(aleatory from Latin alea, “dice”), 20th-century music in which chance or indeterminate elements are left for the performer to realize. The term is a loose one, describing compositions with strictly demarcated areas for improvisation according to specific directions and also unstructured pieces consisting of vague directives, such as “Play for five minutes.”

The indeterminate portion of aleatory music commonly occurs in two areas. The performers may be told to arrange the structure of the piece—e.g., by reordering its sections or by playing sections simultaneously as they wish. The musical score may also indicate points where performers are to improvise or even to include quasi-theatrical gestures. Such requirements may give rise to inventive notation, including brackets enclosing a blacked-out space, suggesting pitch area and duration of the improvisation. Among notable aleatory works are Music of Changes (1951) for piano and Concert for Piano and Orchestra (1958), by the American composer John Cage (Cage, John), and Klavierstück XI (1956; Keyboard Piece XI), by Karlheinz Stockhausen (Stockhausen, Karlheinz) of Germany.