Polytonality (also polyharmony) is the
music
Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspe ...
al use of more than one
key simultaneously. Bitonality is the use of only two different keys at the same time. Polyvalence or polyvalency is the use of more than one
harmonic function
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that is,
: \f ...
, from the same key, at the same time.
Some examples of bitonality superimpose fully
harmonized sections of music in different keys.
History
In traditional music
Lithuanian traditional singing style
sutartines
Lithuanian folk songs (in Lithuanian: "liaudies dainos") are often noted for not only their mythological content but also their relating historical events.
Lithuanian folk music includes romantic songs, wedding songs, as well as work songs and ...
is based on polytonality. A typical sutartines song is based on a six-bar melody, where the first three bars contains 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
Canon or Canons may refer to:
Arts and entertainment
* Canon (fiction), the conceptual material accepted as official in a fictional universe by its fan base
* Literary canon, an accepted body of works considered as high culture
** Western ca ...
, and repetition starts from the fourth bar. As a result, parts are constantly singing in different tonality (key) simultaneously (in G and in A). 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.
Tribes throughout India—including the Kuravan of
Kerala
Kerala ( ; ) is a state on the Malabar Coast of India. It was formed on 1 November 1956, following the passage of the States Reorganisation Act, by combining Malayalam-speaking regions of the erstwhile regions of Cochin, Malabar, South Ca ...
, the
Jaunsari Jaunsari may refer to:
* Jaunsari people, an ethnic group of northern India
* Jaunsari language
Jaunsari () is a Western Pahari language of northern India spoken by the Jaunsari people in the Chakrata
Chakrata is a cantonment town and als ...
of
Uttar Pradesh
Uttar Pradesh (; , 'Northern Province') is a state in northern India. With over 200 million inhabitants, it is the most populated state in India as well as the most populous country subdivision in the world. It was established in 195 ...
, the
Gond, the
Santal
The Santal or Santhal are an Austroasiatic speaking
Munda ethnic group in South Asia. Santals are the largest tribe in the Jharkhand and West Bengal state of India in terms of population and are also found in the states of Odisha, Bihar an ...
, and the
Munda—also use bitonality, in
responsorial song.
In classical music
In
J. S. Bach
Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque period. He is known for his orchestral music such as the '' Brandenburg Concertos''; instrumental compositions such as the Cello Suites; keyboard wo ...
's ''
Clavier-Übung III
The ''Clavier-Übung III'', sometimes referred to as the ''German Organ Mass'', is a collection of compositions for organ by Johann Sebastian Bach, started in 1735–36 and published in 1739. It is considered Bach's most significant and extensiv ...
'', 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."
Another early use of polytonality occurs in the
classical period in the finale of
Wolfgang Amadeus Mozart
Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Joannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical period. Despite his short life, his rapid pace of composition r ...
's composition ''
A Musical Joke
''A Musical Joke'' (in German: ') K. 522, (Divertimento for two horns and string quartet) is a composition by Wolfgang Amadeus Mozart; the composer entered it in his ' (''Catalogue of All My Works'') on June 14, 1787. Commentators have opined th ...
'', which he deliberately ends with the
violins,
violas and
horns Horns or The Horns may refer to:
* Plural of Horn (instrument), a group of musical instruments all with a horn-shaped bells
* The Horns (Colorado), a summit on Cheyenne Mountain
* ''Horns'' (novel), a dark fantasy novel written in 2010 by Joe Hill ...
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
Petrushka ( rus, Петру́шка, p=pʲɪtˈruʂkə, a=Ru-петрушка.ogg) is a stock character of Russian folk puppetry. Italian puppeteers introduced it in the first third of the 19th century. While most core characters came from Italy ...
'', 1911). 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.
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
Heinrich Ignaz Franz Biber ( bapt. 12 August 1644, Stráž pod Ralskem – 3 May 1704, Salzburg) was a Bohemian-Austrian composer and violinist. Biber worked in Graz and Kroměříž before he illegally left his employer, Prince-Bishop Karl L ...
's short composition ''Battalia'', written in 1673.
Stravinsky's ''
The Rite of Spring
, image = Roerich Rite of Spring.jpg
, image_size = 350px
, caption = Concept design for act 1, part of Nicholas Roerich's designs for Diaghilev's 1913 production of '
, composer = Igor Stravinsky
, based_on ...
'' 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)".
Bartók's "Playsong" demonstrates easily perceivable bitonality through "the harmonic motion of each key ...
eingrelatively uncomplicated and very diatonic". 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
"Les Six" () is a name given to a group of six composers, five of them French and one Swiss, who lived and worked in Montparnasse. The name, inspired by Mily Balakirev's '' The Five'', originates in two 1920 articles by critic Henri Collet in ' ...
, particularly
Darius Milhaud
Darius Milhaud (; 4 September 1892 – 22 June 1974) was a French composer, conductor, and teacher. He was a member of Les Six—also known as ''The Group of Six''—and one of the most prolific composers of the 20th century. His compositions ...
, as well as Americans such as
Aaron Copland
Aaron Copland (, ; November 14, 1900December 2, 1990) was an American composer, composition teacher, writer, and later a conductor of his own and other American music. Copland was referred to by his peers and critics as "the Dean of American Com ...
.
Benjamin Britten
Edward Benjamin Britten, Baron Britten (22 November 1913 – 4 December 1976, aged 63) was an English composer, conductor, and pianist. He was a central figure of 20th-century British music, with a range of works including opera, other ...
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) or to express the main character's "maladjustment" in ''
Peter Grimes
''Peter Grimes'', Op. 33, is an opera in three acts by Benjamin Britten, with a libretto by Montagu Slater based on the section "Peter Grimes", in George Crabbe's long narrative poem '' The Borough''. The "borough" of the opera is a fictional ...
''.
Polytonality and polychords
Polytonality requires the presentation of simultaneous key-centers. The term "
polychord
In music and music theory, a polychord consists of two or more chords, one on top of the other. In shorthand they are written with the top chord above a line and the bottom chord below,Policastro, Michael A. (1999). ''Understanding How to Build ...
" 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, but they may not be explained as a single tertian chord. The
Petrushka chord
The Petrushka chord is a recurring polytonal device used in Igor Stravinsky's ballet '' Petrushka'' and in later music. These two major triads, C major and F major – a tritone apart – clash, "horribly with each other", when sounded together ...
is an example of a polychord. This is the norm in jazz, for example, which makes frequent use of "extended" and polychordal harmonies without any intended suggestion of "multiple keys."
Polyvalency
The following passage, taken from
Beethoven
Ludwig van Beethoven (baptised 17 December 177026 March 1827) was a German composer and pianist. Beethoven remains one of the most admired composers in the history of Western music; his works rank amongst the most performed of the classic ...
's
Piano Sonata in E, Op. 81a (''Les Adieux''), suggests clashes between tonic and dominant harmonies in the same key.
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".
Polymodality
Passages of music, such as
Poulenc's ''
Trois mouvements perpétuels'', I., may be misinterpreted as polytonal rather than polymodal. In this case, two scales are recognizable but are assimilated through the common tonic (B).
Polyscalarity
Polyscalarity is defined as "the simultaneous use of musical objects ''which clearly suggest different source-collections''. Specifically in reference to Stravinsky's music, Tymoczko uses the term polyscalarity out of deference to terminological sensibilities. 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
An octatonic scale is any eight- note musical scale. However, the term most often refers to the symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory (in contrast to jazz theory), this symmetric ...
. 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
''Petrushka'' (french: link=no, Pétrouchka; russian: link=no, Петрушка) is a ballet and orchestral concert work by Russian composer Igor Stravinsky. It was written for the 1911 Paris season of Sergei Diaghilev's Ballets Russes company; ...
''s second tableau was conceived "in two keys".. 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
Paul Hindemith (; 16 November 189528 December 1963) was a German composer, music theorist, teacher, violist and conductor. He founded the Amar Quartet in 1921, touring extensively in Europe. As a composer, he became a major advocate of the ' ...
have questioned whether polytonality is a useful or meaningful notion or "viable auditory possibility". 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 (or part writing) is the linear progression of individual melodic lines (Part (music), voices or parts) and their interaction with one another to create Harmony, harmonies, typically in accordance with the principles of Common practi ...
unit".. Other theorists to question or reject polytonality include
Allen Forte Allen, Allen's or Allens may refer to:
Buildings
* Allen Arena, an indoor arena at Lipscomb University in Nashville, Tennessee
* Allen Center, a skyscraper complex in downtown Houston, Texas
* Allen Fieldhouse, an indoor sports arena on the Univ ...
and
Benjamin Boretz
Benjamin Aaron Boretz (born October 3, 1934) is an American composer and music theorist.
Life and work
Benjamin Boretz was born in Brooklyn, New York to Abraham Jacob Boretz and Leah (Yullis) Boretz. He graduated with a degree in music from Br ...
, who hold that the notion involves logical incoherence.
Other theorists, such as
Dmitri Tymoczko
Dmitri Tymoczko is a composer and music theorist. His music, which draws on rock, jazz, and romanticism, has been performed by ensembles such as the Amernet String Quartet, the Brentano Quartet, Janus, Newspeak, the San Francisco Contemporary Playe ...
, respond that the notion of "tonality" is a psychological, not a logical notion. 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.
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. 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.
See also
*
List of polytonal pieces
*
Bimodality
*
Polymodal chromaticism In music, polymodal chromaticism is the use of any and all musical modes sharing the same tonic simultaneously or in succession and thus creating a texture involving all twelve notes of the chromatic scale ( total chromatic). Alternately it is th ...
*
Elektra chord
The ''Elektra'' chord is a "complexly dissonant signature- chord"Lawrence Kramer. "Fin-de-siècle Fantasies: ''Elektra'', Degeneration and Sexual Science", ''Cambridge Opera Journal'', Vol. 5, No. 2. (Jul., 1993), pp. 141-165. and motivic elabo ...
*
Bridge chord
*
Woody Shaw
Woody Herman Shaw Jr. (December 24, 1944 – May 10, 1989) was an American jazz trumpeter, flugelhornist, cornetist, composer, arranger, band leader, and educator. Shaw is widely known as one of the most important and influential jazz trumpet ...
References
Sources
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* 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, ).
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Further reading
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*
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.
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{{Tonality