The answer to the question is Art Ensemble of Chicago.
Avant garde music is a term that's simply used for describing the styles of music that came into being after 1945.
Some of their musical styles include serialism, musique concrete, aleatoric music, etc.
Many of their important innovators were from the Art Ensemble of Chicago and the Experimental Band. Some of their key composers were John Cage, Arnold Schönberg, and Pierre Schaeffer.
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