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812:) in works including String Quartets Nos. 6 and 7. Each permutation contains a just chromatic scale, however, transformations (transposition and inversion) produce pitches outside of the primary row form, as already occurs in the inversion of P0. The pitches of each hexachord are drawn from different
50:
689:
Schoenberg specified many strict rules and desirable guidelines for the construction of tone rows such as number of notes and intervals to avoid. Tone rows that depart from these guidelines include the above tone row from Berg's Violin
Concerto which contains triads and tonal emphasis, and the tone
857:
681:
331:
Minuet Trio, where P-0 is used to construct the opening melody and later varied through transposition, as P-6, and also in articulation and dynamics. It is then varied again through inversion, untransposed, taking form I-0. However, rows may be combined to produce melodies or harmonies in more
137:
797:
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In this tone row, if the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion, the next three are retrograde, and the last three are its inversion. A row created in this manner, through variants of a
265:
723:
537:
603:
A "weighted aggregate" is an aggregate in which the twelfth pitch does not appear until at least one pitch has appeared at least twice, supplied by segments of different set forms. It seems to have been first used in
665:
569:
A "secondary set" is a tone row which is derived from or, "results from the reversed coupling of hexachords", when a given row form is immediately repeated. For example, the row form consisting of two hexachords:
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when repeated immediately results in the following succession of two aggregates, in the middle of which is a new and complete aggregate beginning with the second hexachord:
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343:—such as the use of consecutive imperfect consonances (thirds or sixths)—when constructing tone rows, reserving such use for the time when the dissonance is completely
655:
263:
767:
276:, which may also appear as RI11 or RI–11). The numbers indicate the initial (P or I) or final (R or RI) pitch-class number of the given row form, most often with
612:. An aggregate may be vertically or horizontally weighted. An "all-partition array" is created by combining a collection of hexachordally combinatorial arrays.
721:
259:
fills in a chromatic fourth, with B as the pivot (end of P1 and beginning of IR8), and thus linked by the prominent tritone in the center of the row.
1497:
733:
used a five-tone row, chromatically filling out the space of a major third centered tonally on C (C–E), in one of his early serial compositions,
550:, each vertical line (four trichords labeled a–d) is an aggregate while each horizontal line (four trichords labeled a–d) is also an aggregate
1783:
183:
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In his twelve-tone practice, Stravinsky preferred the inverse-retrograde (IR) to the retrograde-inverse (RI), as for example in his
507:
The "set-complex" is the forty-eight forms of the set generated by stating each "aspect" or transformation on each pitch class.
414:
37:
202:
also used the technique but, on the whole, "Mozart seems to have employed serial technique far more often than
Beethoven".
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complicated ways, such as taking successive or multiple pitches of a melody from two different row forms, as described at
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A twelve-tone composition will take one or more tone rows, called the "prime form", as its basis plus their
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for details). These forms may be used to construct a melody in a straightforward manner as in
Schoenberg's
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is a tone row arranged so that it contains one instance of each interval within the octave, 0 through 11.
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421:
359:
1549:
1432:
Hunter, David J.; Hippel, Paul T. von (February 2003). "How Rare Is
Symmetry in Musical 12-Tone Rows?".
536:
664:
461:
The tone rows of many of Webern's other late works are similarly intricate. The tone row for Webern's
351:, however, sometimes incorporated tonal elements into his twelve-tone works. The main tone row of his
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and that "Schoenberg repressed his knowledge of classical serialism because it would have injured his
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Serial
Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern
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1329:, translated from the Dutch by Stephen Taylor (Amsterdam: Amsterdam University Press, 2005).
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Some tone rows have a high degree of internal organization. An example is the tone row from
243:
132:, the registrally fixed pitches of which correspond with duration units and metronome marks.
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1620:
1341:(Utrecht: Oosthoek, 1964; third impression, Utrecht: Bohn, Scheltema & Holkema, 1977).
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199:
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Stephen C. Brown, "Twelve-Tone Rows and
Aggregate Melodies in the Music of Shostakovich,"
8:
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643:, B) a descending perfect fifth followed by an ascending major second and a descending
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1361:(4th ed.). Berkeley, Los Angeles, and London: University of California Press.
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1380:(2nd, revised and expanded ed.). Berkeley: University of California Press.
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Schoenberg's Serial
Odyssey: The Evolution of his Twelve-Tone Method, 1914–1928
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605:
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208:
1314:
529:. An "array" is a succession of aggregates. The term is also used to refer to
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Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur
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323:(inversion, retrograde, retrograde inversion, as well as transposition; see
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Shostakovich to the Avant-garde. Dmitri
Shostakovich: The String Quartets
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1261:, "Ben Johnston's Extended Just Intonation: A Guide for Interpreters",
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178:(1742) and by the late eighteenth century it is found in works such as
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Contemplating
Shostakovich: Life, Music and Film: Life, Music and Film
157:. Tone rows were widely used in 20th-century contemporary music, like
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1539:
1510:
1327:
Music of the
Twentieth Century: A Study of Its Elements and Structure
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20:
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161:'s use of twelve-tone rows, "without dodecaphonic transformations."
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340:
272:
Tone rows are designated by letters and subscript numbers (e.g.: RI
389:. This whole tone scale reappears in the second movement when the
636:
390:
128:
1402:. Cambridge Introductions to Music. Cambridge University Press.
717:, symmetrical about the central tone with one note (D) repeated.
700:
which contains a repeated note making it a 'thirteen-tone row':
216:
claims that Schoenberg was aware of this serial practice in the
1588:
339:
Initially, Schoenberg required the avoidance of suggestions of
237:
816:
or utonality on A+ utonality, C otonality and utonality, and E
1303:(Autumn 1955). "Strict Serial Technique in Classical Music".
540:
First array of four aggregates (numbered 1–4 at bottom) from
58:
284:"P" indicates prime, a forward-directed right-side up form.
110:, though both larger and smaller sets are sometimes found.
771:
which "retained only the rudiments of the 12-note series".
992:
495:
Audio playback is not supported in your browser. You can
427:
Audio playback is not supported in your browser. You can
365:
Audio playback is not supported in your browser. You can
165:
1200:
3, no. 2 (Spring–Summer 1965): 104–126, citation on 118.
404:
is quoted literally in the woodwinds (mostly clarinet).
232:"Prime (music)" redirects here. For the prime form, see
1505:
1172:
1160:
1137:(Rochester: University of Rochester Press, 2009): 228.
164:
A tone row has been identified in the A minor prelude,
1058:
1010:
998:
377:
This tone row consists of alternating minor and major
227:
1131:
Intimate Voices: The Twentieth-Century String Quartet
385:
of the violin, followed by a portion of an ascending
32:"Mirror forms", P, R, I, and RI, of a tone row (from
1148:
1111:
1087:
1034:
1099:
1022:
930:
19:"Reihe" redirects here. For the music journal, see
1267:29, no. 2 (Summer 1991): 106–137, citation on 127.
1219:17, no. 2 (Spring 1999): 231–271, citation on 242.
1046:
1209:Joseph N. Strauss, "Stravinsky's Serial 'Mistakes
1794:
765:Unordered sets from the second of Stockhausen's
631:series consists of three cells: A) an ascending
1227:
1225:
1077:
1075:
1073:
788:Unordered sets from the third of Stockhausen's
315:, for example P8 is a T(4) transposition of P4.
920:
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206:used a twelve-tone row in the opening of his
1784:List of dodecaphonic and serial compositions
1222:
1070:
84:
1242:
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915:
98:, is a non-repetitive ordering of a set of
1779:
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1484:
983:"Discovery Reveals Bach's Postmodern Side"
397:" (It is enough) from J.S. Bach's cantata
952:. (Farnham: Ashgate Publishing, 2013): .
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833:Primary forms of the just tone row from
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948:Andrew Kirkman and Alexander Ivashkin,
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1190:Claudio Spies, "Notes on Stravinsky's
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1016:
1004:
973:, Vol. 59, No. 2 (Fall 2015): 191–234.
668:Prime form of five-note tone row from
291:, a forward-directed upside-down form.
188:String Quartet in E-flat major, K. 428
16:Sequence of all twelve chromatic tones
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554:An aggregate may be achieved through
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1472:, Harald Fripertinger, Peter Lackner
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113:
247:Principal forms of the tone row of
228:Theory and compositional techniques
102:, typically of the twelve notes in
13:
1425:
753:Basic row forms from Stravinsky's
14:
1819:
1463:
1435:The American Mathematical Monthly
298:, a backwards right-side up form.
192:String Quintet in G minor, K. 516
1778:
1587:
1470:Database on tone rows and tropes
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547:Composition for Four Instruments
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305:, a backwards upside-down form.
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184:C major String Quartet, K. 157
44:because...they are identical".
1:
896:
415:Concerto for Nine Instruments
1708:All-interval twelve-tone row
891:List of tone rows and series
808:uses a "just tone row" (see
707:Thirteen-note tone row from
512:all-interval twelve-tone row
492:
424:
362:
7:
1285:. Oxford: Clarendon Press.
864:
481:) and is composed of three
196:Symphony in G minor, K. 550
145:Tone rows are the basis of
10:
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1309:. New Series (37): 12–24.
231:
129:Gruppen für drei Orchester
18:
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1596:
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1517:
1315:10.1017/S0040298200055212
1264:Perspectives of New Music
1216:The Journal of Musicology
1197:Perspectives of New Music
822:- otonality, outlining a
400:O Ewigkeit, du Donnerwort
175:The Well-Tempered Clavier
912:, 154. Italics original.
735:In memoriam Dylan Thomas
674:In memoriam Dylan Thomas
521:(or "aggregate") is the
355:hints at this tonality:
236:. For the interval, see
38:Variations for Orchestra
971:Journal of Music Theory
497:download the audio file
429:download the audio file
367:download the audio file
1713:All-trichord hexachord
1661:Second Viennese School
1376:Perle, George (1996).
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1507:Twelve-tone technique
1281:Haimo, Ethan (1990).
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616:Nonstandard tone rows
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463:String Quartet Op. 28
417:Op. 24, shown below.
334:twelve-tone technique
325:twelve-tone technique
246:
168:889, from book II of
151:twelve-tone technique
124:Karlheinz Stockhausen
121:
31:
1656:Josef Matthias Hauer
1621:Retrograde inversion
1378:Twelve-Tone Tonality
839:String Quartet No. 7
610:String Quartet No. 4
303:retrograde-inversion
253:Variations for piano
1738:Formula composition
995:, 6 September 2009.
629:Second Piano Sonata
159:Dmitri Shostakovich
1249:, pp. 176–177
1129:Evan Allan Jones,
871:Musical set theory
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768:Klavierstücke I–IV
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329:Piano Suite Op. 25
311:is indicated by a
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153:and most types of
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104:musical set theory
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1743:Modernism (music)
1671:Arnold Schoenberg
1337:. Translation of
1192:Abraham and Isaac
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755:Requiem Canticles
743:Requiem Canticles
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519:"total chromatic"
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147:Arnold Schoenberg
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114:History and usage
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34:Arnold Schoenberg
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1701:Related articles
1683:Charles Wuorinen
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731:Igor Stravinsky
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309:Transposition
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68:
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43:
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35:
30:
26:
22:
1688:
1676:Anton Webern
1598:Permutations
1566:
1518:Fundamentals
1439:
1433:
1399:
1377:
1358:
1338:
1326:
1323:Ton de Leeuw
1304:
1301:Keller, Hans
1282:
1274:
1273:
1262:
1254:
1214:
1205:
1195:
1191:
1186:
1174:
1162:
1150:
1134:
1133:. Volume 2:
1130:
1125:
1113:
1101:
1089:
1060:
1048:
1036:
1024:
1012:
1000:
986:
978:
970:
965:
949:
944:
932:
905:
838:
835:Ben Johnston
806:Ben Johnston
804:
789:
766:
754:
741:
739:
734:
729:
712:
695:
688:
673:
647:, and B1) B
628:
602:
597:
593:
589:
585:
581:
577:
573:
568:
553:
545:
516:
509:
506:
460:
453:
438:
411:Anton Webern
408:
406:
399:
395:Es ist genug
383:open strings
376:
338:
318:
312:
277:
271:
249:Anton Webern
207:
173:
163:
155:serial music
144:
127:
122:Tone row of
95:
91:
83:
66:
62:
56:
42:mirror forms
41:
25:
1748:Punctualism
1733:Equivalence
1029:Keller 1955
1017:Keller 1955
1005:Keller 1955
598:6 7 8 9 t e
594:0 1 2 3 4 5
590:6 7 8 9 t e
586:0 1 2 3 4 5
578:6 7 8 9 t e
574:0 1 2 3 4 5
483:tetrachords
455:derived row
448:called the
345:emancipated
234:set (music)
214:Hans Keller
204:Franz Liszt
1797:Categories
1763:Time point
1758:Set theory
1666:Alban Berg
1611:Retrograde
1550:Invariance
1535:Derivation
1247:Leeuw 2005
1155:Leeuw 2005
1118:Haimo 1990
1106:Perle 1996
1094:Perle 1977
1053:Perle 1996
1041:Leeuw 2005
937:Leeuw 2005
925:Perle 1977
910:Leeuw 2005
897:References
757:: P R I IR
564:hexachords
467:BACH motif
446:tetrachord
349:Alban Berg
296:retrograde
222:narcissism
1718:Atonality
1638:composers
1616:Inversion
1606:Prime row
1572:Aggregate
1555:Partition
1540:Hexachord
1511:serialism
1418:237192271
1400:Serialism
814:otonality
475:, A, C, B
450:generator
289:inversion
257:hexachord
200:Beethoven
170:J.S. Bach
72:‹See Tfd›
21:Die Reihe
1753:Semitone
1567:Tone row
1398:(2008).
1357:(1977).
1019:, 22–23.
1007:, 14–21.
991:Sunday,
865:See also
841:, mov. 2
819:♭
649:inverted
531:lattices
478:♮
472:♭
442:trichord
402:, BWV 60
341:tonality
313:T number
198:(1788).
186:(1772),
90:), also
86:Tonreihe
67:note row
63:tone row
1636:Notable
1456:3647771
1275:Sources
637:tritone
391:chorale
106:of the
1454:
1416:
1406:
1384:
1365:
1345:
1333:
1289:
1181:, 195.
1169:, 127.
1157:, 166.
1141:
1120:, 183.
1096:, 100.
1043:, 158.
956:
939:, 174.
639:and a
379:triads
238:unison
180:Mozart
92:series
76:German
1768:Trope
1452:JSTOR
1306:Tempo
1234:, 139
1108:, 20.
1084:, 271
1067:, 97.
1031:, 23.
714:Nones
697:Nones
280:= 0.
80:Reihe
59:music
1690:more
1577:List
1509:and
1414:OCLC
1404:ISBN
1382:ISBN
1363:ISBN
1343:ISBN
1331:ISBN
1287:ISBN
1139:ISBN
1055:, 3.
954:ISBN
792:I–IV
517:The
510:The
61:, a
1693:...
1687:...
1444:doi
1440:110
1311:doi
1213:",
1194:",
993:NPR
927:, 3
837:'s
711:'s
694:'s
672:'s
627:'s
608:'s
558:or
544:'s
523:set
444:or
413:'s
251:'s
224:."
182:'s
172:'s
166:BWV
149:'s
126:'s
96:set
94:or
82:or
65:or
57:In
36:'s
1799::
1450:.
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1412:.
1325:,
1239:^
1224:^
1072:^
985:.
917:^
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533:.
485::
469:(B
458:.
347:.
336:.
274:11
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190:,
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651:.
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369:.
278:c
240:.
69:(
23:.
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