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).
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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.
Bartók's "Playsong" demonstrates easily perceivable bitonality through, "the harmonic motion of each key...[being] relatively uncomplicated and very diatonic" (Kostka & Payne 1995, 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, 76).
Many music theorists, including Milton Babbitt and Paul Hindemith have questioned whether polytonality is a useful or meaningful notion or "viable auditory possibility" (Baker 1983, 163). Babbitt called polytonality a "self-contradictory expression which, if it is to possess any meaning at all, can only be used as a label to designate a certain degree of expansion of the individual elements of a well-defined harmonic or voice-leading unit" (Babbitt 1949, 380). Other theorists to question or reject polytonality include Allen Forte and Benjamin Boretz, who hold that the notion involves logical incoherence (Tymoczko 2002, 84).
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 Dmitri Tymoczko respond that the notion of "tonality" is a psychological, not a logical notion (Tymoczko 2002, 84). 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, Tymoczko argues that we can, at least at a rudimentary level, hear two separate key-areas at one and the same time: for example, when listening to two different pieces played by two different instruments in two areas of a room (Tymoczko 2002, 84). 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 critics of the notion of polytonality, such as Pieter van den Toorn, argue that the octatonic scale accounts in concrete pitch-relational terms for the qualities of "clashing," "opposition," "stasis," "polarity," and "superimposition" found in Stravinsky's music and, far from negating them, explains these qualities on a deeper level (Van den Toorn and Tymoczko 2003, 179). 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" (Van den Toorn and Tymoczko 2003, p. 27).
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.
Leeuw points to Beethoven's use of the clash between tonic and dominant, such as in his Third Symphony, as polyvalency rather than bitonality, with polyvalency being, "the telescoping of diverse functions that should really occur in succession to one another" (Leeuw 2006, 87).
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 (B♭) (Vincent 1951, 272).
Polyscalarity is defined as "the simultaneous use of musical objects which clearly suggest different source-collections (Tymoczko 2002, 83). "Specifically in reference to Stravinsky's music, Tymoczko uses the term polyscalarity out of deference to terminological sensibilities (Tymoczko 2002, 85). In other words, the term is meant to avoid any implication that the listener can perceive two keys at once. Though Tymoczko believed that polytonality is perceivable, he believed polyscalarity is better suited to describe Stravinsky's music. This term is also used as a response to Van den Toorn's analysis against polytonality. Van den Toorn, in an attempt to dismiss polytonal analysis used a monoscalar approach to analyze the music with the octatonic scale. However, Tymoczko states that this was problematic in that it does not resolve all instances of multiple interactions between scales and chords. Moreover, Tymoczko quotes Stravinsky's claim that the music of Petrouchka's second tableau was conceived "in two keys" (Tymoczko 2002, 85). Polyscalarity is then a term encompassing multiscalar superimpositions and cases which give a different explanation than the octatonic scale.