Aleatoric Music - Types of Indeterminate Music

Types of Indeterminate Music

Some writers do not make a distinction between aleatory, chance, and indeterminancy in music, and use the terms interchangeably (Griffiths 2001; Joe and Song 2002, 264; Roig-Franconí 2008, 280). From this point of view, indeterminate or chance music can be divided into three groups: (1) the use of random procedures to produce a determinate, fixed score, (2) mobile form, and (3) indeterminate notation, including graphic notation and texts (Griffiths 2001).

The first group includes scores in which the chance element is involved only in the process of composition, so that every parameter is fixed before their performance. In John Cage’s Music of Changes (1951), for example, the composer selected duration, tempo, and dynamics by using the I-Ching, an ancient Chinese book which prescribes methods for arriving at random numbers (Joe and Song 2002, 268). Because this work is absolutely fixed from performance to performance, Cage regarded it as an entirely determinate work made using chance procedures (Pritchett 1993, 108). On the level of detail, Iannis Xenakis used probability theories to define some microscopic aspects of Pithoprakta (1955-56), which is Greek for “actions by means of probability.” This work contains four sections, characterized by textural and timbral attributes, such as glissandi and pizzicati. At the macroscopic level, the sections are designed and controlled by the composer while the single components of sound are controlled by mathematical theories (Joe and Song 2002, 268).

In the second type of indeterminate music, chance elements involve the performance. Notated events are provided by the composer, but their arrangement is left to the determination of the performer. Karlheinz Stockhausen’s Klavierstück XI (1956) presents nineteen events which are composed and notated in a traditional way, but the arrangement of these events is determined by the performer spontaneously during the performance. In Earle Brown’s Available forms II (1962), the conductor is asked to decide the order of the events at the very moment of the performance (Joe and Song 2002, 269).

In this second type of music, control and chance merged in some composers' works in the late 1950s. One type of music in which this might occur is called in sound-mass composition or textural composition, where individual pitches and lines are integrated into complexes of sound ("sound masses").

In sound masses we do not perceive individual pitches, but rather chromatically filled complexes of sound. These sound blocks may result from multiple, minutely notated chromatic lines that fuse into each other (and then the sound masses are dynamic, in constant motion and transformation), as in Gyorgy Ligeti's Atmosphères (1961), or they may result from more static clusters (blocks of sound made up of adjacent chromatic or microtonal steps), as in Krzysztof Penderecki's Threnody for the Victims of Hiroshima of 1960. … At times, clusters are notated pitch by pitch in conventional notation, whereas at other times they are indicated graphically, usually by means of solid black bands on the score. In sound-mass compositions, musical elements such as texture, density, register, dynamics, and instrumental color replace such musical parameters as rhythm, meter, lines, chords, and harmony, usually considered as "primary" in a more traditional compositional context (Roig-Francolí 2008, 280–81).

The greatest degree of indeterminacy is reached by the third type of indeterminate music, where traditional musical notation is replaced by visual or verbal signs suggesting how a work can be performed, for example in Graphic score pieces. Earle Brown’s December 1952 (1952) shows lines and rectangles of various lengths and thicknesses that can read as loudness, duration, or pitch. The performer chooses how to read them. Another example is Morton Feldman’s Intersection No. 2 (1951) for piano solo, written on coordinate paper. Time unit are represented by the squares viewed horizontally, while relative pitch levels high, middle and low are indicated by three vertical squares in each row. The performer determines what particular pitches and rhythms to play (Joe and Song 2002, 269).