211:, 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."
546:. 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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141:, 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.
595:, 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.
136:
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
575:
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
603:
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,
75:
290:(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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114:
192:
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388:" 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:
550:. 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
297:
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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559:
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.
478:
450:
412:
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."
400:
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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
266:, 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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Although it is only used in one section and intended to represent drunken soldiers, there is an early example of polytonality in
462:, 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).
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Van den Toorn, Pieter C., and Dmitri
Tymoczko (2003). "Colloquy: Stravinsky and the Octatonic: The Sounds of Stravinsky".
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Thus polychords do not necessarily suggest polytonality, but they may not be explained as a single tertian chord. The
1207:
Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur, met 111 muziekvoorbeelden en 7 figuren
449:
94:
1230:
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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1209:. Utrecht: A. Oosthoek's Uitg. Mij., 1964 (third printing, Utrecht: Bohn, Scheltema & Holkema, 1977,
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relationships, for example to signify the conflict between
Claggart (F minor) and Billy (E major) in
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1195:, foreword by Rokus De Groot, translated by Stephen Taylor. Amsterdam: Amsterdam University Press.
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1327:. 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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317:(1920), right hand in B major and left hand in G major, or both hands in extended G major
1175:, third edition, consulting editor in music, Allan W. Schindler. New York: McGraw-Hill.
458:
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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31:
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explains these qualities on a deeper level. For example, the passage from
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1965:
438:, suggests clashes between tonic and dominant harmonies in the same key.
608:, 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
1938:
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Tonal Harmony, with an Introduction to Twentieth-Century Music
1336:. Berkeley and Los Angeles: University of California Press.
311:
Example of polytonality or extended tonality from Milhaud's
1934:
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Soft and Sweet, Loud and Sour: Looking Back on Polytonality
1000:
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Models of Musical Analysis: Early Twentieth-Century Music
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588:, who hold that the notion involves logical incoherence.
370:) 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.
1255:, 47â48. Hong Kong: Hong Kong University Press, 2005,
1282:
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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1089:Casella, Alfred (1924). "Tone Problems of Today".
544:which clearly suggest different source-collections
684:
144:Tribes throughout Indiaâincluding the Kuravan of
821:
214:Another early use of polytonality occurs in the
137:A major). This six-bar melody is performed as a
1385:. New Haven and London: Yale University Press.
1357:The New Grove Dictionary of Music and Musicians
1225:. Englewood Cliffs, New Jersey: Prentice-Hall.
1100:Cole, Richard, and Ed Schwartz (eds.) (2012).
101:Some examples of bitonality superimpose fully
1950:
1496:
1247:Ryker, Harrison (2005). Invited paper no. 5,
8:
1410:. 3 vols. Mainz, B. Schott's Söhne, 1937â70.
1140:Materials and Concepts in Jazz Improvisation
358:(note the shared enharmonically equivalent G
1074:. Oxford: Basil Blackwell. pp. 20â41.
884:
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1142:(fifth ed.). Grand Rapids: Keytone.
1107:Virginia Tech Multimedia Music Dictionary
1025:(1949). "The String Quartets of BartĂłk".
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27:Simultaneous use of multiple musical keys
1048:. Chicago: University of Chicago Press.
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395:Separate chords within an extended chord
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1066:(1993). "Post-Tonal Voice-Leading". In
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228:, which he deliberately ends with the
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132:Lithuanian traditional singing style
105:sections of music in different keys.
7:
1334:Benjamin Britten His Life and Operas
1324:The Diatonic Modes in Modern Music
1275:. London: Oxford University Press.
445:Polyvalency suggested in Beethoven
420:The following passage, taken from
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1129:America's Musical Life: A History
1918:
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1404:The Craft of Musical Composition
567:Some music theorists, including
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117:Mozart used polytonality in his
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1001:Van den Toorn and Tymoczko 2003
338:, as well as Americans such as
1782:Modes of limited transposition
1421:. Greenwood Publishing Group.
1223:Twentieth Century Music Idioms
1:
1383:Aspects of Schenkerian Theory
1273:The Oxford Companion to Music
1160:Who Asked the First Question?
1316:25, no. 1 (Spring): 167â202.
1171:, and Dorothy Payne (1995).
490:Polyvalency in Stravinsky's
67:is the use of more than one
1832:Quartal and quintal harmony
1521:List of modernist composers
1332:White, Eric Walter (1970).
1221:Marquis, G. Welton (1964).
525:Trois mouvements perpétuels
518:Passages of music, such as
380:Polytonality and polychords
2121:
1138:Ellenberger, Kurt (2005).
1125:Crawford, Richard (2001).
271:Heinrich Ignaz Franz Biber
29:
1987:Consonance and dissonance
1972:
1896:
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1466:. Yale University Press.
1441:"Comments by Carl Wilson"
1360:, 2nd edition, edited by
1157:Jordania, Joseph (2006).
1133:. New York: W. W. Norton.
1031:35, no. 3 (July): 377â85.
726:RaÄiĆ«naitÄ-VyÄinienÄ 2006
591:Other theorists, such as
168:âalso use bitonality, in
1464:The Music of BĂ©la BartĂłk
1280:Seymour, Claire (2007).
642:List of polytonal pieces
473:Polyvalency in Beethoven
30:Not to be confused with
2044:Otonality and utonality
1446:The Pet Sounds Sessions
1408:Unterweisung im Tonsatz
294:of Stravinsky (1913)".
220:Wolfgang Amadeus Mozart
1883:Second Viennese School
1876:Schools of composition
1354:(2001). "Bitonality".
1321:Vincent, John (1951).
685:Cole and Schwartz 2012
652:Polymodal chromaticism
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1867:Twelve-tone technique
1462:Wilson, Paul (1992).
1381:Beach, David (1983).
1313:Music Theory Spectrum
1302:Music Theory Spectrum
1271:. (1970). "Harmony".
1092:The Musical Quarterly
1028:The Musical Quarterly
822:Kostka and Payne 1995
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292:Le Sacre du Printemps
273:'s short composition
183:
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48:use of more than one
2064:Schenkerian analysis
2059:Progressive tonality
1368:. London: Macmillan.
254:Fourteen Bagatelles,
128:In traditional music
277:, written in 1673.
2002:Secondary function
1234:52, no. 2: 26â39.
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283:The Rite of Spring
256:Op. 6, 1908), and
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176:In classical music
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1997:Diatonic function
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1473:978-0-300-05111-7
1428:978-0-313-20478-4
1392:978-0-300-02800-3
1343:978-0-520-01679-8
1305:24, no. 1:68â102.
1291:978-1-84383-314-7
1284:. Boydell Press.
1261:978-96-2209-772-8
1201:978-90-5356-765-4
1181:978-0-07-035874-4
1169:Kostka, Stefan M.
1055:978-0-226-57409-7
1042:Philip V. Bohlman
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466:to one another".
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426:Piano Sonata in E
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208:Clavier-Ăbung III
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750:Babiracki 1991
742:
730:
718:
706:
689:
676:
674:
671:
670:
669:
664:
659:
654:
649:
644:
637:
634:
600:
597:
573:Paul Hindemith
569:Milton Babbitt
564:
561:
539:
536:
515:
512:
460:Third Symphony
417:
414:
381:
378:
336:Darius Milhaud
225:A Musical Joke
177:
174:
129:
126:
120:A Musical Joke
110:
107:
53:simultaneously
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2117:
2106:
2103:
2102:
2100:
2085:
2084:Voice leading
2082:
2080:
2077:
2075:
2072:
2070:
2067:
2065:
2062:
2060:
2057:
2055:
2052:
2050:
2047:
2045:
2042:
2040:
2037:
2035:
2032:
2030:
2027:
2025:
2022:
2020:
2017:
2015:
2012:
2010:
2007:
2003:
2000:
1999:
1998:
1995:
1993:
1990:
1988:
1985:
1983:
1980:
1978:
1975:
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1971:
1967:
1960:
1955:
1953:
1948:
1946:
1941:
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1937:
1925:
1921:
1917:
1915:
1907:
1906:
1904:
1903:
1895:
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1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1767:Expressionism
1765:
1763:
1760:
1758:
1755:
1754:
1752:
1744:
1732:
1729:
1727:
1724:
1722:
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1696:
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1676:
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1596:
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1576:
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1506:
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1499:
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1483:
1475:
1469:
1465:
1460:
1456:
1452:
1448:
1447:
1442:
1438:
1434:
1430:
1424:
1420:
1416:
1415:Reti, Rudolph
1412:
1409:
1405:
1401:
1398:
1394:
1388:
1384:
1379:
1378:
1374:
1367:
1363:
1362:Stanley Sadie
1359:
1358:
1353:
1349:
1345:
1339:
1335:
1330:
1326:
1325:
1319:
1315:
1314:
1308:
1304:
1303:
1297:
1293:
1287:
1283:
1278:
1274:
1270:
1266:
1262:
1258:
1254:
1250:
1245:
1241:
1237:
1233:
1228:
1224:
1219:
1216:
1215:9789031302444
1212:
1208:
1202:
1198:
1194:
1190:
1189:Leeuw, Ton de
1186:
1182:
1178:
1174:
1170:
1166:
1162:
1161:
1155:
1151:
1149:0-9709811-3-9
1145:
1141:
1136:
1131:
1130:
1123:
1112:
1111:Virginia Tech
1108:
1104:
1103:"Polyharmony"
1098:
1094:
1093:
1087:
1083:
1081:9780631143352
1077:
1073:
1069:
1065:
1061:
1057:
1051:
1047:
1043:
1039:
1034:
1030:
1029:
1024:
1020:
1015:
1014:
1009:
1002:
997:
994:
990:
989:Tymoczko 2002
985:
983:
981:
977:
973:
968:
965:
961:
956:
953:
949:
948:Tymoczko 2002
944:
942:
938:
934:
933:Tymoczko 2002
929:
926:
922:
917:
914:
910:
905:
902:
898:
893:
890:
886:
881:
878:
874:
869:
867:
863:
859:
854:
851:
847:
842:
839:
835:
830:
827:
823:
818:
815:
811:
806:
803:
799:
794:
791:
787:
786:Crawford 2001
782:
779:
775:
774:Whittall 2001
770:
767:
763:
758:
755:
751:
746:
743:
739:
734:
731:
727:
722:
719:
715:
714:Jordania 2006
710:
707:
703:
698:
696:
694:
690:
686:
681:
678:
672:
668:
665:
663:
660:
658:
657:Elektra chord
655:
653:
650:
648:
645:
643:
640:
639:
635:
633:
607:
598:
596:
594:
589:
587:
583:
579:
578:voice-leading
574:
570:
562:
560:
555:
554:
549:
545:
538:Polyscalarity
537:
535:
527:
526:
521:
513:
499:
495:
494:
488:
471:
467:
465:
464:in succession
461:
443:
439:
437:
435:
423:
415:
413:
411:
393:
389:
387:
379:
377:
375:
374:
357:
356:
351:
347:
343:
341:
340:Aaron Copland
337:
333:
316:
315:
309:
305:
295:
293:
289:
285:
284:
280:Stravinsky's
278:
276:
272:
267:
265:
264:
259:
255:
251:
247:
243:
239:
235:
231:
227:
226:
221:
217:
212:
210:
209:
204:
188:by J. S. Bach
187:
182:
175:
173:
171:
167:
163:
159:
155:
154:Uttar Pradesh
151:
147:
142:
140:
135:
127:
122:
121:
115:
108:
106:
104:
87:
83:
82:
76:
72:
70:
66:
62:
58:
54:
51:
47:
43:
39:
33:
19:
2105:Polytonality
2079:Tonicization
2054:Polytonality
2053:
2049:Parallel key
2009:Figured bass
1900:
1862:Tone cluster
1817:Polytonality
1816:
1762:Experimental
1463:
1444:
1437:Wilson, Carl
1418:
1407:
1403:
1382:
1366:John Tyrrell
1355:
1333:
1323:
1311:
1300:
1281:
1272:
1252:
1248:
1231:
1222:
1206:
1192:
1172:
1158:
1139:
1128:
1114:. Retrieved
1106:
1090:
1071:
1064:Baker, James
1045:
1026:
996:
972:Babbitt 1949
967:
955:
928:
921:Vincent 1951
916:
904:
897:Marquis 1964
892:
880:
873:Marquis 1964
853:
846:Seymour 2007
841:
834:Marquis 1964
829:
817:
810:Casella 1924
805:
793:
781:
769:
762:Scholes 1970
757:
745:
733:
721:
709:
680:
662:Bridge chord
605:
602:
599:Octatonicism
590:
566:
551:
543:
541:
523:
517:
514:Polymodality
491:
463:
457:
433:
419:
407:
383:
373:Peter Grimes
371:
353:
344:
329:
312:
296:
291:
281:
279:
274:
268:
261:
253:
245:
242:Charles Ives
223:
213:
206:
200:
185:
170:responsorial
143:
131:
118:
100:
79:
64:
60:
56:
41:
38:Polytonality
37:
36:
2069:Sonata form
2034:Neotonality
1812:Polyrhythms
1787:Neotonality
1675:Szymanowski
1449:(Booklet).
1402:(1941â42).
1095:10:159â171.
1038:Bruno Nettl
582:Allen Forte
416:Polyvalency
250:BĂ©la BartĂłk
65:polyvalency
61:Polyvalence
42:polyharmony
2029:Modulation
1857:Surrealism
1852:Stochastic
1842:Sound mass
1777:Microtonal
1749:techniques
1747:Genres and
1695:Stravinsky
1655:Skalkottas
1560:Schoenberg
1116:2007-08-04
960:Baker 1993
909:Leeuw 2005
858:White 1970
848:, 141â142.
798:Ryker 2005
764:, 448â449.
738:Anon. 2010
716:, 119â120.
702:Leeuw 2005
673:References
667:Woody Shaw
647:Bimodality
563:Challenges
553:Petrouchka
498:Leeuw 2005
434:Les Adieux
355:Billy Budd
350:enharmonic
258:Stravinsky
203:J. S. Bach
164:, and the
134:sutartines
103:harmonized
57:Bitonality
1837:Serialism
1757:Atonality
1685:Prokofiev
1528:Composers
1240:0024-5089
606:Petrushka
422:Beethoven
386:polychord
263:Petrushka
81:Petrushka
44:) is the
32:Polyphony
2099:Category
2039:Ostinato
1966:Tonality
1914:Category
1847:Spectral
1772:Futurism
1706:Americas
1690:Scriabin
1661:Hungary
1636:Germany
1620:Messiaen
1615:Koechlin
1591:Finland
1581:Czechia
1575:Pousseur
1571:Belgium
1541:Austria
1439:(1997).
1417:(1978).
1232:Lituanus
1191:(2005).
1163:. Logos.
1044:(eds.).
636:See also
629:♯
623:♯
617:♯
611:♯
531:♭
429:♭
367:♭
361:♯
301:♯
275:Battalia
246:Psalm 67
150:Jaunsari
1977:Cadence
1899: â
1827:Process
1716:Antheil
1681:Russia
1671:Poland
1651:Greece
1645:Strauss
1625:Milhaud
1610:Jolivet
1601:France
1595:Bergman
1070:(ed.).
1010:Sources
520:Poulenc
332:Les Six
304:minor.
288:Casella
230:violins
109:History
46:musical
18:Bitonal
1924:Portal
1726:Cowell
1721:Carter
1665:BartĂłk
1630:VarĂšse
1565:Webern
1555:Mahler
1550:Krenek
1535:Europe
1470:
1425:
1389:
1340:
1288:
1259:
1238:
1213:
1199:
1179:
1146:
1078:
1052:
1003:, 179.
974:, 380.
923:, 272.
860:, 119.
824:, 495.
812:, 164.
788:, 503.
626:âGâAâA
234:violas
172:song.
162:Santal
160:, the
156:, the
148:, the
146:Kerala
84:(see:
40:(also
1802:Noise
1640:Reger
1605:Henry
1251:. In
991:, 84.
962:, 35.
950:, 85.
935:, 83.
911:, 88.
887:, 20.
752:, 76.
704:, 87.
557:'
500:, 88)
238:horns
166:Munda
139:canon
1731:Ives
1585:HĂĄba
1545:Berg
1468:ISBN
1423:ISBN
1387:ISBN
1364:and
1338:ISBN
1286:ISBN
1257:ISBN
1236:ISSN
1211:ISBN
1197:ISBN
1177:ISBN
1144:ISBN
1076:ISBN
1050:ISBN
620:âEâF
584:and
571:and
493:Mass
236:and
158:Gond
2019:Key
899:, .
875:, .
534:).
522:'s
424:'s
205:'s
201:In
152:of
63:or
50:key
2101::
1453:.
1443:.
1217:).
1109:.
1105:.
1040:;
979:^
940:^
865:^
692:^
632:.
614:âD
376:.
364:/A
342:.
232:,
55:.
1958:e
1951:t
1944:v
1504:e
1497:t
1490:v
1476:.
1457:.
1431:.
1395:.
1346:.
1294:.
1263:.
1242:.
1203:.
1183:.
1152:.
1119:.
1084:.
1058:.
836:.
800:.
776:.
740:.
728:.
687:.
496:(
436:)
298:C
260:(
252:(
244:(
88:)
34:.
20:)
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