459:
436:
556:, and in most cases purposely abstains from consonant triads, or indeed referential or centric sonorities at all. Music theorist Joseph Straus has attempted to define more rigorously what it is about atonality that precludes prolongational hearing. His own definition of prolongation is "the sense of continuation of a musical object, particularly when not literally present ... prolongation is a cognitive act of the listener". He formulated four conditions for the possibility of Schenkerian prolongation in any musical style (1987) These are:
1282:
324:
518:. Developments in more recent music theory have sought to clarify the conditions under which prolongation may obtain, so that other repertoires may either be opened up or more justifiably be precluded. Schenker pupil Felix Salzer, for example, detects the rudiments of prolongational horizontalization in music as early as 12th-century plainchant and argues that it is a musical principle that persists through
401:
590:), he argues that in practice most post-tonal music does not display this. Instead, he suggests that in post-tonal music, including atonal music, a model of 'association' is more defensible than strict prolongation. However, Lerdahl argues that Straus' argument is based on circular criteria. Lerdahl's own formulation of prolongation is more amenable to atonal structures. For example, in
372:
364:
356:
346:
466:
447:
477:
In
Schenkerian analysis, the analyst discerns ways in which prolongation creates the details of a musical composition by elaborating the background structure. Most of these methods involve contrapuntal processes, to such a degree that Schenkerian theory is a theory that almost completely synthesizes
223:
is important for
Schenker because he believes that showing how a masterpiece of free composition remains rooted in the laws of strict counterpoint explains its utter unity, its "synthesis". The means and techniques of passing from one level to the next are subsumed in Schenker's notion of "composing
243:
and others, disseminate and clarify it; (3) it is used within attempted formalisations of
Schenkerian analysis; (4) new theories evoking Schenker make use of it; (5) it is used within theories amplifying Schenker's own; (6) definitions are proposed in theories beyond the Schenkerian canon; and (7)
794:
Deriding the lack of the "art of prolongation" in
Bruckner, he writes "his ear could not hear the beginning and end of a motion as an entity. The two points remain without inner relationship to one another; and everything shoved and squeezed in between, though executed with so much art on an
742:
Schenker claims among others that three-voice counterpoint is subject to the same laws as two-voice counterpoint, of which it represents a "Prolongation": "In three-voice settings, the two-voice settings actually continue to apply; three-voice setting therefore represents merely a prolonged
74:
Prolongation can be thought of as a way of generating musical content through the linear elaboration of simple and basic tonal structures with progressively increasing detail and sophistication, and thus analysis consists of a reduction from detail to structure. Important to the operation of
715:
For instance when he explained that the task of the study of counterpoint is to reveal how its fundamental laws can be extended to apply to free composition: "But to reveal the basic form together with its variants, and to uncover only prolongations of a fundamental law even where apparent
106:
A pitch is located in a pitch class, a pitch class is located within a chord, a chord is located in a key region, a key is located in pitch space including the circle of fifths and their relative minors. A rhythmic event is located within the meter which is located within the form. Thus
228:, a German neologism), which for him is a mechanism of elaborating pitch materials in musical time. The means of elaboration are described below as "prolongational techniques", in conformity with the modern Schenkerian English usage, but should better be termed "elaborations".
498:, "the elaboration in time of a governing vertical sonority – a chord or an interval. When an interval is horizontalized, its tones unfold against a background determined in the vertical dimension by the governing sonority of which it is part."
192:". The "gradual growth" illustrated is a global phenomenon, always concerning the piece as a whole. The figure is further commented upon on p. 45 of the same volume. Schenker stresses that it starts with the two-voice setting of the
411:
208:, he confirms that the word still refers to the passing from one voice-leading level to another: "For the sake of continuity with my earlier theoretical and analytical works, I am retaining in this volume the words of Latin derivation
334:
423:
125:
The early 20th-century music theorist
Heinrich Schenker (1868–1935) was responsible for developing both the conceptual framework for prolongation and a means of analyzing music in terms of prolonged musical structures (called
772:
5 (1923), p. 8, Fig. 1; English translation (2004), p. 180. Later in the same volume, p. 33 (transl., p. 202), Schenker describes a similar figure as showing "the succession of prolongations, that is, the layers of the
606:
has proposed a related theory of 'Pitch-Class-Set
Extension', in which contiguous harmonic units are linked through common-tone or chromatic connection and successive harmonies are understood to 'extend' earlier ones.
102:
can be prolonged within tonal music.) "In chord prolongation, one chord governs a prolongation of various chords; these different chords are subordinated to that one chord which they help to express and prolong."
720:
I (1910), p. 315; English translation (1987), p. 241. This is the usage to which Oswald Jonas refers in the quotation from note 1 above. See also J. Dubiel, "When You are a
Beethoven: Kinds of Rules in Schenker's
581:
Straus concludes that such conditions do not exist in atonal music and therefore that "atonal prolongation" is impossible; although he is open to the possibility that prolongation is a possibility in other
623:"It is one of the most valuable services of Schenkerian theory to have revealed for the first time the unity of composing-out and the prolonged application and validity of the laws of voice leading."
111:" are often made at different levels excluding the prolongational from the structural events; these may express the relationships through time-reductions or prologational reductions (which may be
598:
of an event versus movement to a different event, while weak prolongation, repetition of an event in altered form, may not easily be distinguished due to the lack of a referential triad (
384:
145:) of strict composition in free composition and the phenomena resulting from the extension of these laws. He used the word mainly to denote the transformation of a given level of
137:
is not common, and
Schenker first used it in a very specific meaning (maybe originating in legal, possibly Viennese vocabulary), referring to the extension of the primal laws (
530:. Music theorist Robert Morgan has argued that a central tenet of Schenkerian thought—that only consonant triads are capable of prolongation—needlessly excludes a class of
1166:
458:
287:
as "composing out" and others use "compositional elaboration" or, short, "elaboration." Drabkin quotes as "methods of prolongation" techniques that include
534:
sonorities, such as diminished sevenths or a more arbitrarily defined set of pitches; Morgan claims that, starting in the 19th century, composers such as
91:, and this is said to be "prolonged" across durations of music that may feature many other different harmonies. (However, in principle any other type of
546:, began "composing out" these dissonant configurations as rigorous a manner as is usually ascribed to the triadic prolongation of tonal composers.
552:
poses a stark challenge to prolongational hearing and analysis, as its harmonic makeup by definition eschews the long-range controlling force of
435:
1126:
1159:
1103:
1069:
1031:
1014:
993:
964:
686:
649:
188:. He explains that this figure "shows the gradual growth of the voice-leading prolongations, all predetermined in the womb of the
1344:
1325:
729:
34/2 (1990), p. 293, and R. Snarrenberg, "The Art of
Translating Schenker: A Commentary on 'The Masterwork in Music,' Vol. 1",
440:
1349:
1152:
17:
631:, trans. John Rothgeb (New York: Longman, 1982), p. 54. 2nd English edition (Ann Arbor: Musicalia Press, 2005), p. 59.
561:
531:
92:
1299:
603:
583:
808:
Anthony Pople, "Using
Complex Set Theory for Tonal Analysis: An Introduction to the 'Tonalities' Project",
157:
appears to be responsible for the shift of meaning where "prolongation" became the American translation of
507:
170:
1281:
1201:
1196:
760:
21/3, pp. 311-329. This conception of "prolongation" may have its origin in the teaching of Hans Weisse.
665:
165:
113:
47:
is considered to govern spans of music when not physically sounding. It is a central principle in the
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699:
491:
483:
479:
52:
478:
harmony and linear counterpoint in the service of the more global phenomenon of tonal prolongation.
1221:
899:
Robert Snarrenberg, "The Art of Translating Schenker: A Commentary on 'The Masterwork in Music'",
1313:
1211:
595:
543:
487:
393:
988:
Forte, Allen (1979). Tonal Harmony in Concept and Practice, p.426. Holt, Rinehart, and Winston.
439:
Fleshing out the structural tonic arpeggio as prolongation of that chord in Bach's Sinfonia 15,
371:
363:
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99:
56:
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Morgan, Robert (1976). "Dissonant Prolongation: Theoretical and Compositional Precedents" in
1306:
1251:
377:
185:
48:
40:
204:, a specific freedom taken with respect to the laws expressed in the previous step. And in
664:
William Drabkin. "Prolongation." Grove Music Online. Oxford Music Online. 2 Aug. 2011 <
587:
527:
515:
795:
individual level, exhausts itself purely physically without any concern for connection."
178:
5, Schenker proposes what may be his earliest figure showing the steps through which the
235:
in seven steps: (1) Schenker proposes it as an operational concept in his teaching; (2)
1266:
539:
523:
345:
1338:
1271:
1236:
1216:
1206:
812:
23/2-3 (2004), pp. 162-164. Pople describes "prolongation" as "a Humpty-Dumpty Word".
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44:
36:
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24:
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510:, and there to a select class of mostly Austro-German composers in a line from
1246:
1191:
519:
133:
Schenker’s own usage of the term differs from the modern one. The German word
1081:
Straus, Joseph N. (1987). "The Problem of Prolongation in Post-Tonal Music",
1026:
Salzer, Felix (1962). Structural Hearing: Tonal Coherence in Music, p. 267.
591:
511:
462:...and on a larger scale in Chopin's Nocturne in C minor, Op. 48-1, mm. 1-4
245:
76:
79:
differentiation of pitches within a passage of tonal music. Typically, the
327:
32:
570:
Ways in which less structural pitches embellish more structural pitches.
1144:
349:
189:
84:
231:
The broadening of the meaning of "prolongation" has been described by
63:(better translated as "composing out" or "elaboration"). According to
957:
Schenker Guide: A Brief Handbook and Website for Schenkerian Analysis
666:
http://www.oxfordmusiconline.com/subscriber/article/grove/music/22408
180:
937:, The New Grove Handbooks in Music, London, Macmillan, 1987, p. 128.
785:, 2d edition (1956), § 45, p. 57; English translation (1979), p. 25.
716:
contradictions hold sway – this alone is the task of counterpoint!"
252:
by "prolongation" appeared in step (2), as an English translation.
216:
as designations for the voice-leading levels in the middleground".
344:
149:
to the next one, describing the passage from level to level as a
756:
Adele T. Katz (1935). "Heinrich Schenker's Method of Analysis",
1148:
1094:
Lerdahl, Fred (1989). "Atonal Prolongational Structure", p.67,
311:, which Schenker would rather have described as techniques of
196:– an expression, therefore, of the fundamental laws of strict
594:, strong prolongation may be distinguished from progression,
933:
William Drabkin, "Prolongation," in I. Bent and W. Drabkin,
71:(Schenker's own intention for the term is open to debate)."
506:
Schenker intended his theory to apply only to music of the
1127:"A Theory of Pitch-Class-Set Extension in Atonal Music"
586:
music (he gives the example of music composed with the
275:, "prolongation" is more than once used to translate
833:
1959: "Schenker's Conception of Musical Structure",
244:
definitions of the term are proposed in relation to
747:II (1922), p. 1; English translation (1987), p. 1.
59:. The English term usually translates Schenker's
567:A scale of stability among consonant harmonies .
200:. Each of the following steps is described as a
629:Introduction to the Theory of Heinrich Schenker
248:music. The replacement of Schenker's own term
1160:
8:
1060:," C. Schachter and H. Siegel, eds. (2006).
679:Structural Hearing: Tonal Coherence in Music
255:The English "prolongation" has been used in
87:of highest hierarchical significance is the
1098:. McAdams, Stephen and Irene Deliege, eds.
1056:Maisel, Arthur, "Voice leading as drama in
984:
982:
67:, "The term 'prolongation' usually means '
1167:
1153:
1145:
1005:Salzer, Felix and Carl Schachter (1989).
660:
658:
573:A clear relationship between harmony and
457:
434:
399:
330:, the first technique of composing-out.
322:
616:
799:5, p. 46; English translation, p. 213.
396:prolong harmonies through elaboration.
1085:31, p. 1-21. cited in Lerdahl (1989).
224:out" or "compositional elaboration" (
7:
922:Rivista di Analisi e Teoria Musicale
848:Introduction to Schenkerian Analysis
259:to translate German words including
861:A Generative Theory of Tonal Music
121:Prolongation in Schenkerian theory
14:
494:, etc., in general aiming at the
55:, conceived by Austrian theorist
1280:
1096:Music and the Cognitive Sciences
370:
362:
354:
872:Neumeyer 1987, Beach 1988, 1990
859:e.g. Lerdahl & Jackendoff,
560:Consistent distinction between
1125:Roig-FrancolĂ, Miguel (2001).
924:XXI/2 (2015), p. 105, note 12.
920:: A Transformational Theory",
1:
283:. Oster otherwise translates
141:) or of the primal concepts (
18:Prolongation (disambiguation)
1007:Counterpoint in Composition
502:Conditions for prolongation
1366:
15:
1323:
1289:
1278:
1182:
562:consonance and dissonance
480:Prolongational techniques
319:Prolongational techniques
171:Little Prelude in D minor
976:Pankhurst (2008), p. 51.
846:e.g. Forte and Gilbert,
419:as elaboration of I–V–I
1345:Post-tonal music theory
1131:College Music Symposium
1083:Journal of Music Theory
1045:Journal of Music Theory
955:Pankhurst, Tom (2008).
835:Journal of Music Theory
727:Journal of Music Theory
522:music as well, such as
257:The Masterwork in Music
1064:(pp. 160-186), p.178.
903:15/2-3 (1996), p. 325.
733:15/2-3 (1996), p. 324.
677:Salzer, Felix (1962).
640:Lerdahl, Fred (2001).
508:common practice period
474:
455:
432:
397:
342:
1202:Fundamental structure
1115:Lerdahl (1989), p.74.
758:The Musical Quarterly
698:See N. MeeĂąs (2021),
461:
438:
403:
348:
326:
1350:Schenkerian analysis
1176:Schenkerian analysis
604:Miguel Roig-FrancolĂ
279:and "prolonged" for
128:Schenkerian analysis
75:prolongation is the
53:Schenkerian analysis
16:For other uses, see
1222:Obligatory register
946:Jonas (1982), p.37.
890:Straus, 1987, 1997.
488:linear progressions
394:Linear progressions
164:In his analysis of
117:or tree diagrams).
1212:Linear progression
1062:Schenker Studies 2
822:Structural Hearing
475:
456:
433:
398:
343:
184:develops into the
31:is the process in
1332:
1331:
1294:Heinrich Schenker
1242:Register transfer
1187:Bass arpeggiation
706:6/3, pp. 109-124.
642:Tonal Pitch Space
496:horizontalization
405:Bass prolongation
100:harmonic function
57:Heinrich Schenker
1357:
1307:Free Composition
1284:
1252:Structural level
1197:Fundamental line
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35:through which a
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773:voice-leading."
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516:Johannes Brahms
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285:Auskomponierung
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261:Auskomponierung
250:Auskomponierung
226:Auskomponierung
219:The concept of
159:Auskomponierung
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61:Auskomponierung
51:methodology of
45:consonant triad
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5:
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918:Der freie Satz
905:
901:Music Analysis
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852:
839:
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810:Music Analysis
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783:Der freie Satz
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731:Music Analysis
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524:Paul Hindemith
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174:, BWV 926, in
122:
119:
69:composing out'
49:music-analytic
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1070:0-521-02832-9
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1032:0-486-22275-6
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881:Morgan, 1976.
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155:Adele T. Katz
152:
148:
147:voice-leading
144:
140:
136:
131:
129:
120:
118:
116:
115:
110:
104:
101:
97:
94:
90:
86:
82:
78:
72:
70:
66:
62:
58:
54:
50:
46:
42:
38:
34:
30:
26:
19:
1312:
1305:
1300:Counterpoint
1298:
1232:Prolongation
1231:
1227:Primary tone
1134:
1130:
1120:
1111:
1095:
1090:
1082:
1077:
1061:
1057:
1052:
1047:20/1, 49–91.
1044:
1039:
1022:
1006:
1001:
972:
956:
951:
942:
934:
929:
921:
917:
913:
908:
900:
895:
886:
877:
868:
860:
855:
847:
842:
834:
829:
821:
817:
809:
804:
797:Der Tonwille
796:
790:
782:
778:
770:Der Tonwille
769:
765:
757:
752:
744:
738:
730:
726:
723:Counterpoint
722:
717:
711:
703:
700:Prolongation
694:
678:
673:
641:
636:
628:
625:Oswald Jonas
619:
592:atonal music
580:
554:monotonality
550:Atonal music
548:
505:
495:
476:
404:
328:Arpeggiation
312:
309:Untergreifen
308:
304:
301:Tieferlegung
300:
296:
292:
288:
284:
280:
276:
272:
268:
264:
260:
256:
254:
249:
237:Felix Salzer
230:
225:
221:Prolongation
220:
218:
213:
210:Prolongation
209:
205:
202:Prolongation
201:
198:counterpoint
193:
179:
176:Der Tonwille
175:
169:
163:
158:
151:Prolongation
150:
142:
138:
135:Prolongation
134:
132:
127:
124:
112:
108:
105:
98:, pitch, or
77:hierarchical
73:
68:
65:Fred Lerdahl
60:
29:prolongation
28:
25:music theory
22:
1257:Tonal space
914:Formenlehre
824:, 1952/1962
745:Kontrapunkt
718:Kontrapunkt
407:: I–IV–V–I
305:Ăśbergreifen
269:Auswicklung
241:Allen Forte
33:tonal music
1339:Categories
1247:Scale-step
1192:Diminution
1009:, p. 144.
837:3/1, 1959.
596:repetition
584:post-tonal
520:post-tonal
492:unfoldings
443:, mm. 3-4
293:Ausfaltung
265:ausdrĂĽcken
214:Diminution
206:Freie Satz
186:foreground
143:Urbegriffe
109:reductions
1262:Unfolding
959:, p. 28.
681:, p.111.
532:dissonant
512:J.S. Bach
297:Koppelung
166:J.S. Bach
139:Urgesetze
93:consonant
1326:Glossary
1137:: 57–90.
935:Analysis
544:Scriabin
482:include
114:Urlinien
41:interval
1314:Harmony
1058:Wozzeck
863:, 1983.
850:, 1982.
611:Sources
441:BWV 801
376:over I–
350:Urlinie
289:Anstieg
190:Urlinie
85:harmony
1102:
1068:
1030:
1013:
992:
963:
685:
648:
542:, and
540:Wagner
246:atonal
194:Ursatz
181:Ursatz
1207:Klang
704:Orfeu
668:>.
600:klang
536:Liszt
271:. In
96:chord
89:tonic
43:, or
37:pitch
1100:ISBN
1066:ISBN
1028:ISBN
1011:ISBN
990:ISBN
961:ISBN
683:ISBN
646:ISBN
526:and
468:Play
449:play
425:Play
413:Play
386:Play
336:Play
307:and
267:and
212:and
81:note
916:in
725:",
602:).
514:to
380:–I
168:'s
130:).
83:or
23:In
1341::
1135:41
1133:.
1129:.
981:^
702:,
657:^
627:,
538:,
490:,
486:,
392:.
352::
315:.
303:,
299:,
295:,
291:,
263:,
239:,
161:.
153:.
39:,
27:,
1168:e
1161:t
1154:v
1106:.
1072:.
1034:.
1017:.
996:.
967:.
689:.
652:.
577:.
564:.
431:.
378:V
368:–
360:–
107:"
20:.
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