The Oxford English Dictionary defines ‘aleatory’ as ‘dependent on the throw of a dice, dependent on uncertain contingencies’. John Cage explains the concept of ‘chance’ in his Music for Piano as ‘operations channelled within certain limits (which are established in relation to relative difficulty of performance) – derived from the I-Ching are employed to determine the number of sounds per page’. The process is to use a pencil on transparent pieces of paper, applying the result to a master – page, tossing a coin to determine clefs, using I-Ching possibilities to determine categories of notes and keys, then applying all of this to freedom in performance of time length, silences, duration of notes and their dynamics. While avoiding any mention of Cage, Boulez describes this kind of process as ‘puerile magic’. His own application has been discussed in relation to a concept of improvisation and mobile elements in Pli selon pli. A conductor is entitled to an opinion on either composer, but might find him/herself having to conduct works by both of them. In such circumstances judgement must remain private.

The period 1955–65 shows many composers experimenting with serendipity in various ways, some taking Cage’s direction, others that of Boulez. But one in particular took a highly distinctive approach. In the programme note to his Jeux vénitiens (1961) Lutosławski discusses his own version as ‘the loosening of time connections between sounds’. He sees this as an ‘enrichment of the rhythmical side of the work’, giving performers the scope for ‘free and individual playing’ in an ensemble. He is careful to underline that the ‘chance factor’ is not the leading one to influence the way a composition is constructed, no matter how this will make each performance slightly different. Like Boulez, he puts the composer in control of events, not the performers, as in Cage. The distinctiveness of his technique is the comparatively simple form of notation which avoids virtuosic demands from the performers. Lutosławski rightly observes that many of his contemporaries who used his solutions to aleatoric techniques tended to be concerned only with rhythm,9 the organisation of time and timbres and never, or very rarely, the organisation of pitch.