Initially I didn't really "get" minimalist composers and hated atonalism (eg. Schoenberg). It was fairly easy to grasp modern composers like Walter Piston or Aaron Copeland so that music I really liked. After taking a music appreciation course in college and further listening my palette got broader but to this day I really don't care for atonal music. However, I became a serious fan of Phillip Glass! I think it was probably either Glassworks or Koyaanisqatsi that first captivated me.
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“I'd rather have questions that cannot be answered than answers that can't be questioned.” —Richard Feynman