Gruppen ("Groups") for three orchestras (1955-57) is amongst the best-known works of German composer Karlheinz Stockhausen. In it, a large group of 107 players is divided into three orchestral units, each with its own conductor, which are deployed in a horseshoe shape to the left, front, and right of the audience. The spatial separation was principally motivated by the compositional requirement of keeping simultaneously played but musically separate passages distinct from one another, but led to some orgiastic passages in which a single musical process is passed from one orchestra to another. The title refers to the work's construction in 174 units, mainly composed in what Stockhausen terms "groups"--cohesive groupings of notes unified through one or more common characteristics (dynamics, instrumental color, register, etc.). This category is contrasted with the "punctual" style of early Darmstadt serialism, which nevertheless also occurs in Gruppen, along with a third category of "statistical" swarms or crowds, too dense for the listener to be able to accurately distinguish individual notes or their order of succession. Karlheinz Stockhausen (born August 22, 1928) is a German composer, one of the most important and controversial composers of the 20th century. ... Darmstadt is a city in the Bundesland (federal state) of Hessen in Germany. ... Serialism is a technique for composing music that uses sets to describe musical elements, and allows the composer manipulations of those sets to create music. ...

References

• Harvey, Jonathan. 1975. The Music of Stockhausen: An Introduction. Berkeley and Los Angeles: University of California Press.
• Koenig, Gottfried Michael. 1962. “Commentary”. Die Reihe 8 ("Retrospective") [English edition, 1968], 80–98.
• Misch, Imke. 1998. “On the Serial Shaping of Stockhausen’s Gruppen für drei Orchester”. Perspectives of New Music 36, no. 1 (Winter): 143–87.
• Misch, Imke. 1999. Zur Kompositionstechnik Karlheinz Stockhausens Gruppen für 3 Orchester (1955–57). Signale aus Köln: Beiträge zur Musik der Zeit 2, edited by Christoph von Blumröder. Saarbrücken: Pfau-Verlag.
• Smalley, Roger. 1967. “Stockhausen’s Gruppen.” Musical Times no. 1495 (September): 794–97.