The development of structure has been a huge influence on contemporary music: primarily, the use of stochastisc, aloeatric and indeterminate processes in composition. The development of stochastic processes in the treatment of form by composers such as Pierre Boulez, John Cage, Karl Stockhausen signify a move away from the ‘classical’ structures that have dominated Western composition since the Baroque era (such as sonata, tertiary form, opera, etc). While structures such as the sonata, the suite, the canon and the opera are incredibly specific and give performers very little room to improvise or include creative succession, the stochastic process involves non-deterministic behaviours, and the way the process works musically is determined by predictable actions (such as notation and performance directions) and random elements (such as fragmented phrasing, free-form melodies and rhythms and allowing several possibilities for performance).
Stochastism involves leaving elements of the composition being left to chance – these elements may be pitch, rhythm and its overall structure. Stockhausen’s “Klavierstuck XI” (1936) has 19 fragments of music, which are to be played in any order the performer desires. Henry Cowell’s “Mosaic Quartet”(1934) similarily allows the performers to re-arrange the five patterns of music into a number of different sequences so that the structure of the piece is different in each performance. This aspect of ‘chance’ – where the performers can choose between the several possibilities the composer has set out for them – means that the realization of the composition is determined by the decisions the performer makes. For example, if a composer instructs a group of performers to play a succession of notes in a random succession, and at whatever pitch, then the realization of the work as a piece of music is dependent on the performer’s choice of what pitch to play and what rhythm to play the notes.
Cowell’s “Mosaic Quartet”, self-described as a “crazy quilt of 5 patterns”, is an example of chance music. The mosaics, all of which are self-contained, are played in any order the performer desires: "all players start and stop as they please, and choose the order of the movements as they please--there is no score." (Instructions by Cowell, quoted by Goldstein). Goldstein argues that this piece was an example of Cowell’s “most significant contribution to the music of chance…” as a development of “Elastic Form.” The piece was written for clarinet, violin, violoncello, piano and percussion, and its structure consists of a set of brief fragments written for each individual instrument. The individual pieces are to be played at will by each performer, allowing them to choose the rhythm, tempo and starting point of each fragment without regard to what the other performers are playing. Here, the structure, tempo, and overall form of the piece is placed entirely in each performers hand, so no two performances are alike. By contrast, Stockhausen’s “Klavierstuck XI” consists of 19 separate fragments for piano. While the structure of the work is decided by the performer, Stockhausen has written instructions concerning tempo (Stockhausen instructs that the performer chooses between 6 various speeds for each fragment), dynamic and expressive techniques. Concert pianist James Wiman argues that this piece is in fact an exploration of intedeterminancy, where an element of the piece (ie. the structure) is left solely up to the performer, with instructions on how to perform the music or sounds in terms of dynamics, tempo, and rhythm.
Goldstein, Louis. Sonneck Society for American Muisc Bulletin, Volume XXIII, no. 2 (Summer 1997), 1997
Wiman, James, Stockhausen- Klavierstuck XI, Pianist and the Advocate for the Avante Garde (Blog). 2011.