Polytonality (also polyharmony (Cole & Schwartz)) is the musical use of more than one key simultaneously. 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).

Example of C and F sharp major chords together in Stravinsky's Petrushka.  Play (help·info)

Some examples of bitonality superimpose fully harmonized sections of music in different keys.

History

Mozart used polytonality in his A Musical Joke for comic effect.  Play (help·info)

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), Béla 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).

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:

Bitonality in the opening to Bartók's "Playsong", Mikrokosmos No. 105 (Kostka & Payne 1995, 495).  Play (help·info)

Example of polytonality or extended tonality from Milhaud's Saudades do Brasil (1920)  Play (help·info), right hand in B major and left hand in G major, or both hands in extended G major (Leeuw 2005, 87).

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).

Sextet for String Quartet, Clarinet, and Piano (Marquis 1964, 23)  Play (help·info)

Benjamin Britten used bi and polytonality in his operas, as well as enharmonic relationships, for example to signify the conflict between Claggart (F minor) and Billy (E major) in Billy Budd (note the shared enharmonically equivalent G♯/A♭) (Seymour 2007, 141-142) or to express the main character's "maladjustment" in Peter Grimes (White 1970, 119).

Bitonal tremolo in Britten's Peter Grimes, Act III (White 1970, 119). F minor and E major, which share G♯/A♭.  Play (help·info)

Bitonality is also found in folk music: for example, tribes throughout India use bitonality in responsorial song (Babiracki 1991, 76).

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:

Separate chords within an extended chord (Marquis 1964).  Play (help·info)

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{{music, suggests clashes between tonic and dominant harmonies in the same key (Marquis 1964).

Bitonality suggested in Beethoven (Marquis 1964).  Play (help·info)

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).

Polyvalency in Beethoven  Play (help·info) (Leeuw 2006, 88).

Polyvalency in Stravinsky's Mass  Play (help·info) (Leeuw 2006, 88).

Polymodality

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

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.

Challenges

Some 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).

Other theorists, such as Dmitri Tymoczko, respond that the notion of "tonality" is a psychological, not a logical notion (Tymoczko 2002, 84). Furthermore, Tymoczko argues that two separate key-areas can, at least at a rudimentary level, be heard 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).

Octatonicism

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♯.

Sources

• Babiracki, Carol M. (1991). "Tribal Music in the Study of Great and Little Traditions of Indian Music". In Comparative Musicology and Anthropology of Music: Essays on the History of Ethnomusicology, edited by Bruno Nettl and Philip V. Bohlman, 69–90. Chicago: University of Chicago Press. ISBN 0-226-57409-1.
• Babbitt, Milton (1949). "The String Quartets of Bartók". Musical Quarterly 35, no. 3 (July): 377–85.
• Baker, James (1983). "Schenkerian Analysis and Post-Tonal Music", In Aspects of Schenkerian Theory, edited by David Beach, 153–86. New Haven and London: Yale University Press. ISBN 0-300-02800-8 (cloth); ISBN 0-300-02803-2 (pbk).
• Casella, Alfred (1924). "Tone Problems of Today". Musical Quarterly 10:159–71.
• Crawford, Richard (2001). America's Musical Life: a History. New York: Norton.
• Cole, Richard, and Ed Schwartz, ed. "Polyharmony". Virginia Tech Multimedia Music Dictionary. Virginia Tech. http://www.music.vt.edu/musicdictionary/textp/Polyharmony.html. Retrieved 2007-08-04. 
• Hindemith, Paul (1941–42). The Craft of Musical Composition, vols. 1 and 2, translated by Arthur Mendel and Otto Ortmann. New York: Associated Music Publishers; London: Schott & Co. Original German edition as Unterweisung im Tonsatz. 3 vols. Mainz, B. Schott's Söhne, 1937–70.
• Kostka, Stefan, and Dorothy Payne (1995). Tonal Harmony, with an Introduction to Twentieth-Century Music, third edition. New York: McGraw-Hill. ISBN 0-07-035874-5.
• Leeuw, Ton de (2005). Music of the Twentieth Century: A Study of Its Elements and Structure. Amsterdam: Amsterdam University Press. ISBN 90-5356-765-8.
• Marquis, G. Welton (1964). Twentieth Century Music Idioms. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.
• Seymour, Claire (2007). The Operas of Benjamin Britten: Expression and Evasion. ISBN 9781843833147.
• Tymoczko, Dmitri. 2002. "Stravinsky and the Octatonic: A Reconsideration". Music Theory Spectrum 24, no. 1:68–102.
• Van den Toorn, Pieter C., and Dmitri Tymoczko (2003) "Colloquy: Stravinsky and the Octatonic: The Sounds of Stravinsky". Music Theory Spectrum 25, no. 1 (Spring): 167–202.
• Vincent, John (1951). The Diatonic Modes in Modern Music. University of California Publications in Music 4. Berkeley: University of California Press.
• White, Eric Walter (1970). Benjamin Britten: His Life and Operas. ISBN 9780520016798.
• Whittall, Arnold (2001). "Bitonality". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
• Wilson, Paul (1992). The Music of Béla Bartók. Composers of the Twentieth Century. New Haven: Yale University Press. ISBN 0-300-05111-5.

Further reading

• Reti, Rudolph (1958). Tonality, Atonality, Pantonality: A Study of Some Trends in Twentieth Century Music. Westport, Connecticut: Greenwood Press. ISBN 0-313-20478-0.