If you are a student of Music History or Composition, here is a more detailed list of composers you should know from this period.
Name
Birth
Death
Nationality
Representative Pieces
1947
American
Short Ride in a Fast Machine(orchestra)
Phyrgian Gates(piano solo)
1927
American
Evensong (soprano, choir, & orchestra)
Postcard from Morocco (opera)
1925
2003
Italian
Visage(tape)
Sequenza IV(piano)
Sequenza VIII(violin)
1934
British
Gawain's Journey (orchestra)
1938
American
1953
Chinese
Suite for Cello and Chamber Winds(chamber ensemble)
1932
American / Canadian
Urban Requiem (4 saxophones & wind ensemble)
1938
American
The Red Violin(film score)
Symphony No. 2
1929
American
Ancient Voices of Children(soprano & chamber)
A Haunted Landscape(orchestra)
1956
American
An American Requiem (opera)
1954
American
Deus ex Machina (piano & orchestra)
1937
American
Ballad in Lavender (piano)
1957
Chinese
Out of Peking Opera (violin & orchestra)
1937
American
Satyagraha(opera)
Glassworks(chamber ensemble)
Photographer(theatre piece)
Koyaanisqatsi(film score)
1933
2010
Polish
Kleines Requiem für eine Polka (piano & chamber ensemble)
1962
American
Piano Trio(violin, cello, & piano)
1943
American
Two-Piano Inventions
1960
American
Symphony in Waves (orchestra)
1950
American
Chanting to Paradise(soprano & piano)
A Lover's Journey(choral)
1923
2006
Hungarian-Austrian
Lux Aeterna(choral)
Atmospheres(orchestra)
1931
American
I Am Sitting in a Room (tape)
Music on a Long Thin Wire (electronic)
1953
American
Death and the Powers (opera)
Hyperstring Trilogy (hyperviolin, hyperviola, hypercello, & chamber orchestra)
1959
Scottish
7 Last Words from the Cross (chorus & chamber orchestra)
1934
English
An Orkney Wedding with Sunrise (orchestra & bagpipes)
1942
American
Atlas (opera)
1932
2016
American
The Ready Made Boomerang (chamber ensemble)
1935
Estonian
Magnificat(a cappellachoir)
Für Alina(piano)
1933
Polish
Violin Concerto No. 1(violin & orchestra)
De Natura Sonoris No. 1 & 2(orchestra)
1936
American
Music for 18 Musicians(mixed chamber ensemble)
Pendulum Music(4 performers)
Clapping Music(2 performers)
1935
American
A Rainbow in Curved Air(keyboards & percussion)
1923
American
Stopping by Woods on a Snowy Evening (voice & piano)
1952
Finnish
Jardin Secret No. 1 (electronic music)
Laterna Magica (orchestra)
1950
American
Wright Flight (piano and orchestra)
1935
American
Symphony No. 1 "Songlines"
String Quartet No. 5
A Year in the Catskills(woodwind quintet)
1925
American
Seven Studies on Themes of Paul Klee (orchestra)
1943
American
Sparrows(soprano & chamber ensemble)
Chasing Light(orchestra)
1928
2007
German
Klavierstück IX(piano solo)
Kontakte(electronic sounds, piano, & percussion)
Gruppen(3 orchestras)
1933
American
All My Hummingbirds Have Alibis (interactive orchestra and electronic)
1944
British
Ikon of Light(two choirs and chamber ensemble)
1938
American
Fanfare for the Uncommon Woman(brass and orchestra)
1970
American
Ghost Train Triptych(wind symphony)
Paradise Lost: Shadows and Wings(musical theatre)
1934
American
Keyboard Miscellany (piano)
1938
American
Mass for the Restoration of St. Luke in the Fields (chorus & orchestra)
Orchestral and Electronic Exchanges (orchestra & tape)
1922
2001
Greek
Pleiades(percussion)
1935
American
The Well-Tuned Piano (solo)
1939
American
Rituals (5 percussionists & orchestra)