20th Century (1920-2000)
The distinctive feature of classical music composed in the twentieth century is that there is no such thing as a "twentieth century style." Composers in different countries, and even within a country, took radically different paths, and the result was a multitude of styles, none of which dominated over the others in the way that, for example, the style of Haydn, Mozart, and Beethoven dominated the last quarter of the eighteenth century.
The most radical break with the past occurred in Germany, where Arnold Schoenberg and his followers rejected the rules that had governed composition for the previous three centuries and began composing "twelve-tone" or "atonal" works. An offshoot of this movement was "serialism," which attempted to create entire compositions out of mathematically precise formulas for pitch, rhythm, and dynamics.
Serialism swept France after World War II, but in the first half of the century French composers looked back to the eighteenth century, and their music was appropriately called "neoclassical." The greatest Neoclassical composer in France (and later in America) was Igor Stravinsky, an import from Russia who also composed fiery ballets in his youth and serial works in his old age.
In Eastern Europe, Béla Bartók collected Hungarian folk tunes and incorporated them in his compositions, while in Russia the Soviet government kept close rein on what music composers were allowed to write. Dmitri Shostakovich and Sergei Prokofiev were the two greatest Soviet composers; Shostakovich's music in particular demonstrates the composer's conflict between personal expression and political expediency.
English composers such as Ralph Vaughan Williams and Benjamin Britten were perhaps the most "mainstream" composers of mid-century, writing in familiar idioms but also influenced by English hymns and English composers of the Renaissance. On the other side of the Atlantic, classical music in the United States reached its maturity in the first part of the century. Aaron Copland integrated American folk tunes with a very traditional European style, while George Gershwin was heavily influenced by ragtime and jazz.
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If you want more
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01 - Igor Stravinsky; Petroushka, Le Sacre du Printemps - Stravinsky, CSO (Sony 1990)
02 - Shostakovich & Tchaikovsky Trios - Argerich, Kremer, Maisky (DG 1999)
03 - Bela Bartok; Concerto for Orchestra, Hungarian Sketches - Reiner & CSO (RCA 1993)
04 - Sergei Prokofiev; Romeo and Juliet, Symphony No. 1 'Classical' - Solti & CSO (Decca 1991)
05 - Dmitrij Shostakovich; Symphony & Cello Concerto; Ma, Ormandy, Bernstein, NYPO (Sony 1990)
06 - Aaron Copland; Appalachian Spring, Rodeo, Billy, Fanfare - Bernstein & NYPO (Sony 1997)
07 - Berg; Violin Concerto, Rihm; 'Time Chant' - Mutter, Levine, CSO (DG 1993)
08 - Gershwin & Grofe; Rhapsody in Blue, American in Paris - Corigliano, Bernstein, CSO (Sony 1997)
09 - Brahms, Stravinsky - Violin Concertos - Hilary Hahn, Marriner & Academy of St Martin(Sony 2001)
10 - Olivier Messiaen - Quatuor Pour Le Fin Du Temps - Shaham, Meyer, Chung, Wang (DG 2001)
11 - Benjamin Britten; Serenade, Les Illuminations, Nocturne - Britten, Pears, (Polygram 1993)