162:
102:
94:
171:
833:
642:
90:(1947–48) uses the rhythmic set 5-1-4-2 (sum: 12), whose permutation and function varies with each piece. In the first piece this governs the number of attacks within phrases, in the second rhythms are generated as multiples of a unit. (for example: 5×
115:(1948) uses a four-element duration row: 1 4 3 2 (the second note is four times the duration of the first, etc.). The duration of the initial note changes every phrase, varying the durations throughout the piece. Babbitt's
17:
204:
of pitches). For example, the first four notes equal about 13% of the total duration while the last four equal over 53% (each being 33% of the values). A duration set based on the
73:
separately. Messiaen had, however, previously used this chromatic duration series as an ordered set in the opening episode of "Turangalîla 2", a movement from the
62:
138:: "can we be expected to hear a family resemblance between a dotted half note followed by a sixteenth note (the opening 'interval' of duration set P
550:
836:
181:, for example, successive durations may be used for successive pitches of a row, or each pitch row may use only one duration, while in
121:(1948) uses a twelve-element duration set to serialize the rhythms as well as the pitches. He would later employ an approach based on
86:
wrote "The
Function of Set Structures in the Twelve-Tone System", outlining a theory of complete (total) serialism. Babbitt's
237:
69:
piece, but, as well as being predated by
Babbitt, both lacks order and views each note as a unit, rather than composing each
200:", and criticized it because the intervals between successive degrees are perceived as having different sizes (unlike the
543:
161:
117:
362:
4, no. 1: 109-18, citation on p.113. Quoted by
Taruskin, Richard (with "half note" changed to "quarter note") (2009).
502:
478:
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371:
342:
321:
300:
263:
111:
101:
93:
170:
688:
536:
658:
760:
629:
602:
279:, revised and updated edition (London: J. M. Dent; Berkeley: University of California Press, 1989): 94.
855:
785:
134:
16:
434:
3:13–42. Translation by Cardew, Cornelius, as "... How Time Passes ..." in the
English edition of
75:
205:
354:
Westergaard, Peter (1965). "Some
Problems Raised by the Rhythmic Procedures in Milton Babbitt's
765:
713:
678:
142:) and an eighth note followed by a dotted eighth note (the opening 'interval' of duration set P
559:
189:
52:
25:
708:
673:
8:
790:
650:
860:
810:
742:
663:
582:
528:
795:
723:
668:
498:
474:
409:
388:
367:
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317:
296:
259:
233:
209:
129:
70:
735:
624:
577:
193:
58:
44:
518:
438:
3 (1959): 10–40. Revised version, annotated by Heike, Dr. Georg, in
Stockhausen's
775:
612:
443:
201:
698:
597:
83:
849:
820:
703:
149:
728:
490:
466:
197:
154:
446:, 99–139 (Cologne: Verlag M. DuMont Schauberg, 1963). Citation on p.16 of
800:
607:
587:
196:" which, "compared to a scale constructed of chromatic intervals, … is a
40:
364:
The Oxford
History of Western Music: Music in the Late Twentieth Century
335:
The Oxford
History of Western Music: Music in the Late Twentieth Century
256:
Serial Music, Serial
Aesthetics: Compositional Theory in Post-War Europe
815:
718:
122:
770:
592:
563:
430:
66:
314:
Music of the
Twentieth-Century Avant-Garde: A Biocritical Sourcebook
293:
Music of the Twentieth-Century Avant-Garde: A Biocritical Sourcebook
805:
619:
48:
406:
Unfolding Time: Studies in Temporality in Twentieth Century Music
428:
Stockhausen, Karlheinz (1957). "... wie die Zeit vergeht ...",
152:
used the values in Messiaen's piece to order the rhythms in his
641:
128:
Babbitt's use of rhythm in the latter piece was criticized by
558:
847:
383:Pam Hurry, Mark Phillips, Mark Richards (2001).
232:, p.165. New York: Cambridge University Press.
424:
422:
544:
450:(p.13 of the English edition), pp.103–104 of
837:List of dodecaphonic and serial compositions
419:
158:(1952). These range from a demisemiquaver (
20:Six-element set of rhythmic values used in
832:
551:
537:
462:
460:
287:
285:
15:
250:
248:
246:
230:The Cambridge Introduction to Serialism
848:
532:
457:
282:
192:described this additive series as "a
185:new methods are constantly invented.
243:
13:
512:
356:Composition for Twelve Instruments
118:Composition for Twelve Instruments
14:
872:
831:
640:
523:Rencontres avec Olivier Messiaen
169:
160:
112:Composition for Four Instruments
100:
92:
484:
194:subharmonic proportional series
63:Mode de valeurs et d'intensités
497:, p.74. Cambridge: MIT Press.
471:Music of the Twentieth Century
398:
377:
348:
327:
306:
269:
222:
65:" is often cited as the first
1:
525:. Paris: René Julliard, 1960.
761:All-interval twelve-tone row
404:Crispin, Darla, ed. (2009).
88:Three Compositions for Piano
7:
166:, 1) to a dotted crotchet (
10:
877:
333:Taruskin, Richard (2009).
215:
829:
753:
687:
649:
638:
570:
360:Perspectives of New Music
228:Whittall, Arnold (2008).
135:Perspectives of New Music
385:Heinemann Advanced Music
275:Robert Sherlaw Johnson,
766:All-trichord hexachord
714:Second Viennese School
312:Sitsky, Larry (2002).
291:Sitsky, Larry (2002).
47:, in analogy with the
28:
560:Twelve-tone technique
254:Grant, M. J. (2005).
190:Karlheinz Stockhausen
76:Turangalîla-Symphonie
19:
709:Josef Matthias Hauer
674:Retrograde inversion
39:is an ordering of a
22:Variazioni canoniche
791:Formula composition
29:
843:
842:
796:Modernism (music)
724:Arnold Schoenberg
238:978-0-521-68200-8
210:irrational values
130:Peter Westergaard
868:
856:Rhythm and meter
835:
834:
754:Related articles
736:Charles Wuorinen
644:
578:Combinatoriality
553:
546:
539:
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444:Schnebel, Dieter
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208:would introduce
176:
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105:
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59:Olivier Messiaen
876:
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866:
865:
846:
845:
844:
839:
825:
781:Duration series
776:Chromatic scale
749:
690:
683:
645:
636:
613:Cross partition
583:Complementation
566:
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513:Further reading
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440:Texte zur Musik
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206:harmonic series
202:chromatic scale
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37:duration series
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5:
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699:Milton Babbitt
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679:Multiplication
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598:Interval class
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519:Goléa, Antoine
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84:Milton Babbitt
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704:Pierre Boulez
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503:0-262-18215-7
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491:Roads, Curtis
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479:9789053567654
476:
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468:
467:Leeuw, Ton de
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461:
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442:1, edited by
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414:9789058677358
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393:9780435812584
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372:9780195384857
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343:9780195384857
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322:9780313296895
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301:9780313017230
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264:9780521619929
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179:Structures Ic
172:
163:
157:
156:
151:
150:Pierre Boulez
147:
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729:Anton Webern
651:Permutations
571:Fundamentals
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155:Structures I
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116:
110:
108:
87:
81:
74:
57:
36:
33:duration row
32:
30:
21:
801:Punctualism
786:Equivalence
123:time-points
79:(1946–48).
53:twelve-tone
850:Categories
816:Time point
811:Set theory
719:Alban Berg
664:Retrograde
603:Invariance
588:Derivation
495:Microsound
177:, 12). In
109:Babbitt's
26:Luigi Nono
24:(1950) by
861:Serialism
771:Atonality
691:composers
669:Inversion
659:Prime row
625:Aggregate
608:Partition
593:Hexachord
564:serialism
473:, p.171.
448:Die Reihe
436:Die Reihe
431:Die Reihe
387:, p.127.
366:, p.168.
337:, p.168.
71:parameter
45:durations
806:Semitone
620:Tone row
493:(2001).
469:(2006).
408:, p.76.
316:, p.18.
295:, p.78.
277:Messiaen
258:, p.62.
188:In 1957
106:, etc.)
82:In 1946
49:tone row
689:Notable
216:Sources
501:
477:
412:
391:
370:
341:
320:
299:
262:
240:(pbk).
236:
67:serial
821:Trope
452:Texte
55:set.
743:more
630:List
562:and
499:ISBN
475:ISBN
410:ISBN
389:ISBN
368:ISBN
339:ISBN
318:ISBN
297:ISBN
260:ISBN
234:ISBN
198:mode
146:)?"
98:, 1Ă—
61:'s "
746:...
740:...
358:",
132:in
51:or
43:of
41:set
35:or
852::
521:.
459:^
454:1.
421:^
284:^
245:^
212:.
183:Ib
125:.
31:A
552:e
545:t
538:v
505:.
481:.
416:.
395:.
374:.
345:.
324:.
303:.
266:.
174:.
144:2
140:0
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