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Prolongation : ウィキペディア英語版
Prolongation
In music theory, prolongation is the process in tonal music through which a pitch, interval, or consonant triad is able to govern spans of music when not physically sounding. It is a central principle in the music-analytic methodology of Schenkerian analysis, conceived by Austrian theorist Heinrich Schenker.〔"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." Oswald Jonas, ''Introduction to the Theory of Heinrich Schenker'', trans. John Rothgeb (New York: Longman, 1982), p. 54.〕
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.〔William Drabkin. "Prolongation." Grove Music Online. Oxford Music Online. 2 Aug. 2011 .〕 Important to the operation of prolongation is the hierarchical differentiation of pitches within a passage of tonal music. Typically, the note or harmony of highest hierarchical significance is the tonic, 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 consonant chord, pitch, or harmonic function can be prolonged within tonal music.) Conversely, in a chord progression, harmonies are said to ''prolong'' a triad when they are subordinated to that governing chord in a systematic manner; the job of such prolonging harmonies is to express and extend the influence of that hierarchically super-ordinate pitch or triad.〔Salzer, Felix (1962). ''Structural Hearing: Tonal Coherence in Music'', p.111. ISBN 0-486-22275-6.〕 Because it enables a pitch or pitches to remain in effect over the course of a piece, even as many other harmonic events intervene, prolongation is central to the concept of tonality in music.
==Prolongation in Heinrich Schenker==
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 Schenkerian analysis).
Schenker’s own usage of the term differs from the modern one. The German word ''Prolongation'' 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 (''Urgesetze'') or of the primal concepts (''Urbegriffe'') of strict composition in free composition〔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 contradictions hold sway – this alone is the task of counterpoint!" ''Kontrapunkt'' I (1910), p. 315; English translation (1987), p. 241. See also J. Dubiel, "When You are a Beethoven: Kinds of Rules in Schenker's ''Counterpoint''", ''Journal of Music Theory'' 34/2 (1990), p. 293, and R. Snarrenberg, "The Art of Translating Schenker: A Commentary on 'The Masterwork in Music,' Vol. 1", ''Music Analysis'' 15/2-3 (1996), p. 324.〕 and the phenomena resulting from the extension of these laws.〔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 (of ) two-voice settings actually continue to apply; three-voice setting therefore represents merely a prolonged phenomenon". ''Kontrapunkt'' II (1922), p. 1; English translation (1987), p. 1.〕 He used the word mainly to denote the transformation of a given level of voice-leading to the next one, describing the passage from level to level as a ''Prolongation''. Adele T. Katz appears to be responsible for the shift of meaning where "prolongation" became the American translation of ''Auskomponierung'', "elaboration".〔Adele T. Katz (1935). "Heinrich Schenker's Method of Analysis", ''The Musical Quarterly'' 21/3, pp. 311-329. This conception of "prolongation" may have its origin in the teaching of Hans Weisse.〕
In his analysis of J.S. Bach's ''"Little" Prelude in d minor'', BWV 926, in ''Der Tonwille'' 5, Schenker proposes what may be his earliest figure showing the steps through which the ''Ursatz'' develops into the foreground. He explains that this figure "shows the gradual growth of the voice-leading prolongations, all predetermined in the womb of the Urlinie".〔''Der Tonwille'' 5 (1923), p. 8, Fig. 1; English translation (2004), p. 180.〕 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 (probably because it was the first of its kind). Schenker stresses that it starts with the two-voice setting of the ''Ursatz'' – an expression, therefore, of the fundamental laws of strict counterpoint. Each of the following steps is described as a ''Prolongation'', a specific freedom taken with respect to the laws expressed in the previous step. And in ''Freie Satz'', 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 ''prolongation'' and ''diminution'' as designations for the voice-leading levels in the middelground".〔''Der freie Satz'', 2d edition (1956), § 45, p. 57; English translation (1979), p. 25.〕
The concept of prolongation 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".〔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 individual level, exhausts itself purely physically without any concern for connection." ''Der Tonwille'' 5, p. 46; English translation, p. 213.〕 The means and techniques of passing from one level to the next are subsumed in Schenker's notion of "composing out" or "compositional elaboration" (''Auskomponierung'', 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".

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