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harmony, in music, simultaneous sounding of two or more tones and, especially, the study of chords and their relations. Harmony was the last in the development of what may be considered the basic elements of modern music : harmony, melody, rhythm, and tone quality or timbre. The polyphonic superposition (see polyphony; counterpoint) of horizontal melodic lines prevailed until the 16th cent., when the vertical or harmonic construction of chords was established. Rameau, in 1722, presented the idea that different groupings of the same notes were but inversions of the same chord. During the 18th cent. the concept of tonality, with the major and minor modes as its basis and with a certain chord serving as the key center of a composition, became general. The polyphonic music of Bach has a harmonic structure. As the system of triads and their relations was explored, the principle of modulation appeared, and composers developed freer concepts of tonality; Liszt, Wagner, and Richard Strauss greatly expanded the chordal vocabulary of tonal harmony. Finally, in the 20th cent., some have discarded tonality in favor of music that is composed in terms of horizontal contrapuntal lines. See atonality; serial music.
See W. J. Mitchell, Elementary Harmony (3d ed. 1965); A. Schoenberg, Structural Functions of Harmony (rev. ed. 1969); W. Piston, Harmony (5th ed. 1987).
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