200:, 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 worldsâthe homotonal one of his own day and (prophetically) the polytonal one of a couple of centuries later."
535:. Specifically about 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
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130:, 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.
64:
431:
584:, 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 the same time: for example, when listening to two different pieces played by two different instruments in two areas of a room.
181:
125:
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
103:
564:
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
592:
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,
182:
279:(1924) describe him as the progenitor of the technique: "the first work presenting polytonality in typical completenessânot merely in the guise of a more or less happy 'experiment', but responding throughout to the demands of expressionâis beyond all question the grandiose
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539:. 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
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BartĂłk's "Playsong" demonstrates easily perceivable bitonality through "the harmonic motion of each key ... relatively uncomplicated and very diatonic". Here, the "duality of key" featured is A minor and
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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.
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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."
80:
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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
255:, 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.
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517:, I., may be misinterpreted as polytonal rather than polymodal. In this case, two scales are recognizable but are assimilated through the common tonic (B
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1395:, vols. 1 and 2, translated by Arthur Mendel and Otto Ortmann. New York: Associated Music Publishers; London: Schott. Original German edition as
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Although it is only used in one section and intended to represent drunken soldiers, there is an early example of polytonality in
451:, as polyvalency rather than bitonality, with polyvalency being, "the telescoping of diverse functions that should really occur
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Anon. 2010. "SutartinÄs, Lithuanian
Multipart Songs". UNESCO Intangible Cultural Heritage website (accessed 29 January 2016).
1299:
Van den Toorn, Pieter C., and Dmitri
Tymoczko (2003). "Colloquy: Stravinsky and the Octatonic: The Sounds of Stravinsky".
1945:
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Thus polychords do not necessarily suggest polytonality, but they may not be explained as a single tertian chord. The
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1196:
Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur, met 111 muziekvoorbeelden en 7 figuren
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1068:
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RaÄiĆ«naitÄ-VyÄinienÄ, Daiva (2006). "The
Lithuanian Archaic Polyphonic Chant SutartinÄ", translated by E. Novickas.
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Babiracki, Carol M. (1991). "Tribal Music in the Study of Great and Little
Traditions of Indian Music". In
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1198:. Utrecht: A. Oosthoek's Uitg. Mij., 1964 (third printing, Utrecht: Bohn, Scheltema & Holkema, 1977,
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1975:
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relationships, for example to signify the conflict between
Claggart (F minor) and Billy (E major) in
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1184:, foreword by Rokus De Groot, translated by Stephen Taylor. Amsterdam: Amsterdam University Press.
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1316:. University of California Publications in Music 4. Berkeley: University of California Press.
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Comparative
Musicology and Anthropology of Music: Essays on the History of Ethnomusicology
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8:
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306:(1920), right hand in B major and left hand in G major, or both hands in extended G major
1164:, third edition, consulting editor in music, Allan W. Schindler. New York: McGraw-Hill.
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Leeuw points to
Beethoven's use of the clash between tonic and dominant, such as in his
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Other polytonal composers influenced by
Stravinsky include those in the French group,
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Tonality, Atonality, Pantonality A Study of Some Trends in
Twentieth Century Music
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is widely credited with popularizing bitonality, and contemporary writers such as
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Polytonality requires the presentation of simultaneous key-centers. The term "
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New Music in China and The C.C. Liu Collection at the University of Hong Kong
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Tymoczko, Dmitri (2002). "Stravinsky and the Octatonic: A Reconsideration".
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explains these qualities on a deeper level. For example, the passage from
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597:, cited above, uses only notes drawn from the C octatonic collection CâC
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Music of the Twentieth Century: A Study of Its Elements and Structure
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Polyscalarity is defined as "the simultaneous use of musical objects
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unit". Other theorists to question or reject polytonality include
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Example of C- and F-sharp major chords together in Stravinsky's
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Tonal Harmony, with an Introduction to Twentieth-Century Music
34:
1325:. Berkeley and Los Angeles: University of California Press.
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Example of polytonality or extended tonality from Milhaud's
1923:
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Soft and Sweet, Loud and Sour: Looking Back on Polytonality
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Models of Musical Analysis: Early Twentieth-Century Music
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577:, who hold that the notion involves logical incoherence.
359:) or to express the main character's "maladjustment" in
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is the use of only two different keys at the same time.
1244:, 47â48. Hong Kong: Hong Kong University Press, 2005,
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The Operas of Benjamin Britten Expression and Evasion
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used bi- and polytonality in his operas, as well as
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1115:
1078:Casella, Alfred (1924). "Tone Problems of Today".
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533:which clearly suggest different source-collections
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133:Tribes throughout Indiaâincluding the Kuravan of
2085:
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203:Another early use of polytonality occurs in the
126:A major). This six-bar melody is performed as a
1374:. New Haven and London: Yale University Press.
1346:The New Grove Dictionary of Music and Musicians
1214:. Englewood Cliffs, New Jersey: Prentice-Hall.
1089:Cole, Richard, and Ed Schwartz (eds.) (2012).
368:
90:Some examples of bitonality superimpose fully
1939:
1485:
1236:Ryker, Harrison (2005). Invited paper no. 5,
1399:. 3 vols. Mainz, B. Schott's Söhne, 1937â70.
1129:Materials and Concepts in Jazz Improvisation
347:(note the shared enharmonically equivalent G
1126:
1063:. Oxford: Basil Blackwell. pp. 20â41.
873:
1946:
1932:
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1131:(fifth ed.). Grand Rapids: Keytone.
1096:Virginia Tech Multimedia Music Dictionary
1024:
1014:(1949). "The String Quartets of BartĂłk".
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16:Simultaneous use of multiple musical keys
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1037:. Chicago: University of Chicago Press.
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1055:(1993). "Post-Tonal Voice-Leading". In
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94:sections of music in different keys.
1323:Benjamin Britten His Life and Operas
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1313:The Diatonic Modes in Modern Music
1264:. London: Oxford University Press.
434:Polyvalency suggested in Beethoven
409:The following passage, taken from
14:
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1118:America's Musical Life: A History
1907:
1898:
1897:
1393:The Craft of Musical Composition
556:Some music theorists, including
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106:Mozart used polytonality in his
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990:Van den Toorn and Tymoczko 2003
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327:, as well as Americans such as
1771:Modes of limited transposition
1410:. Greenwood Publishing Group.
1212:Twentieth Century Music Idioms
404:
1:
1372:Aspects of Schenkerian Theory
1262:The Oxford Companion to Music
1149:Who Asked the First Question?
661:
551:
1953:
1305:25, no. 1 (Spring): 167â202.
1160:, and Dorothy Payne (1995).
479:Polyvalency in Stravinsky's
56:is the use of more than one
7:
1821:Quartal and quintal harmony
1510:List of modernist composers
1321:White, Eric Walter (1970).
1210:Marquis, G. Welton (1964).
624:
514:Trois mouvements perpétuels
507:Passages of music, such as
369:Polytonality and polychords
10:
2110:
1127:Ellenberger, Kurt (2005).
1114:Crawford, Richard (2001).
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260:Heinrich Ignaz Franz Biber
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1976:Consonance and dissonance
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1455:. Yale University Press.
1430:"Comments by Carl Wilson"
1349:, 2nd edition, edited by
1146:Jordania, Joseph (2006).
1122:. New York: W. W. Norton.
1020:35, no. 3 (July): 377â85.
715:RaÄiĆ«naitÄ-VyÄinienÄ 2006
580:Other theorists, such as
157:âalso use bitonality, in
1453:The Music of BĂ©la BartĂłk
1269:Seymour, Claire (2007).
631:List of polytonal pieces
462:Polyvalency in Beethoven
19:Not to be confused with
2033:Otonality and utonality
1435:The Pet Sounds Sessions
1397:Unterweisung im Tonsatz
283:of Stravinsky (1913)".
209:Wolfgang Amadeus Mozart
1872:Second Viennese School
1865:Schools of composition
1343:(2001). "Bitonality".
1310:Vincent, John (1951).
674:Cole and Schwartz 2012
641:Polymodal chromaticism
499:
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1856:Twelve-tone technique
1451:Wilson, Paul (1992).
1370:Beach, David (1983).
1302:Music Theory Spectrum
1291:Music Theory Spectrum
1260:. (1970). "Harmony".
1081:The Musical Quarterly
1017:The Musical Quarterly
811:Kostka and Payne 1995
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281:Le Sacre du Printemps
262:'s short composition
172:
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37:use of more than one
2053:Schenkerian analysis
2048:Progressive tonality
1357:. London: Macmillan.
243:Fourteen Bagatelles,
117:In traditional music
266:, written in 1673.
1991:Secondary function
1223:52, no. 2: 26â39.
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303:Saudades do Brasil
272:The Rite of Spring
245:Op. 6, 1908), and
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165:In classical music
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1986:Diatonic function
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1462:978-0-300-05111-7
1417:978-0-313-20478-4
1381:978-0-300-02800-3
1332:978-0-520-01679-8
1294:24, no. 1:68â102.
1280:978-1-84383-314-7
1273:. Boydell Press.
1250:978-96-2209-772-8
1190:978-90-5356-765-4
1170:978-0-07-035874-4
1158:Kostka, Stefan M.
1044:978-0-226-57409-7
1031:Philip V. Bohlman
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455:to one another".
441:
415:Piano Sonata in E
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237:, c. 1898â1902),
207:in the finale of
197:Clavier-Ăbung III
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175:Clavier-Ăbung III
112:for comic effect.
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58:harmonic function
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1971:Circle of fifths
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1075:
1069:
1049:
1043:
1022:
1008:
1002:
1000:
997:
995:
994:
982:
965:
953:
941:
926:
914:
902:
890:
878:
866:
851:
839:
827:
815:
803:
791:
779:
767:
755:
743:
739:Babiracki 1991
731:
719:
707:
695:
678:
665:
663:
660:
659:
658:
653:
648:
643:
638:
633:
626:
623:
589:
586:
562:Paul Hindemith
558:Milton Babbitt
553:
550:
528:
525:
504:
501:
449:Third Symphony
406:
403:
370:
367:
325:Darius Milhaud
214:A Musical Joke
166:
163:
118:
115:
109:A Musical Joke
99:
96:
42:simultaneously
15:
9:
6:
4:
3:
2:
2106:
2095:
2092:
2091:
2089:
2074:
2073:Voice leading
2071:
2069:
2066:
2064:
2061:
2059:
2056:
2054:
2051:
2049:
2046:
2044:
2041:
2039:
2036:
2034:
2031:
2029:
2026:
2024:
2021:
2019:
2016:
2014:
2011:
2009:
2006:
2004:
2001:
1999:
1996:
1992:
1989:
1988:
1987:
1984:
1982:
1979:
1977:
1974:
1972:
1969:
1967:
1964:
1963:
1960:
1956:
1949:
1944:
1942:
1937:
1935:
1930:
1929:
1926:
1914:
1910:
1906:
1904:
1896:
1895:
1893:
1892:
1884:
1878:
1875:
1873:
1870:
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1863:
1857:
1854:
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1802:
1799:
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1784:
1782:
1779:
1777:
1774:
1772:
1769:
1767:
1764:
1762:
1759:
1757:
1756:Expressionism
1754:
1752:
1749:
1747:
1744:
1743:
1741:
1733:
1721:
1718:
1716:
1713:
1711:
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1703:
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1677:
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1662:
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1627:
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1607:
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1600:
1597:
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1579:
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1481:
1476:
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1472:
1464:
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1454:
1449:
1445:
1441:
1437:
1436:
1431:
1427:
1423:
1419:
1413:
1409:
1405:
1404:Reti, Rudolph
1401:
1398:
1394:
1390:
1387:
1383:
1377:
1373:
1368:
1367:
1356:
1352:
1351:Stanley Sadie
1348:
1347:
1342:
1338:
1334:
1328:
1324:
1319:
1315:
1314:
1308:
1304:
1303:
1297:
1293:
1292:
1286:
1282:
1276:
1272:
1267:
1263:
1259:
1255:
1251:
1247:
1243:
1239:
1234:
1230:
1226:
1222:
1217:
1213:
1208:
1205:
1204:9789031302444
1201:
1197:
1191:
1187:
1183:
1179:
1178:Leeuw, Ton de
1175:
1171:
1167:
1163:
1159:
1155:
1151:
1150:
1144:
1140:
1138:0-9709811-3-9
1134:
1130:
1125:
1120:
1119:
1112:
1101:
1100:Virginia Tech
1097:
1093:
1092:"Polyharmony"
1087:
1083:
1082:
1076:
1072:
1070:9780631143352
1066:
1062:
1058:
1054:
1050:
1046:
1040:
1036:
1032:
1028:
1023:
1019:
1018:
1013:
1009:
1004:
1003:
991:
986:
979:
978:Tymoczko 2002
974:
972:
970:
962:
957:
950:
945:
938:
937:Tymoczko 2002
933:
931:
923:
922:Tymoczko 2002
918:
911:
906:
899:
894:
887:
882:
875:
870:
863:
858:
856:
848:
843:
836:
831:
824:
819:
812:
807:
800:
795:
788:
783:
776:
775:Crawford 2001
771:
764:
763:Whittall 2001
759:
752:
747:
740:
735:
728:
723:
716:
711:
704:
703:Jordania 2006
699:
692:
687:
685:
683:
675:
670:
666:
657:
654:
652:
649:
647:
646:Elektra chord
644:
642:
639:
637:
634:
632:
629:
628:
622:
596:
585:
583:
578:
576:
572:
568:
567:voice-leading
563:
559:
549:
544:
543:
538:
534:
527:Polyscalarity
524:
516:
515:
510:
488:
484:
483:
477:
460:
456:
454:
453:in succession
450:
432:
428:
426:
424:
412:
402:
400:
382:
378:
376:
366:
364:
363:
346:
345:
340:
336:
332:
330:
329:Aaron Copland
326:
322:
305:
304:
298:
294:
284:
282:
278:
274:
273:
269:Stravinsky's
267:
265:
261:
256:
254:
253:
248:
244:
240:
236:
232:
228:
224:
220:
216:
215:
210:
206:
201:
199:
198:
193:
177:by J. S. Bach
176:
171:
162:
160:
156:
152:
148:
144:
143:Uttar Pradesh
140:
136:
131:
129:
124:
111:
110:
104:
95:
93:
76:
72:
71:
65:
61:
59:
55:
51:
47:
43:
40:
36:
32:
28:
22:
2094:Polytonality
2068:Tonicization
2043:Polytonality
2042:
2038:Parallel key
1998:Figured bass
1889:
1851:Tone cluster
1806:Polytonality
1805:
1751:Experimental
1452:
1433:
1426:Wilson, Carl
1407:
1396:
1392:
1371:
1355:John Tyrrell
1344:
1322:
1312:
1300:
1289:
1270:
1261:
1241:
1237:
1220:
1211:
1195:
1181:
1161:
1147:
1128:
1117:
1103:. Retrieved
1095:
1079:
1060:
1053:Baker, James
1034:
1015:
985:
961:Babbitt 1949
956:
944:
917:
910:Vincent 1951
905:
893:
886:Marquis 1964
881:
869:
862:Marquis 1964
842:
835:Seymour 2007
830:
823:Marquis 1964
818:
806:
799:Casella 1924
794:
782:
770:
758:
751:Scholes 1970
746:
734:
722:
710:
698:
669:
651:Bridge chord
594:
591:
588:Octatonicism
579:
555:
540:
532:
530:
512:
506:
503:Polymodality
480:
452:
446:
422:
408:
396:
372:
362:Peter Grimes
360:
342:
333:
318:
301:
285:
280:
270:
268:
263:
257:
250:
242:
234:
231:Charles Ives
212:
202:
195:
189:
174:
159:responsorial
132:
120:
107:
89:
68:
53:
49:
45:
30:
27:Polytonality
26:
25:
2058:Sonata form
2023:Neotonality
1801:Polyrhythms
1776:Neotonality
1664:Szymanowski
1438:(Booklet).
1391:(1941â42).
1084:10:159â171.
1027:Bruno Nettl
571:Allen Forte
405:Polyvalency
239:BĂ©la BartĂłk
54:polyvalency
50:Polyvalence
31:polyharmony
2018:Modulation
1846:Surrealism
1841:Stochastic
1831:Sound mass
1766:Microtonal
1738:techniques
1736:Genres and
1684:Stravinsky
1644:Skalkottas
1549:Schoenberg
1105:2007-08-04
949:Baker 1993
898:Leeuw 2005
847:White 1970
837:, 141â142.
787:Ryker 2005
753:, 448â449.
727:Anon. 2010
705:, 119â120.
691:Leeuw 2005
662:References
656:Woody Shaw
636:Bimodality
552:Challenges
542:Petrouchka
487:Leeuw 2005
423:Les Adieux
344:Billy Budd
339:enharmonic
247:Stravinsky
192:J. S. Bach
153:, and the
123:sutartines
92:harmonized
46:Bitonality
1826:Serialism
1746:Atonality
1674:Prokofiev
1517:Composers
1229:0024-5089
595:Petrushka
411:Beethoven
375:polychord
252:Petrushka
70:Petrushka
33:) is the
21:Polyphony
2088:Category
2028:Ostinato
1955:Tonality
1903:Category
1836:Spectral
1761:Futurism
1695:Americas
1679:Scriabin
1650:Hungary
1625:Germany
1609:Messiaen
1604:Koechlin
1580:Finland
1570:Czechia
1564:Pousseur
1560:Belgium
1530:Austria
1428:(1997).
1406:(1978).
1221:Lituanus
1180:(2005).
1152:. Logos.
1033:(eds.).
625:See also
618:♯
612:♯
606:♯
600:♯
520:♭
418:♭
356:♭
350:♯
290:♯
264:Battalia
235:Psalm 67
139:Jaunsari
1966:Cadence
1888: â
1816:Process
1705:Antheil
1670:Russia
1660:Poland
1640:Greece
1634:Strauss
1614:Milhaud
1599:Jolivet
1590:France
1584:Bergman
1059:(ed.).
999:Sources
509:Poulenc
321:Les Six
293:minor.
277:Casella
219:violins
98:History
35:musical
1913:Portal
1715:Cowell
1710:Carter
1654:BartĂłk
1619:VarĂšse
1554:Webern
1544:Mahler
1539:Krenek
1524:Europe
1459:
1414:
1378:
1329:
1277:
1248:
1227:
1202:
1188:
1168:
1135:
1067:
1041:
992:, 179.
963:, 380.
912:, 272.
849:, 119.
813:, 495.
801:, 164.
777:, 503.
615:âGâAâA
223:violas
161:song.
151:Santal
149:, the
145:, the
137:, the
135:Kerala
73:(see:
29:(also
1791:Noise
1629:Reger
1594:Henry
1240:. In
980:, 84.
951:, 35.
939:, 85.
924:, 83.
900:, 88.
876:, 20.
741:, 76.
693:, 87.
546:'
489:, 88)
227:horns
155:Munda
128:canon
1720:Ives
1574:HĂĄba
1534:Berg
1457:ISBN
1412:ISBN
1376:ISBN
1353:and
1327:ISBN
1275:ISBN
1246:ISBN
1225:ISSN
1200:ISBN
1186:ISBN
1166:ISBN
1133:ISBN
1065:ISBN
1039:ISBN
609:âEâF
573:and
560:and
482:Mass
225:and
147:Gond
2008:Key
888:, .
864:, .
523:).
511:'s
413:'s
194:'s
190:In
141:of
52:or
39:key
2090::
1442:.
1432:.
1206:).
1098:.
1094:.
1029:;
968:^
929:^
854:^
681:^
621:.
603:âD
365:.
353:/A
331:.
221:,
44:.
1947:e
1940:t
1933:v
1493:e
1486:t
1479:v
1465:.
1446:.
1420:.
1384:.
1335:.
1283:.
1252:.
1231:.
1192:.
1172:.
1141:.
1108:.
1073:.
1047:.
825:.
789:.
765:.
729:.
717:.
676:.
485:(
425:)
287:C
249:(
241:(
233:(
77:)
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
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