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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 ordered set or sets, and variations on them. The elements thus controlled may be the pitch of the notes, their length, their dynamics, their accents, or virtually any other musical quantity, which, in serial terms is called a parameter. More generally, serialism is any music which uses any ordered sets applied to any musical element. However, this article discusses the more specific serialism.

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 find a new way 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 be 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.

The vocabulary of serialism is rooted in set theory, and uses a quasi mathematical language to describe how the basic sets are manipulated to produce the final result. 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. 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 led to increased use of electronics and other applications of mathematical notation to composition, developed by theorists such as the composer and mathematician Milton Babbitt.

Other composers to use serialism include Luigi Nono, 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. Philip Glass described the School of Paris as "crazy creepy people writing crazy creepy music", while on the other hand one critic said that Boulez' Sonatas "reveal a sparkling world of turbulent passion and abstract beauty. " Many composers, such as Rochberg, who had been ardent serialists have largely abandoned the style, while many younger composers, such as Glass, never used it. Various terms have been introduced to describe this trend, such as the New Romanticism, etc. See: minimalism