HARMONY

in music, the sound of two or more notes heard simultaneously. In practice, this broad definition can also include some instances of notes sounded one after the other. If the consecutively sounded notes call to mind the notes of a familiar chord (a group of notes sounded together), the ear creates its own simultaneity in the same way that the eye perceives movement in a motion picture. In such cases the ear perceives the harmony that would result if the notes had sounded together. In a narrower sense, harmony refers to the extensively developed system of chords and the rules that allow or forbid relations between chords that characterizes Western music. Musical sound may be regarded as having both horizontal and vertical components. The horizontal aspects are those that proceed during time such as melody, counterpoint (or the interweaving of simultaneous melodies), and rhythm. The vertical aspect comprises the sum total of what is happening at any given moment: the result either of notes that sound against each other in counterpoint, or, as in the case of a melody and accompaniment, of the underpinning of chords that the composer gives the principal notes of the melody. In this analogy, harmony is primarily a vertical phenomenon. It also has a horizontal aspect, however, since the composer not only creates a harmonic sound at any given moment but also joins these sounds in a succession of harmonies that gives the music its distinctive personality. Melody and rhythm can exist without harmony. By far the greatest part of the world's music is nonharmonic. Many highly sophisticated musical styles, such as those of India and China, consist basically of unharmonized melodic lines and their rhythmic organization. In only a few instances of folk and primitive music are simple chords specifically cultivated. Harmony in the Western sense is a comparatively recent invention having a rather limited geographic spread. It arose less than a millennium ago in the music of western Europe and is embraced today only in those musical cultures that trace their origins to that area. The concept of harmony and harmonic relationships is not an arbitrary creation. It is based on certain relationships among musical tones that the human ear accepts almost reflexively and that are also expressible through elementary scientific investigation. These relationships were first demonstrated by the Greek philosopher Pythagoras in the 6th century BC. In one of his most famous experiments, a stretched string was divided by simple arithmetical ratios (1:2, 2:3, 3:4, . . . ) and plucked. By this means he demonstrated that the intervals, or distances between tones, that the string sounded before and after it was divided are the most fundamental intervals the ear perceives. These intervals, which occur in the music of nearly all cultures, either in melody or in harmony, are the octave, the fifth, and the fourth. (An octave, as from C to the C above it, encompasses eight white notes on a piano keyboard, or a comparable mixture of white and black notes. A fifth, as from C to G, encompasses five white notes; a fourth, as from C to F, four white notes.) In Pythagoras' experiment, for example, a string sounding C when cut in half sounds C, or the note an octave above it. In other words, a string divided in the ratio 1:2 yields the octave (c) of its fundamental note (C). Likewise the ratio 2:3 (or two-thirds of its length) yields the fifth, and the ratio 3:4, the fourth. These notesthe fundamental and the notes a fourth, fifth, and octave above itform the primary musical intervals, the cornerstones on which Western harmony is built. two or more musical notes heard simultaneously or, more narrowly, in Western music, the sounding of two or more sonorities (chords) and their movement to other chords. Harmony is both a vertical dimension of music, in that the notation of chords requires the placing of noteheads on the same vertical axis, and a horizontal one, the process of movement from one chord to the next, or harmonic progression. As such, harmony is inextricably linked to counterpoint (q.v.), the interaction of simultaneously sounding melodic lines. Harmony and counterpoint are two constantly interacting dimensions of music; the melodic lines can be thought of as giving rise to the harmony, and the harmonic progressions influence linear movement. Central to harmony throughout the history of Western music are the concepts of consonance and dissonance. A consonant chord is perceived as being at rest, whereas a dissonant one is in a state of tension that requires a resolution. This tensionresolution relationship has been a key aspect of music composition from its beginnings. The perception of which intervals constitute a consonant or dissonant chord, however, has been in a constant state of flux. The relative degree of tension in a chord is, therefore, not an intrinsic quality but an associative one, as the presence of consonance and dissonance are associated with particular chords and intervals according to their place in the context of the prevailing style. The same chord found in compositions from different musical eras will often have different significance and meaning and, therefore, use. Broadly speaking, the pattern of historical development has been a constantly expanding group of chords considered consonant, as chords of greater complexity enter the musical vocabulary and chords formerly of relative intensity become less intense in the new context. In the prevailing harmonic practice from the 9th century, organum, octaves, fifths, and fourths were the only consonant intervals. These intervals are simplest in their intervallic proportions, that is, the numerical proportion of the frequencies (cycles per second) of the constituent members of the chord. More complex proportions, such as those at thirds and sixths were considered dissonant at the time, though by the early 15th century these intervals were heard as consonant. The seconds and sevenths, however, retained their dissonant associations until the late-19th and early-20th centuries, when Claude Debussy and Arnold Schoenberg, among others, used these intervals in ways that were not part of the immediately preceding harmonic system. Harmony, then, is a system of classification of chords that is relevant to a particular and limited body of musical worksproviding order and facilitating structural meaning. Additional reading Two works by 20th-century composers that give considerable insight into the role of all musical elements in composition are Paul Hindemith, Unterweisung im Tonsatz (193739; Eng. trans., The Craft of Musical Composition, 2 bks., 194142); and Arnold Schoenberg, Harmonielehre, 3rd ed. (1922; abridged Eng. translation, Theory of Harmony, 1948). Schoenberg's formulation of his 12-tone theories may be found in his Style and Idea (1950). Other theoretical works that trace the fluid state of harmony since the later 19th century include Elliott Zuckerman, The First Hundred Years of Wagner's Tristan (1964); Henry Cowell, New Musical Resources (1930, reprinted 1968); and George Perle, Serial Composition and Atonality, 2nd. ed. (1968). Standard textbooks based on the theories of Rameau include Walter Piston, Harmony, 3rd ed. (1962); and Roger Sessions, Harmonic Practice (1951).