Music in which some aspect is decided by performers or someone other than the composer is called

Aleatoric Music

Explanation:

  In the twentieth century, various trends and musical styles were established. Among the trends and techniques established in this period are impressionism, nationalism, jazz influences, polytonality, atonality, expressionism, serialism, neoclassicism, microtonality, electronic music, and aleatoric music.

  The principles of Aleatoric Music were developed by American John Cage in the early 1950s, who took advantage of side proposals put forward by Pierre Boulez. Other composers, such as Xenakis, used computer and mathematics as part of the creation process (Factral Music). Other precursors such as Luigi Nono, Luciano Bério and György Ligeti were also of great importance to random music.

  To the extent that the composer leaves the interpreter the freedom to improvise, he participates in the creation of the work, which is renewed in each performance, that is, a work may or may not be interpreted in the same way. We can draw an analogy with a playful composition practice of the thirteenth and nineteenth centuries, with Mozart as a precursor. The term random is not always used in music whose composer does not maintain total control over the work. In plays where certain decisions are left to the performer but not the result of chance, the terms indeterminate music or limited randomness are sometimes used.

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