in defined dependencies". With examples of three artistic viewpoints from music history of the nineteen fifties, it will be first pointed out how different the paths to achieving a goal can be, even though all three artists used aleatoric or serial methods. Beside any considerations of musical theory, the question that needs to be discussed is what contextual and formal possibilities the application of such methods offer. John Cage used chance as a defined rule in a rigorous fashion to exclude predetermined connections. He was concerned with making sounds possible in a way completely independent of the composer. To do this, Cage for example used sound carriers (instruments) which were completely independent of his composition. In "Imaginary Landscape No. 4" (1951), he wrote a piece for 24 radios. He laid out rhythms and sequences Using traditional notation. The result, however, remained unplanned, dependent upon the place and time of the performance, broadcast frequencies and radio programme structures. Cage's efforts culminated in the piece entitle "4'33" (1952). There is only one hard and fast parameter: the length of the piece. Without any help from musicians, the

resulting sound is produced from the moment the piece starts from different accompanying noises; for example, the rustling and the clearing of throats by the public, or the rush of traffic. His artistic goal was to have the sounds sort themselves out. Serial music, which developed out of the tradition of aleatoric works[4], mainly represented by Karlheinz Stockhausen, Pierre Boulez, Henri Pousseur or Gottfried Michael Koenig, took the exact opposite approach in the nineteen fifties. Serial compositions subordinate all acoustic characteristics, such as pitch, duration, touch, tone colouring, and loudness independently of each other to the same principles of order; for example, number ratios. In this way, it is possible to force separate musical aspects into a complete relationship on a higher order. As a system of order, mostly series (dependent upon the twelve-tone system) or continuous tones are used, which, in order to avoid repetition, vary constantly. Aesthetic criteria of music are subordinated to the principles of order. This method gives the composer total control over every imaginable detail of composition. The work is independent from the nuances of interpretation and