Read Part I here.
Delving into another group of composers/compositions, IMO, high-school-age composition students should familiarize themselves with, here are what I call Late 20th-century Modernists.
Post-Modernism). However, I'd also say, arbitrarily I suppose, that their basic language is dissonant, atonal, frequently non-pulsitile, completely outside the common practice use of melodic devices/voice-leading with resolutions, and so forth, which is the criteria I'm using.
I'm also making a distinction between Modernists and what I'm calling Avant-gardists, which is indeed splitting hairs with more than a few (the late 20th century Avant-garde will be the next post). So Morton Feldman, Alvin Lucier, Pauline Oliveros, and others whose language is either directly or indirectly influenced by Cage, instead of the mid-century Modernists (Boulez, Babbitt), I'm lumping together as the Avant-garde.
At any rate, this list is a work-in-progress, but these guys are important! Listen and absorb.....
Listen to "Music You Should Know: Late 20th Century Modernists"