aleatory
Music in which some element of the composition is left to chance or to the performer's discretion.
In Depth
Aleatory music, from the Latin alea meaning "dice," encompasses a wide spectrum of approaches to indeterminacy in composition. At one extreme, a composer might use chance operations (such as coin tosses or the I Ching) to make compositional decisions; at the other, performers might be given graphic scores or text instructions that allow considerable freedom in interpretation.
John Cage was the most prominent advocate of chance music, using methods like the I Ching to determine pitch, duration, and dynamics in works such as Music of Changes (1951). European composers like Witold Lutosławski developed "controlled aleatorism," where passages of free counterpoint alternate with precisely notated sections, giving performers limited freedom within a carefully designed framework.
John Cage's 4'33" (1952), where performers play nothing for four minutes and thirty-three seconds, is the most famous aleatory work — the "music" is whatever ambient sounds occur.