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807:) 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
684:
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
699:
326:
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
49:
851:
841:
434:
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
50:
852:
676:
132:
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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
677:
133:
564:
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:
793:
772:
717:
652:
260:
718:
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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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660:
338:—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
1492:
271:, 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
607:. An aggregate may be vertically or horizontally weighted. An "all-partition array" is created by combining a collection of hexachordally combinatorial arrays.
48:
850:
1778:
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254:
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.
28:
728:
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,
675:
131:
409:
545:, each vertical line (four trichords labeled a–d) is an aggregate while each horizontal line (four trichords labeled a–d) is also an aggregate
37:
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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
393:
824:
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The "set-complex" is the forty-eight forms of the set generated by stating each "aspect" or transformation on each pitch class.
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604:
339:
182:
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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
247:
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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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1655:
1620:
509:
is a tone row arranged so that it contains one instance of each interval within the octave, 0 through 11.
347:
315:
1600:
1544:
1501:
1427:
Hunter, David J.; Hippel, Paul T. von (February 2003). "How Rare Is
Symmetry in Musical 12-Tone Rows?".
328:
319:
303:
164:
145:
118:
456:
The tone rows of many of Webern's other late works are similarly intricate. The tone row for Webern's
346:, however, sometimes incorporated tonal elements into his twelve-tone works. The main tone row of his
215:
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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1133:
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1324:, translated from the Dutch by Stephen Taylor (Amsterdam: Amsterdam University Press, 2005).
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1305:
818:
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404:
Some tone rows have a high degree of internal organization. An example is the tone row from
381:
127:, the registrally fixed pitches of which correspond with duration units and metronome marks.
1336:(Utrecht: Oosthoek, 1964; third impression, Utrecht: Bohn, Scheltema & Holkema, 1977).
1722:
1717:
1554:
1390:
1300:
982:
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Stephen C. Brown, "Twelve-Tone Rows and
Aggregate Melodies in the Music of Shostakovich,"
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725:
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639:
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70:
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638:, B) a descending perfect fifth followed by an ascending major second and a descending
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1356:(4th ed.). Berkeley, Los Angeles, and London: University of California Press.
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1375:(2nd, revised and expanded ed.). Berkeley: University of California Press.
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198:
94:
1278:
Schoenberg's Serial
Odyssey: The Evolution of his Twelve-Tone Method, 1914–1928
1757:
1660:
1309:
524:. An "array" is a succession of aggregates. The term is also used to refer to
477:
461:
440:
343:
216:
1412:
1334:
Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur
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1684:
1534:
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558:
318:(inversion, retrograde, retrograde inversion, as well as transposition; see
251:
149:
20:
1583:
1747:
1130:
Shostakovich to the Avant-garde. Dmitri
Shostakovich: The String Quartets
436:
335:
1450:
1256:, "Ben Johnston's Extended Just Intonation: A Guide for Interpreters",
631:
385:
173:(1742) and by the late eighteenth century it is found in works such as
123:
945:
Contemplating
Shostakovich: Life, Music and Film: Life, Music and Film
152:. Tone rows were widely used in 20th-century contemporary music, like
1322:
Music of the
Twentieth Century: A Study of Its Elements and Structure
232:
1442:
156:'s use of twelve-tone rows, "without dodecaphonic transformations."
267:
Tone rows are designated by letters and subscript numbers (e.g.: RI
823:
778:
755:
743:
697:
658:
614:
530:
384:. This whole tone scale reappears in the second movement when the
237:
112:
58:
27:
1397:. Cambridge Introductions to Music. Cambridge University Press.
712:, symmetrical about the central tone with one note (D) repeated.
695:
which contains a repeated note making it a 'thirteen-tone row':
211:
claims that Schoenberg was aware of this serial practice in the
1474:
334:
Initially, Schoenberg required the avoidance of suggestions of
987:
811:
or utonality on A+ utonality, C otonality and utonality, and E
160:
1298:(Autumn 1955). "Strict Serial Technique in Classical Music".
535:
First array of four aggregates (numbered 1–4 at bottom) from
279:"P" indicates prime, a forward-directed right-side up form.
105:, though both larger and smaller sets are sometimes found.
766:
which "retained only the rudiments of the 12-note series".
490:
Audio playback is not supported in your browser. You can
422:
Audio playback is not supported in your browser. You can
360:
Audio playback is not supported in your browser. You can
1195:
3, no. 2 (Spring–Summer 1965): 104–126, citation on 118.
399:
is quoted literally in the woodwinds (mostly clarinet).
227:"Prime (music)" redirects here. For the prime form, see
1132:(Rochester: University of Rochester Press, 2009): 228.
159:
A tone row has been identified in the A minor prelude,
372:
This tone row consists of alternating minor and major
1126:
Intimate Voices: The Twentieth-Century String Quartet
380:
of the violin, followed by a portion of an ascending
32:"Mirror forms", P, R, I, and RI, of a tone row (from
1695:
1629:
1591:
1512:
19:"Reihe" redirects here. For the music journal, see
1262:29, no. 2 (Summer 1991): 106–137, citation on 127.
1214:17, no. 2 (Spring 1999): 231–271, citation on 242.
1204:Joseph N. Strauss, "Stravinsky's Serial 'Mistakes
760:Unordered sets from the second of Stockhausen's
626:series consists of three cells: A) an ascending
1222:
1220:
1072:
1070:
1068:
783:Unordered sets from the third of Stockhausen's
310:, for example P8 is a T(4) transposition of P4.
915:
913:
1486:
201:used a twelve-tone row in the opening of his
8:
1779:List of dodecaphonic and serial compositions
79:
1237:
1235:
93:, is a non-repetitive ordering of a set of
1774:
1493:
1479:
1471:
978:"Discovery Reveals Bach's Postmodern Side"
392:" (It is enough) from J.S. Bach's cantata
947:. (Farnham: Ashgate Publishing, 2013): .
1226:
1173:
1161:
1076:
1059:
828:Primary forms of the just tone row from
943:Andrew Kirkman and Alexander Ivashkin,
897:
1185:Claudio Spies, "Notes on Stravinsky's
1023:
1011:
999:
968:, Vol. 59, No. 2 (Fall 2015): 191–234.
663:Prime form of five-note tone row from
286:, a forward-directed upside-down form.
183:String Quartet in E-flat major, K. 428
16:Sequence of all twelve chromatic tones
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1100:
1088:
1047:
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549:An aggregate may be achieved through
7:
1566:
1467:, Harald Fripertinger, Peter Lackner
242:Principal forms of the tone row of
223:Theory and compositional techniques
97:, typically of the twelve notes in
748:Basic row forms from Stravinsky's
14:
1430:The American Mathematical Monthly
293:, a backwards right-side up form.
187:String Quintet in G minor, K. 516
1773:
1582:
1465:Database on tone rows and tropes
847:
837:
788:
767:
713:
672:
647:
542:Composition for Four Instruments
255:
128:
45:
300:, a backwards upside-down form.
179:C major String Quartet, K. 157
44:because...they are identical".
1:
410:Concerto for Nine Instruments
1703:All-interval twelve-tone row
886:List of tone rows and series
803:uses a "just tone row" (see
702:Thirteen-note tone row from
507:all-interval twelve-tone row
487:
419:
357:
1280:. Oxford: Clarendon Press.
476:) and is composed of three
191:Symphony in G minor, K. 550
140:Tone rows are the basis of
1819:
1304:. New Series (37): 12–24.
226:
124:Gruppen für drei Orchester
18:
1771:
1580:
1310:10.1017/S0040298200055212
1259:Perspectives of New Music
1211:The Journal of Musicology
1192:Perspectives of New Music
817:- otonality, outlining a
395:O Ewigkeit, du Donnerwort
170:The Well-Tempered Clavier
907:, 154. Italics original.
730:In memoriam Dylan Thomas
669:In memoriam Dylan Thomas
516:(or "aggregate") is the
350:hints at this tonality:
231:. For the interval, see
38:Variations for Orchestra
966:Journal of Music Theory
492:download the audio file
424:download the audio file
362:download the audio file
1708:All-trichord hexachord
1656:Second Viennese School
1371:Perle, George (1996).
856:
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722:
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1798:Twelve-tone technique
1502:Twelve-tone technique
1276:Haimo, Ethan (1990).
827:
782:
759:
747:
701:
662:
618:
611:Nonstandard tone rows
534:
458:String Quartet Op. 28
412:Op. 24, shown below.
329:twelve-tone technique
320:twelve-tone technique
241:
163:889, from book II of
146:twelve-tone technique
119:Karlheinz Stockhausen
116:
31:
1651:Josef Matthias Hauer
1616:Retrograde inversion
1373:Twelve-Tone Tonality
834:String Quartet No. 7
605:String Quartet No. 4
298:retrograde-inversion
248:Variations for piano
1733:Formula composition
990:, 6 September 2009.
624:Second Piano Sonata
154:Dmitri Shostakovich
1244:, pp. 176–177
1124:Evan Allan Jones,
866:Musical set theory
857:
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763:Klavierstücke I–IV
754:
723:
682:
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324:Piano Suite Op. 25
306:is indicated by a
265:
148:and most types of
138:
99:musical set theory
55:
1785:
1784:
1738:Modernism (music)
1666:Arnold Schoenberg
1332:. Translation of
1187:Abraham and Isaac
853:
843:
794:
773:
750:Requiem Canticles
738:Requiem Canticles
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514:"total chromatic"
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142:Arnold Schoenberg
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109:History and usage
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34:Arnold Schoenberg
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1803:Musical symmetry
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1696:Related articles
1678:Charles Wuorinen
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1520:Combinatoriality
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382:whole tone scale
376:starting on the
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189:(1790), and the
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40:Op. 31, "Called
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805:just intonation
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685:row below from
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665:Igor Stravinsky
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316:transformations
296:"RI" indicates
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256:
250:, Op. 27. Each
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103:chromatic scale
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1175:
1174:Whittall 2008
1170:
1167:
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1162:Whittall 2008
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1155:
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1138:9781580463225
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1077:Whittall 2008
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1060:Whittall 2008
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876:Side-slipping
874:
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871:Unified field
869:
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786:
785:Klavierstücke
781:
765:
764:
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751:
746:
742:
740:
739:
733:
731:
727:
711:
710:
705:
704:Luciano Berio
700:
696:
694:
693:
688:
687:Luciano Berio
670:
666:
661:
645:
641:
637:
633:
629:
628:perfect fifth
625:
621:
620:Pierre Boulez
617:
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523:
522:pitch classes
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317:
309:
305:
304:Transposition
302:
299:
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288:
285:
281:
278:
277:
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253:
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126:
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100:
96:
95:pitch-classes
92:
88:
84:
82:
76:
72:
68:
64:
60:
43:
39:
35:
30:
26:
22:
1683:
1671:Anton Webern
1593:Permutations
1561:
1513:Fundamentals
1434:
1428:
1394:
1372:
1353:
1333:
1321:
1318:Ton de Leeuw
1299:
1296:Keller, Hans
1277:
1269:
1268:
1257:
1249:
1209:
1200:
1190:
1186:
1181:
1169:
1157:
1145:
1129:
1128:. Volume 2:
1125:
1120:
1108:
1096:
1084:
1055:
1043:
1031:
1019:
1007:
995:
981:
973:
965:
960:
944:
939:
927:
900:
833:
830:Ben Johnston
801:Ben Johnston
799:
784:
761:
749:
736:
734:
729:
724:
707:
690:
683:
668:
642:, and B1) B
623:
597:
592:
588:
584:
580:
576:
572:
568:
563:
548:
540:
511:
504:
501:
455:
448:
433:
406:Anton Webern
403:
401:
394:
390:Es ist genug
378:open strings
371:
333:
313:
307:
272:
266:
244:Anton Webern
202:
168:
158:
150:serial music
139:
122:
117:Tone row of
90:
86:
78:
66:
62:
56:
42:mirror forms
41:
25:
1743:Punctualism
1728:Equivalence
1024:Keller 1955
1012:Keller 1955
1000:Keller 1955
593:6 7 8 9 t e
589:0 1 2 3 4 5
585:6 7 8 9 t e
581:0 1 2 3 4 5
573:6 7 8 9 t e
569:0 1 2 3 4 5
478:tetrachords
450:derived row
443:called the
340:emancipated
229:set (music)
209:Hans Keller
199:Franz Liszt
1792:Categories
1758:Time point
1753:Set theory
1661:Alban Berg
1606:Retrograde
1545:Invariance
1530:Derivation
1242:Leeuw 2005
1150:Leeuw 2005
1113:Haimo 1990
1101:Perle 1996
1089:Perle 1977
1048:Perle 1996
1036:Leeuw 2005
932:Leeuw 2005
920:Perle 1977
905:Leeuw 2005
892:References
752:: P R I IR
559:hexachords
462:BACH motif
441:tetrachord
344:Alban Berg
291:retrograde
217:narcissism
1713:Atonality
1633:composers
1611:Inversion
1601:Prime row
1567:Aggregate
1550:Partition
1535:Hexachord
1506:serialism
1413:237192271
1395:Serialism
809:otonality
470:, A, C, B
445:generator
284:inversion
252:hexachord
195:Beethoven
165:J.S. Bach
21:Die Reihe
1748:Semitone
1562:Tone row
1393:(2008).
1352:(1977).
1014:, 22–23.
1002:, 14–21.
986:Sunday,
860:See also
836:, mov. 2
814:♭
644:inverted
526:lattices
473:♮
467:♭
437:trichord
397:, BWV 60
336:tonality
308:T number
193:(1788).
181:(1772),
85:), also
81:Tonreihe
67:note row
63:tone row
1631:Notable
1451:3647771
1270:Sources
632:tritone
386:chorale
101:of the
1449:
1411:
1401:
1379:
1360:
1340:
1328:
1284:
1176:, 195.
1164:, 127.
1152:, 166.
1136:
1115:, 183.
1091:, 100.
1038:, 158.
951:
934:, 174.
634:and a
374:triads
233:unison
175:Mozart
87:series
71:German
1763:Trope
1447:JSTOR
1301:Tempo
1229:, 139
1103:, 20.
1079:, 271
1062:, 97.
1026:, 23.
709:Nones
692:Nones
275:= 0.
75:Reihe
59:music
1685:more
1572:List
1504:and
1409:OCLC
1399:ISBN
1377:ISBN
1358:ISBN
1338:ISBN
1326:ISBN
1282:ISBN
1134:ISBN
1050:, 3.
949:ISBN
787:I–IV
512:The
505:The
61:, a
1688:...
1682:...
1439:doi
1435:110
1306:doi
1208:",
1189:",
988:NPR
922:, 3
832:'s
706:'s
689:'s
667:'s
622:'s
603:'s
553:or
539:'s
518:set
439:or
408:'s
246:'s
219:."
177:'s
167:'s
161:BWV
144:'s
121:'s
91:set
89:or
77:or
65:or
57:In
36:'s
1794::
1445:.
1433:.
1407:.
1320:,
1234:^
1219:^
1067:^
980:.
912:^
821:.
741::
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591:/
587:/
583:/
571:/
561:.
528:.
480::
464:(B
453:.
342:.
331:.
269:11
207:.
185:,
73::
1494:e
1487:t
1480:v
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1312:.
1308::
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646:.
494:.
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388:"
364:.
273:c
235:.
69:(
23:.
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