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Serialism is a rigorous system of writing music in which various elements of the piece are ordered according to a pre-determined sequence, and variations on it. The elements thus controlled may be the pitch of the notes, their length, their dynamics, their accents, or virtually any other musical parameter.

Serialism is an extension of Arnold Schoenberg's twelve-tone technique (sometimes called dodecaphony), which involves the use of tone rows: the basis of the system is that all the pitches of a composition are drawn from ordering of one (and only one) instance of each of the twelve notes in the chromatic scale and permutations of that row. The terms serial and twelve tone are often used as synonyms. To clarify the terms total serialism or integral serialism are often used to distinguish twelve tone composition from the more expansive kind.

The development of serial composition began by the desire of a group of young composers to pave a wave forward in composition, combining the rhythmic innovations of Igor Stravinsky with twelve-tone technique. The two developers of the idea were Pierre Boulez and Karlheinz Stockhausen, both drawing inspiration from the "parameterization" of influential French composer and teacher Olivier Messiaen. They conceived of taking the structure of 12 tone technique, and expanding on Webern's compositional style, place all elements of music under the control of a unique "series". So instead of merely having "rows" of tones, which Webern would also associate with dynamics and attack, they proposed that each feature would serialized. While the Second Vienna School did not use the term "serial" to describe their music, it was applied to their work by later theorists and composers.

Musical set theory is often used to analyze and compose serial music, but may also be used to study tonal music.

Serialism was enormously influential in post-War music, and established itself as the standard against which other music was to be measured. Theorists such as George Perle codified the system and his 1962 text Serial Composition and Atonality became the standard work on the origins of serial composition in the work of Schoenberg, Berg and Webern. Declaring itself "revolutionary" and "a new tonality", serialism created an environment where experimentation with sound, in a manner similar to the exploration of pure painting in Abstract Expressionism was at the forefront of composition, which lead to increased use of electronics and other applications of mathematical notation to composition.

Other composers to use serialism include Luigi Nono, Milton Babbitt, who developed similar ideas separately, Roger Reynolds, and Charles Wuorinen, the later works of Igor Stravinsky and the early works of George Rochberg. Major centers for serialism were the Darmstadt School and the "School of Paris" centered around Pierre Boulez.

Serial music remains, 50 years after its founding, enormously controversial, attracting both ardent defenders and vehement attacks. Phillip Glass described the School of Paris as "crazy creepy people writing crazy creepy music", while on the other hand one critic described Boulez' Sonatas as "reveal[ing] a sparkling world of turbulent passion and abstract beauty. "