The musical use of more than one key simultaneously is polytonality (also polyharmony (Cole & Schwartz)). Bitonality is the use of only two different keys at the same time. Polyvalence is the use of more than one harmonic function, from the same key, at the same time (Leeuw 2006, 87).
A well-known, controversial example is the fanfare at the beginning of the second tableau of Igor Stravinsky's ballet, Petrushka. The first clarinet plays a melody that uses the notes of the C major chord, while the second clarinet plays a variant of the same melody using the notes of the F sharp major chord.
Some examples of bitonality superimpose fully harmonized sections of music in different keys. Examples can be found in the music of Charles Ives, in particular Variations on "America" (orig. 1891, revised in 1909–10 to include polytonal passages).
Pre-twentieth-century instances of polytonality, such as Biber's "Battaglia" (1673) and Mozart's Ein musikalischer Spass' ending of presto (1787), tend to use the technique for programmatic or comic effect. The earliest uses of polytonality in non-programmatic contexts are found in the twentieth century, particularly in the work of Charles Ives (Psalm 67, ca. 1898–1902), Bartók (Fourteen Bagatelles, op. 6, 1908), and Stravinsky (Petrushka, 1911) (Whittall 2001). Ives claimed that he learned the technique of polytonality from his father, who taught him to sing popular songs in one key while harmonizing them in another (Crawford 2001, 503).
Stravinsky's The Rite of Spring is widely credited with popularizing bitonality, and contemporary writers such as Casella (1924) describe him as progenitor of the technique: "the first work presenting polytonality in typical completeness—not merely in the guise of a more or less happy 'experiment,' but responding throughout to the demands of expression—is beyond all question the grandiose Le Sacre du Printemps of Stravinsky (1913) " (Casella 1924, 164). Béla Bartók's experiments with bitonality become notably more radical in his The Miraculous Mandarin (written 1918-1919), composed after he had obtained a score of the Rite of Spring.
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