Schmidt was born in Bratislava (at that time called Pressburg: now in Slovakia) on December 22, 1874. He briefly studied piano with Theodor Leschetizky, with whom he clashed. He moved to Vienna with his family in 1888, and studied at the Conservatory there (composition with Robert Fuchs and cello with Ferdinand Hellmesberger), graduating "with excellence" in 1896. He beat 13 other applicants in obtaining a post as cellist with the Vienna Court Opera Orchestra, with whom he played (often under the direction of Mahler) until 1914. In that year he took up a professorship (in piano) at the State Academy of Music. In 1925 he became Director of the Academy, and in 1927 Rector. Schmidt's worsening health forced his retirement from the Academy in early 1937. He died on 11 February 1939.
Schmidt composed four symphonies (1899, 1913, 1928 and 1933); two operas: Notre Dame (1904-6) and Fredigundis (1916-21); two string quartets (1925, 1929), a piano quintet (1926) and two quintets for clarinet, string trio and piano (left hand) (1932, 1938); Concertante Variations on a Theme of Beethoven for piano (left hand) and orchestra (1923); a piano concerto (1934); Variations on a Hussar's Song for orchestra (1930); a quantity of important organ music, including the Prelude and Fugue in E flat (1924), the Toccata (1924), the Chaconne (1925, orchestrated 1931) and the Prelude and Fugue in C (1927). His crowning achievement was the oratorio Das Buch mit sieben Siegeln (1935-37), a setting of the Book of Revelation.
Schmidt is generally, if erroneously, regarded as a conservative composer, but the rhythmic subtlety and harmonic complexity of much of his music belie this. His music is modern without being modernist, combining a reverence for the great Austro-German lineage of composers with very personal innovations in harmony and orchestration. The considerable technical accomplishment of his music ought to compel respect, but he seems to have fallen between two stools: his works are too complex for the conservatively-minded, yet too obviously traditional for the avant-garde (they are also notoriously difficult to perform). His posthumous reputation suffered for many years because of ill-founded accusations of Nazism, vigorously rebutted by his many Jewish friends and colleagues (including Oskar Adler and Hans Keller). Since the 1970s his music has enjoyed a modest revival which looks set to continue as it is rediscovered and re-evaluated.