Compare and contrast the approaches to indeterminacy and chance operations as employed by different experimental composers.

Indeterminacy and chance operations are two related but distinct approaches to musical composition that emerged in the mid-20th century, challenging the traditional notion of the composer as the sole authority in determining a work's final form. Both methods involve relinquishing some degree of control over the musical material, but they differ in how and why this control is relinquished. They also manifest differently in various composer's works and create unique approaches to creating musical experiences. Indeterminacy, in its purest form, refers to situations in which certain elements of the musical work are left unspecified by the composer, to be decided by the performer(s), or even by chance during the performance itself. This can include notated elements such as pitch, rhythm, duration, or even the overall form of the piece. This approach was championed by composer John Cage. His works explore how music can be created when removing a composer's subjective intent from the process. For example, in Cage's "4'33"," there is no sound specified by the composer; instead, the piece consists of the sounds that occur in the performance space during the designated four minutes and thirty-three seconds. This piece is an extreme example of indeterminacy as it removes all musical decision-making from the score and places it in the performance context. While the parameters are clearly defined (the time), the content is entirely undefined. Another example is his "Concert for Piano and Orches....