Editing Polytonality (section)

===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}}