Prolongation
[5] 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[6] and the phenomena resulting from the extension of these laws.
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.
[10] 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".
In Schenkerian analysis, the analyst discerns ways in which prolongation creates the details of a musical composition by elaborating the background structure.
Prolongational techniques include arpeggiations, linear progressions, unfoldings, etc., in general aiming at the horizontalization, "the elaboration in time of a governing vertical sonority – a chord or an interval.
"[27] Schenker intended his theory to apply only to music of the common practice period, and there to a select class of mostly Austro-German composers in a line from J.S.
[citation needed] 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.
[29] Atonal music poses a stark challenge to prolongational hearing and analysis, as its harmonic makeup by definition eschews the long-range controlling force of monotonality, and in most cases purposely abstains from consonant triads, or indeed referential or centric sonorities at all.
[citation needed] Music theorist Joseph Straus has attempted to define more rigorously what it is about atonality that precludes prolongational hearing.
[33] Miguel Roig-Francolí 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.
