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.
Example of C and F sharp major chords together in Stravinsky's Petrushka
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 1909-1910 to include polytonal passages).
Mozart used polytonality in his A Musical Joke
for comic effect.
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 Bartók (Fourteen Bagatelles, op. 6 ), Ives (Variations on "America"), Stravinsky (Petrushka ), and Debussy (Preludes, Book 2 ). 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.
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)."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.
Bartók's "Playsong" demonstrates easily perceivable bitonality through, "the harmonic motion of each key...[being] relatively uncomplicated and very diatonic."(Kostka & Payne 1995, p.495) Here, the "duality of key" featured is A minor and C# minor:
Other polytonal composers influenced by Stravinsky include those in the French group, Les Six, particularly Darius Milhaud, as well as Americans such as Aaron Copland (Marquis 1964).
Many contemporary composers are interested in bitonality. Philip Glass uses the technique in his Symphony No. 2, and John Adams's Chamber Symphony suggests polytonality.
Bitonality is also found in folk music: for example, tribes throughout India use bitonality in responsorial song and sometimes sing in parallel harmonies (Babiracki 1991, p. 76).
Many music theorists, including Milton Babbitt and Paul Hindemith have questioned whether polytonality is a useful or meaningful notion or "viable auditory possibility". Hindemith called polytonality a, "self-contradictory expression which, if it is to possess any meaning at all, can be used only to designate a certain degree of expansion of the individual elements of a well-defined harmonic or voice-leading unit". (Beach 1983) Other theorists to question or reject polytonality include Allen Forte, Benjamin Boretz, and Pieter van den Toorn.
There are two main challenges to polytonality, one logical, the other psychological. The logical challenge, as articulated by Hindemith, is that the very meaning of the term "tonality" requires that a single tone be heard (and conceived) as "tonic." The psychological challenge holds that it is impossible for human beings to simultaneously perceive two separate key-centers at once.
Proponents of polytonality, such as Daniel Harrison, Dmitri Tymoczko, Peter Kaminsky, and José Oliveira Martins respond that the notion of "tonality" is a psychological, not a logical notion. Whether two different key centers can be heard simultaneously is a matter for empirical investigation, and cannot be determined by examining the meaning of the term "tonality." Furthermore, proponents of polytonality argue that we can, in fact, hear two separate key-areas at one and the same time: for example, when listening to two different pieces, one through each ear in a pair of headphones. Finally, they note that regardless of perceptual issues, a substantial body of music is composed by superimposing musical fragments that, if heard separately, would suggest different keys. The term "polytonality" can therefore be used in a purely descriptive sense, to identify music that is constructed in this way.
Some opponents of polytonality, such as Pieter van den Toorn, argue that purportedly polytonal music often derives from the octatonic scale. For example, the passage from Petrushka, cited above, uses only notes drawn from the C octatonic collection C-C♯-D♯-E-F♯-G-A-A♯. (The notes can also be derived from the F♯ acoustic scale F♯-G♯-A♯-B♯(C)-C♯-D♯-E.) In a similar vein, Paul Wilson argues against analyzing Bartók's "Diminished Fifth" (no.101, vol. 4, Mikrokosmos) and "Harvest Song" (no.33 of the Forty-Four Duos for two violins) as bitonal since "the larger octatonic collection embraces and supports both supposed tonalities" (ibid, p. 27).
Polytonality and polychords
Polytonality requires the presentation of simultaneous key-centers. The term "polychord" describes chords that can be constructed by superimposing multiple familiar tonal sonorities. For example, familiar ninth, eleventh, and thirteenth chords can be built from or decomposed into separate chords:
Thus polychords do not necessarily suggest polytonality, as they may be heard as belonging to a single key. This is the norm in jazz, for example, which makes frequent use of "extended" and polychordal harmonies without any intended suggestion of "multiple keys."
The following passage, taken from Beethoven's Piano Sonata in E♭ Op.81a (Les Adieux), suggests clashes between tonic and dominant harmonies in the same key (Marquis 1964). Though slightly discordant, the music is not bitonal. Indeed, it is not even clear that the passage involves two separate chords: a traditional tonal analysis might suggest an underlying harmony of E♭ major, with the F acting as an accented passing tone.
Passages of music, such as Poulenc's Mouvements Perpetuels, I., may be misinterpreted as polytonal rather than polymodal. In the example given the two scales are recognizable but are assimilated through the common tonic (Bb). (Vincent 1951, p. 272)
Babiracki, Carol M. (1991) in Nettl, Bruno and Philip V. Bohlman (Eds.). Comparative Musicology and Anthropology of Music: Essays on the History of Ethnomusicology. ISBN 0-226-57409-1.
Beach, David, ed. (1983). "Schenkerian Analysis and Post-Tonal Music", Aspects of Schenkerian Theory. New Haven: Yale University Press.
Casella, Alfred. (1924). "Tone Problems of Today." Musical Quarterly 10: 159-171.
Cole and Schwartz, ed. "Polyharmony". Virginia Tech Multimedia Music Dictionary. Virginia Tech. http://www.music.vt.edu/musicdictionary/textp/Polyharmony.html. Retrieved 2007-08-04.
Kostka & Payne (1995). Tonal Harmony, p.495. Third Edition. ISBN 0-07-300056-6.
Marquis, G. Welton (1964). Twentieth Century Music Idioms. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.
Vincent, John (1951). The Diatonic Modes in Modern Music. University of California Press.
Wilson, Paul (1992). The Music of Béla Bartók. ISBN 0-300-05111-5.
Babbitt, Milton (1949). "Quartets of Bartok", Musical Quarterly 35, p. 380.
Hindemith, Paul (1942). The Craft of Musical Composition, vol. 1, p. 156. New York: Associated Music Publishers.
Reti, Rudolph (1958). Tonality, Atonality, Pantonality: A study of some trends in twentieth century music. Westport, Connecticut: Greenwood Press. ISBN 0-313-20478-0.