmonic function is more about...similarity than equivalence".
for instance V and VII recognized as sharing a dominant function, or IV and II sharing a subdominant one.
Functional harmony
The term functional harmony derives from Hugo Riemann and his textbooks on harmony in the late 19th century, with roots back to Jean-Philippe Rameau's theoretical works amongst others. His main idea was to create a comprehensive theoretical basis for understanding the principles of harmonic relationships typical for the Baroque, Classical and Romantic periods for the first time integrated in the concept of the equal temperament and the two parallel cycles of fifths. His work had huge impact, especially where German influence was strong. A good example in this regard are the textbooks by Hermann Grabner.
Riemann's basic theories have since been adopted, refined and elaborated upon by many authors of textbooks in harmony, arranging and composition. Functional harmony is being taught as a basic discipline in music theory all over the western world, though different labels are used. Other terms used in the English and American tradition include Common Practice Harmony (stemming from Walter Piston), Tonal harmony (as used by Allen Forte), and Traditional harmony (as used by Gordon Delamont. Vincent Persichetti describes the 19th-century harmonic repertoire as "chords evolving around the tonic pillars" (tonic, subdominant, dominant).
Functional theory in the 19th century developed in two competing directions. Functional theory properly speaking, in the German tradition represented mainly by Gottfried Weber, Arthur von Oettingen and Hugo Riemann, is characterized by a preoccupation with chord quality; it distinguishes three main abstract harmonic functions, tonic, subdominant and dominant, each of which can be represented by several chords in the diatonic scale, and always explained by direct reference to the tonal center. The Viennese theory on the other hand, the "Theory of the degrees" (Stufentheorie), represented by Simon Sechter, Heinrich Schenker and Arnold Schoenberg among others, considers that each degree has its own function and refers to the tonal center through the cycle of fifths; its stresses harmonic progressions above chord quality.
In the German tradition, the harmonic functions are denoted by letters, T, S and D, while in the Viennese tradition the degrees are notated with Roman numerals. The description of diatonic functions in the United States and in Western Europe is largely based on the Viennese tradition, while the German tradition remains in usage in Germany and in Scandinavian and Eastern European countries.
Nonfunctional harmony, the opposite of functional harmony, is harmony whose progression is not guided by function.
Functional behaviours
From the viewpoint of musical behaviour or structure there are three essential functions:
Other functions serve to support the Tonic and Dominant functions listed above:
The dominant, dominant preparation and the tonic substitution all involve more than one scale degree with only the tonic and subdominant containing only one scale degree. Several scale degrees exercise more than one function.
The tonic includes four separate activities or roles as the: