Mathematics of music

Serialism

In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were also working to establish serialism as a form of post-tonal thinking. Twelve-tone technique orders the twelve notes of the chromatic scale, forming a row or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and variations. Other types of serialism also work with sets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "parameters"), such as duration, dynamics, and timbre. The idea of serialism is also applied in various ways in the visual arts, design, and architecture, and the musical concept has also been adapted in literature. Integral serialism or total serialism is the use of series for aspects such as duration, dynamics, and register as well as pitch. Other terms, used especially in Europe to distinguish post-World War II serial music from twelve-tone music and its American extensions, are general serialism and multiple serialism. Composers such as Arnold Schoenberg, Anton Webern, Alban Berg, Karlheinz Stockhausen, Pierre Boulez, Luigi Nono, Milton Babbitt, Elisabeth Lutyens, Henri Pousseur, Charles Wuorinen and Jean Barraqué used serial techniques of one sort or another in most of their music. Other composers such as Tadeusz Baird, Béla Bartók, Luciano Berio, Benjamin Britten, John Cage, Aaron Copland, Ernst Krenek, György Ligeti, Olivier Messiaen, Arvo Pärt, Walter Piston, Ned Rorem, Alfred Schnittke, Ruth Crawford Seeger, Dmitri Shostakovich, and Igor Stravinsky used serialism only in some of their compositions or only in some sections of pieces, as did some jazz composers, such as Bill Evans, Yusef Lateef, and Bill Smith. (Wikipedia).

Serialism
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