Hitherto Cage's impact on European music had come in short though perhaps decisive, shocks: in 1949, when he had made his music and his thinking known to Boulez and Messiaen in Paris, and in 1954, when he and Tudor had given performances in several European cities, and when Stockhausen had met them. But by the mid-1950s many of the most prospering musical developments in Europe -- Stockhausen's concern with statistical events, Boulez's pursuit of open form, Kagel's and Berio's extensions of instrumental and vocal technique, almost everyone's effort at electronic music and so at ways of composing untempered sounds-- were making Cage seem far more relevant than could have been the case earlier. In 1957 Maderna discussed Cage's work at Darmstadt, and an issue of Die Reihe included, between Stockhausen's '. . . how time passes . . .' and an elucidation by Pousseur of the current state of his technique, a short piece in which Cage described the compositional process required to create his Music for Piano 21-52 ( 1955) by means of chance operations1 -- this in what had been the journal of total organization. Change was in the air, and the next year Cage and Tudor were themselves at Darmstadt.
By now it was clear that the interests of Stockhausen and Boulez were differently based, even though the Darmstadt comradeship continued until 1965, 2 the last year when Boulez was present. Stockhausen was driven on by what he could learn about the nature of sound, whereas Boulez's essays of the mid-1950s speak of aesthetic issues and models from literature. Both their closenesses and their differences are revealed in the extraordinary conjunction of Stockhausen's Piano Piece XI ( 1956) with Boulez's Third Piano Sonata ( 1955-7), the two first classics of open form in European music.
Stockhausen's piece presents the player with nineteen groups disposed on a single large sheet of paper. According to the instructions, the performer 'begins with whichever group he sees first', 'casts another random glance to find another of the groups', and continues in the same manner until a group has been reached for the third time. There is thus no guarantee that all the groups will be played, and similarly their order is entirely free, though Stockhausen makes some effort at linkage into what he may have seen as a Markov chain, 'a sequence of mutually dependent____________________