Editing Polytonality

{{Short description|Simultaneous use of multiple musical keys}}
{{Distinguish|Polyphony}}
'''Polytonality''' (also '''polyharmony'''{{sfn|Cole and Schwartz|2012}}) is the [[music]]al use of more than one [[key (music)|key]] [[simultaneity (music)|simultaneously]]. '''Bitonality''' is the use of only two different keys at the same time. '''Polyvalence''' or '''polyvalency''' is the use of more than one [[diatonic function|harmonic function]], from the same key, at the same time.{{sfn|Leeuw|2005|loc=87}}
[[File:Stravinsky-petrushka-fanfare.png|thumb|upright=1.5|Example of C- and F-sharp major chords together in Stravinsky's ''[[Petrushka (ballet)|Petrushka]]'' (see: [[Petrushka chord]])[[File:Stravinsky-petrushka-fanfare.mid]]]]

Some examples of bitonality superimpose fully [[harmony|harmonized]] sections of music in different keys.

==History==
[[File:K522 multitonality.png|thumb|upright=1.5|Mozart used polytonality in his ''[[A Musical Joke]]'' for comic effect.]]

===In traditional music===
Lithuanian traditional singing style [[sutartines]] is based on polytonality. A typical sutartines song is based on a six-bar melody, where the first three bars contain melody based on the notes of the triad of a major key (for example, in G major), and the next three bars is based on another key, always a major second higher or lower (for example, in A major). This six-bar melody is performed as a [[canon (music)|canon]], and repetition starts from the fourth bar. As a result, parts are constantly singing in different tonality (key) simultaneously (in G and in A).{{sfn|Jordania|2006|loc=119–120}}{{sfn|Račiūnaitė-Vyčinienė|2006}} As a traditional style, sutartines disappeared in Lithuanian villages by the first decades of the 20th century, but later became a national musical symbol of Lithuanian music.{{sfn|Anon.|2010}}

Tribes throughout India—including the Kuravan of [[Kerala]], the [[Jaunsari people|Jaunsari]] of [[Uttar Pradesh]], the [[Gondi people|Gond]], the [[Santal people|Santal]], and the [[Munda people|Munda]]—also use bitonality, in [[Call and response (music)|responsorial]] song.{{sfn|Babiracki|1991|loc=76}}

===In classical music===
[[File:Duetto II by Bach (polytonality).png|thumb|500px|Duetto II from ''Clavier-Übung III'' by J. S. Bach[[File:Duetto II by Bach (polytonality) - version for audio.wav]]]]
In [[J. S. Bach]]'s ''[[Clavier-Übung III]]'', there is a two-part passage where, according to Scholes: "It will be seen that this is a canon at the fourth below; as it is a strict canon, all the intervals of the leading 'voice' are exactly imitated by the following 'voice', and since the key of the leading part is D minor modulating to G minor, that of the following part is necessarily A minor modulating to D minor. Here, then, we have a case of polytonality, but Bach has so adjusted his progressions (by the choice at the critical moment of notes common to two keys) that while the right hand is doubtless quite under the impression that the piece is in D minor, etc., and the left hand that it is in A minor, etc., the listener feels that the whole thing is homogeneous in key, though rather fluctuating from moment to moment. In other words, Bach is trying to make the best of both worlds—the homotonal one of his own day and (prophetically) the polytonal one of a couple of centuries later."{{sfn|Scholes|1970|loc=448–449}}

Another early use of polytonality occurs in the [[classical period (music)|classical period]] in the finale of [[Wolfgang Amadeus Mozart]]'s composition ''[[A Musical Joke]]'', which he deliberately ends with the [[violins]], [[violas]] and [[French horn|horns]] playing in four discordant keys simultaneously. However, it was not featured prominently in non-programmatic contexts until the twentieth century, particularly in the work of [[Charles Ives]] (''Psalm 67'', c. 1898–1902), [[Béla Bartók]] (''Fourteen Bagatelles,'' Op. 6, 1908), and [[Stravinsky]] (''[[Petrushka (ballet)|Petrushka]]'', 1911).{{sfn|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.{{sfn|Crawford|2001|loc=503}}

Although it is only used in one section and intended to represent drunken soldiers, there is an early example of polytonality in [[Heinrich Ignaz Franz Biber]]'s short composition ''Battalia'', written in 1673.{{sfn|Ryker|2005}}

Stravinsky's ''[[The Rite of Spring]]'' is widely credited with popularizing bitonality, and contemporary writers such as [[Alfredo Casella|Casella]] (1924) describe him as the 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)".{{sfn|Casella|1924|loc=164}}

Bartók's "Playsong" demonstrates easily perceivable bitonality through "the harmonic motion of each key ... [being] relatively uncomplicated and very diatonic".{{sfn|Kostka and Payne|1995|loc=495}} Here, the "duality of key" featured is A minor and C{{music|#}} minor.

[[File:Milhaud - Saudades do Brazil polytonality.png|thumb|upright=1.8|center|Example of polytonality or extended tonality from Milhaud's ''[[Saudades do Brasil]]'' (1920), right hand in B major and left hand in G major, or both hands in extended G major{{sfn|Leeuw|2005|loc=87}}[[File:Milhaud - Saudades do Brazil polytonality.mid]]]]

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]].{{sfn|Marquis|1964}}{{Page needed|date=November 2010}}

[[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 (opera)|Billy Budd]]'' (note the shared enharmonically equivalent G{{music|#}}/A{{music|b}}){{sfn|Seymour|2007|loc=141–142}} or to express the main character's "maladjustment" in ''[[Peter Grimes]]''.{{sfn|White|1970|loc=119}}

==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:

[[File:Thirteenth-polychord.PNG|thumb|upright=1.2|center|Separate chords within an extended chord{{sfn|Marquis|1964|loc={{Page needed|date=October 2010}}}}[[File:Thirteenth-polychord.mid]]]]

Thus polychords do not necessarily suggest polytonality, but they may not be explained as a single tertian chord. The [[Petrushka chord]] is an example of a polychord.{{sfn|Ellenberger|2005|loc=20}} This is the norm in jazz, for example, which makes frequent use of "extended" and polychordal harmonies without any intended suggestion of "multiple keys."{{Citation needed|date=August 2015}}

===Polyvalency===
The following passage, taken from [[Ludwig van Beethoven|Beethoven]]'s [[Piano Sonata No.&nbsp;26 (Beethoven)|Piano Sonata in E{{music|flat}}, Op.&nbsp;81a (''Les Adieux'')]], suggests clashes between tonic and dominant harmonies in the same key.{{sfn|Marquis|1964|loc={{Page needed|date=November 2010}}}}

[[File:Bitonality in Beethoven.PNG|thumb|upright=1.8|center|Polyvalency suggested in Beethoven{{sfn|Marquis|1964|loc={{Page needed|date=October 2010}}}}[[File:Bitonality in Beethoven.mid]]]]

Leeuw points to Beethoven's use of the clash between tonic and dominant, such as in his [[Symphony No. 3 (Beethoven)|Third Symphony]], as polyvalency rather than bitonality, with polyvalency being, "the telescoping of diverse functions that should really occur ''in succession'' to one another".{{sfn|Leeuw|2005|loc=87}}

[[File:Polyvalency in Beethoven.png|thumb|upright=1.8|center|Polyvalency in Beethoven{{sfn|Leeuw|2005|loc=88}}[[File:Polyvalency in Beethoven.mid]]]]
[[File:Polyvalency in Stravinsky's Mass.png|thumb|upright=1.8|center|Polyvalency in Stravinsky's ''[[Mass (Stravinsky)|Mass]]''{{harv|Leeuw|2005|loc=88}}[[File:Polyvalency in Stravinsky.mid]]]]

===Polymodality===
Passages of music, such as [[Francis Poulenc|Poulenc]]'s ''[[Trois mouvements perpétuels]]'', I., may be misinterpreted as polytonal rather than polymodal. In this case, two scales{{Clarify|date=November 2014|reason=Which two scales? If they have a common tonic, are they not just different modal interpretations of the same scale?}} are recognizable but are assimilated through the common tonic (B{{Music|flat}}).{{sfn|Vincent|1951|loc=272}}

===Polyscalarity===

Polyscalarity is defined as "the simultaneous use of musical objects ''which clearly suggest different source-collections''.{{sfn|Tymoczko|2002|loc=83}} Specifically about Stravinsky's music, Tymoczko uses the term polyscalarity out of deference to terminological sensibilities.{{sfn|Tymoczko|2002|loc=85}} In other words, the term is meant to avoid any implication that the listener can perceive two keys at once. Though Tymoczko believes that polytonality is perceivable, he believes 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".{{sfn|Tymoczko|2002|loc=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".{{sfn|Baker|1993|loc=35}} 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|voice-leading]] unit".{{sfn|Babbitt|1949|loc=380}} Other theorists to question or reject polytonality include [[Allen Forte]] and [[Benjamin Boretz]], who hold that the notion involves logical incoherence.{{sfn|Tymoczko|2002|loc=84}}

Other theorists, such as [[Dmitri Tymoczko]], respond that the notion of "tonality" is a psychological, not a logical notion.{{sfn|Tymoczko|2002|loc=84}} Furthermore, Tymoczko argues that two separate key-areas can, at least at a rudimentary level, be heard at the same time: for example, when listening to two different pieces played by two different instruments in two areas of a room.{{sfn|Tymoczko|2002|loc=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.{{sfn|Van den Toorn and Tymoczko|2003|loc=179}} For example, the passage from ''Petrushka'', cited above, uses only notes drawn from the C octatonic collection C–C{{music|#}}–D{{music|#}}–E–F{{music|#}}–G–A–A{{music|#}}.

==See also==
* [[List of polytonal pieces]]
* [[Bimodality]]
* [[Polymodal chromaticism]]
* [[Elektra chord]]
* [[Bridge chord]]
* [[Woody Shaw]]

==References==
{{reflist|18em}}

===Sources===
{{div col|colwidth=45em}}
* {{wikicite|ref={{harvid|Anon.|2010}}|reference=Anon. 2010. "Sutartinės, Lithuanian Multipart Songs". UNESCO Intangible Cultural Heritage website (accessed 29 January 2016).}}
* {{wikicite|ref={{harvid|Babbitt|1949}}|reference=[[Milton Babbitt|Babbitt, Milton]] (1949). "The String Quartets of Bartók". ''[[The Musical Quarterly]]'' 35, no. 3 (July): 377–85.}}
* {{cite book|last=Babiracki|first=Carol M.|year=1991|title=Comparative Musicology and Anthropology of Music: Essays on the History of Ethnomusicology|editor1=[[Bruno Nettl]]|editor2=[[Philip Bohlman|Philip V. Bohlman]]|chapter=Tribal Music in the Study of Great and Little Traditions of Indian Music|location=Chicago|publisher=University of Chicago Press|isbn=978-0-226-57409-7}}
* {{cite book|last=Baker|first=James|author-link=James Baker (composer)|year=1993|chapter=Post-Tonal Voice-Leading|pages=20–41|title=Models of Musical Analysis: Early Twentieth-Century Music|editor=[[Jonathan Dunsby]]|location=Oxford|publisher=Basil Blackwell|isbn= 9780631143352}}
* {{wikicite|ref={{harvid|Casella|1924}}|reference=Casella, Alfred (1924). "Tone Problems of Today". ''[[The Musical Quarterly]]'' 10:159–171.}}
* {{wikicite|ref={{harvid|Cole and Schwartz|2012}}|reference=Cole, Richard, and Ed Schwartz (eds.) (2012). {{cite web |url=http://www.music.vt.edu/musicdictionary/textp/Polyharmony.html |title=Polyharmony |work=Virginia Tech Multimedia Music Dictionary |publisher=[[Virginia Tech]] |access-date=2007-08-04}}}}
* {{cite book|last=Crawford|first=Richard|year=2001|title=America's Musical Life: A History|url=https://archive.org/details/americasmusicall0000craw|url-access=registration|place=New York|publisher=W. W. Norton}}
* {{cite book|last=Ellenberger|first=Kurt|year=2005|title=Materials and Concepts in Jazz Improvisation|edition=fifth|place=Grand Rapids|publisher=Keytone|isbn=0-9709811-3-9}}
* {{wikicite|ref={{harvid|Jordania|2006}}|reference=Jordania, Joseph (2006). ''[[Who Asked the First Question?]]''. Logos.}}
* {{wikicite|ref={{harvid|Kostka and Payne|1995}}|reference=[[Stefan Kostka|Kostka, Stefan M.]], and Dorothy Payne (1995). ''Tonal Harmony, with an Introduction to Twentieth-Century Music'', third edition, consulting editor in music, Allan W. Schindler. New York: McGraw-Hill. {{ISBN|978-0-07-035874-4}}.}}
* {{wikicite|ref={{harvid|Leeuw|2005}}|reference=[[Ton de Leeuw|Leeuw, Ton de]] (2005). ''Music of the Twentieth Century: A Study of Its Elements and Structure'', foreword by Rokus De Groot, translated by Stephen Taylor. Amsterdam: Amsterdam University Press. {{ISBN|978-90-5356-765-4}}.}} Translated from ''Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur, met 111 muziekvoorbeelden en 7 figuren''. Utrecht: A. Oosthoek's Uitg. Mij., 1964 (third printing, Utrecht: Bohn, Scheltema & Holkema, 1977, {{ISBN|9789031302444}}).
* {{cite book|last=Marquis|first=G. Welton|year=1964|title=Twentieth Century Music Idioms|place=Englewood Cliffs, New Jersey|publisher=Prentice-Hall.}}
* {{wikicite|ref={{harvid|Račiūnaitė-Vyčinienė|2006}}|reference=Račiūnaitė-Vyčinienė, Daiva (2006). "The Lithuanian Archaic Polyphonic Chant Sutartinė", translated by E. Novickas. ''Lituanus'' 52, no. 2: 26–39. {{ISSN|0024-5089}}.}}
* {{wikicite|ref={{harvid|Ryker|2005}}|reference=Ryker, Harrison (2005). Invited paper no. 5, ''Soft and Sweet, Loud and Sour: Looking Back on Polytonality''. In ''New Music in China and The C.C. Liu Collection at the University of Hong Kong'', 47–48. Hong Kong: Hong Kong University Press, 2005, {{ISBN|978-96-2209-772-8}}.}}
* {{wikicite|ref={{harvid|Scholes|1970}}|reference=[[Percy Scholes|Scholes, Percy A]]. (1970). "Harmony". ''The Oxford Companion to Music''. London: Oxford University Press.}}
* {{cite book| last = Seymour| first = Claire| title = The Operas of Benjamin Britten Expression and Evasion| year = 2007| publisher = Boydell Press| isbn = 978-1-84383-314-7 }}
* {{wikicite|ref={{harvid|Tymoczko|2002}}|reference=Tymoczko, Dmitri (2002). "Stravinsky and the Octatonic: A Reconsideration". ''[[Music Theory Spectrum]]'' 24, no. 1:68–102.}}
* {{wikicite|ref={{harvid|Van den Toorn and Tymoczko|2003}}|reference=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.}}
* {{cite book|last=Vincent|first=John|year=1951|title=The Diatonic Modes in Modern Music|url=https://archive.org/details/diatonicmodesinm00vinc|series=University of California Publications in Music 4|place=Berkeley|publisher=University of California Press}}
* {{cite book| last = White|first= Eric Walter | title = Benjamin Britten His Life and Operas| year = 1970|place=Berkeley and Los Angeles |publisher = University of California Press| isbn = 978-0-520-01679-8 }}
* {{wikicite|ref={{harvid|Whittall|2001}}|reference=[[Arnold Whittall|Whittall, Arnold]] (2001). "Bitonality". ''[[The New Grove Dictionary of Music and Musicians]]'', 2nd edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan.}}
{{div col end}}

==Further reading==
* {{cite book| last = Beach| first = David| title = Aspects of Schenkerian Theory| year = 1983| place=New Haven and London | publisher = Yale University Press| isbn = 978-0-300-02800-3|ref=none}}
* [[Paul Hindemith|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. Original German edition as ''Unterweisung im Tonsatz''. 3 vols. Mainz, B. Schott's Söhne, 1937–70.
* {{cite book| last = Reti| first = Rudolph |author-link=Rudolph Reti | title = Tonality, Atonality, Pantonality A Study of Some Trends in Twentieth Century Music| year = 1978| publisher = Greenwood Publishing Group| isbn = 978-0-313-20478-4|ref=none}}
* {{cite AV media notes|last=Wilson|first=Carl|author-link=Carl Wilson|chapter=Comments by Carl Wilson|title=[[The Pet Sounds Sessions]]|others=[[The Beach Boys]]|year=1997|publisher=[[Capitol Records]]|type=Booklet|chapter-url=http://albumlinernotes.com/Comments_by_Carl_Wilson.html|ref=none}}
* {{cite book| last = Wilson| first = Paul| title = The Music of Béla Bartók| year = 1992| publisher = Yale University Press| isbn = 978-0-300-05111-7|ref=none}}

{{Modernism (music)}}
{{Tonality}}

[[Category:Polytonality| ]]