Editing Aleatoric music (section)

==Types of indeterminate music==
Some writers do not make a distinction between aleatory, chance, and [[Indeterminacy (music)|indeterminacy in music]], and use the terms interchangeably.{{sfn|Griffiths|2001}}{{sfn|Joe & Song|2002|p=264}}{{sfn|Roig-Francolí|2008|p=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 (music)|graphic notation]] and texts.{{sfn|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.{{sfn|Joe & Song|2002|p=268}} Because this work is absolutely fixed from performance to performance, Cage regarded it as an entirely determinate work made using chance procedures.{{sfn|Pritchett|1993|p=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.{{sfn|Joe & Song|2002|p=268}}{{Vague|date=January 2012|reason=It still is not clear why a piece clearly described as determined at every level by the composer should be brought into a discussion of indeterminacy.}}

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.{{sfn|Joe & Song|2002|p=269}}

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 notation (music)|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 units are represented by the squares viewed horizontally, while relative pitch levels of high, middle, and low are indicated by three vertical squares in each row. The performer determines what particular pitches and rhythms to play.{{sfn|Joe & Song|2002|p=269}}