Nonlinear Mosaic Form: Kraanerg by Iannis Xenakis

One of the features that distinguishes Iannis Xenakis’s music is its non-teleological form. Even in Metastaseis (1954), an early work, there is very little in the monolithic opening to prepare for the intricate serial counterpoint of the middle section. The music proceeds by juxtaposition of contrasts or by transitions that may be sudden or more gradual. In the mid-1960s, Xenakis developed an approach to form based on the “theory of groups,” by which defined states of musical entities and parameters could be combined and ordered by means of logical, mathematical operations. The result of applying this technique was a kind of “mosaic” form, where a composition’s form would proceed by segments of music each delineated by the combination of parameter and/or entity states, the succession of states being logical (according to the constraints of the combinatorial rules), but nonlinear in terms of listener perception. Xenakis outlined his theory of groups in Formalized Music, and discussed in detail the application of the theory to Nomos alpha for solo cello (1966). Sketches for Kraanerg, a ballet for large ensemble and four-channel electroacoustic sounds (1969), indicate that Xenakis approached it in a similar fashion. Kraanerg is Xenakis’s most ambitious work, proceeding continuously for 75 minutes. The work was commissioned for a new ballet by French choreographer Roland Petit. Sketch materials indicate that Xenakis defined the sonic entities and other musical parameters as a point of departure for the composition. This paper presents an accounting of the form of Kraanerg on the basis of temporal deployment of sonic entities (including silence) and other elements such as register, dynamics, timbre/instrumentation, etc