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Studie II (Stockhausen, Karlheinz), 1954Zyklus für einen Schlagzeuger (Stockhausen, Karlheinz), 1959

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can therefore be seen in a larger context. It therefore appears logical that for work on serial compositions, electronic instruments were used. "In principal, it is not at all a matter of the use of unusual sounds, but rather that the musical order in the vibrational structure of the sound processes is driven out, so that sounds that occur in a composition are integral components of this and only this piece, and come about from the rules used to construct it " [5]. With the help of the instruments, sound could be constructed from the individual parameters. The introduction of electronic devices made the translation of the composer's directions into machine-readable instructions necessary, so that mathematical operations came in during the process of composing. With "Studie II" (1954), Karlheinz Stockhausen was the first to publish a score for electronic music, indicating the exact placement of instruments and describing how the piece would unfold. In 1959, however, Stockhausen opened up his compositional work to subjective interpretation. In "Zyklus für einen Schlagzeuger" (cycle for a percussionist) , individual decision possibilities were again allowed, determined


by the presence of a musician. Yannis (Iannis) Xenakis rejected the introduction of series and constructed his serial music (like virtually no other composer) from mathematical, architectonic, and even geological calculations. In establishing his principles of order, he was striving for a working connection between the different spheres of art. He was seeking the threedimensional sound that unites music and architecture. His active collaboration in the studio of Le Corbusier during the 1950s, enabled Xenakis, who had studied architecture in Athens, to introduce his musical skills into architecture. He designed "Pans de Verre Ondulatoires" [6], the window arrangement of the cloister, and the principal façade of "La Tourette" [7] (1955-1959) according to criteria of musical rhythm (see also the "Philips Pavillion" from the 1958 World's Fair in Brussels). Above and beyond this, Xenakis made crucial contributions to the development of the computer programme called UPIC (Unité Polyagogique Informatique du CEMAMu), [8] which translated graphics into music. Complex, computer-controlled universal music was supposed to serve in simplifying the composing and democratising of music. The goal was to

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