Is 1940s classical music similar to traditional classical music, is it similar to contemporary classical music?
Sergei is 100% correct.
To illustrate his answer with some links….
Modern era, late romantic style… very much in the manner of traditional classical.
Samuel Barber ~ Violin Concerto (1940 – on the nose, so to speak) http://www.youtube.com/watch?v=0oXKuXdmzcw
“advanced harmonic language,” Modern… radically different use of harmony and rhythm, heavy on a type of counterpoint more associated with renaissance and earlier music.
Olivier Messiaen ~
Trois petites Liturgies de la Présence Divine (1943-44)
Vingt regards sur l’enfant-Jésus (1944) # X. Regard de l’Esprit de joie
Serial / twelve tone… both like traditional and unlike traditional.
Anton Webern ~ Variations for Orchestra, Op. 30 (1940)
Tonal, to a degree, “neoclassical”… i.e. in a way traditional classical like, but with no conern at all for the formality of structure or traditional classical procedure.
Aaron Copland ~ Appalachian Spring (1944)
Igor Stravinsky… in the middle to late part of his neoclassical period (capped by the Opera “The Rake’s Progress” in 1951.) – all very much “in the spirit” of older traditional classical music.
Symphony in C (1940)
Symphony in Three Movements (1945)
Concerto in D, for string orchestra (1946)
John Cage ~ “experimental / avant-garde” Cage was busy writing for mixed forces, including a number of pieces for prepared piano – nothing to do with tradition here.
Daughters of the Lonesome Isle (1945)
[ I have omitted electronic music, which had its beginnings in the 1930's and which began to be earnestly investigated, with works done in the medium, also during the 1940's - electronic music did not, even as an esoteric minority interest within the avant-garde followers, really begin to take off until the fifties. ]
That should be enough. It is only a small and partial survey of ‘what was going on’ in the 1940′s in Western Classical Music.
P.s. While I thought of Korngold, I left him off my list because his music is very very “Late Romantic,” with the slightest of modern harmonic vocabulary. He was one of the more extremely conservative of modern (1890 – 1975), not contemporary (1975-present) composers.