Aleatoric (or aleatory) music or composition, is music where some element of the composition is left to chance. The term became known to European composers through the lectures which acoustician Werner Meyer-Eppler held at Darmstadt Summer School in the beginning of the fifthies. According to his definition, "aleatoric processes are such processes which have been fixed in their outline but the details of which are left to chance".

The word alea means "dice" in Latin, and the term has become known as referring to a chance element being applied to a limited number of possibilities, a method employed by European composers who felt more bound than the Americans by tradition and who stressed the importance of compositional control, as opposed to indeterminacy and chance where possibilities tend not to be finite and which is an Anglo-Saxon phenomenon.

The term was used by the French composer Pierre Boulez to describe works where the performer was given certain liberties with regard to the order and repetition of parts of a musical work. The term was intended by Boulez to distinguish his work from works composed through the application of chance operations by John Cage and his aesthetic of indeterminacy - see indeterminate music. Other examples of aleatoric music are Klavierstück XI by Stockhausen which features a number of elements to be performed in changing sequences and characteristic sequences to be repeated fast, producing a special kind of oscillating sound, in orchestral works of Lutoslawski and Penderecki.

An early genre of composition that could be considered a precedent for aleatoric compositions were the Musikalische Würfelspiele or Musical Dice Games, popular in the late 18th and early 19th century. (One such dice game is attributed to Wolfgang Amadeus Mozart.) These games consisted of a sequence of musical measures, for which each measure had several possible versions, and a procedure for selecting the precise sequence based on the throwing of a number of dice.

There has been considerable confusion of the terms aleatory and indeterminate / chance music. One of Cage's pieces, HPSCHD, itself composed using chance procedures, uses music from Mozart's Musikalisches Würfelspiel, referred to above, as well as original music and he also generally used coin-tossing and other procedures depending on designs resulting in a pre-defined number of choices to be made. But still, both the aesthetic aims as well as the number of elements controlled by chance make the two methods differ clearly. Douglas Hofstadter, writing in Gödel, Escher, Bach, thus punningly characterises some of the musical compositions of John Cage by using the acronym CAGE to stand for Composition of Aleatorically Generated Elements, in contrast to a Beautiful Aperiodic Crystal of Harmony (or BACH).

Some aleatoric music, such as that of the Mangabros , is inspired by the book The Dice Man by Luke Rhinehart.

See also:

• Aleatory
• Algorithmic music
• Ambient music
• Generative music
• Stochastic music

External links

• http://sunsite.univie.ac.at/Mozart/dice/
• http://www.sciencenews.org/20010901/mathtrek.asp
• http://www.anigraphical.com/