Whether the influence was from Schenker or indirectly from Salzer's Structural Hearing, there is no question that analytical models from the 1970s and early 1980s engaged with the Schenkerian model for traditional European tonal music. In the two best-known systems from that era, Lerdahl and Jackendoff reinscribe prolongation in terms of what were then contemporary theories of cognition, and Leonard Meyer sets up his implication-realization model as a different kind of "shadow Schenker" on the basis of earlier Gestalt theories.
Meyer informally adopts notions of hierarchy and reduction, but like Lerdahl (and unlike Schenker) he is wary of assigning any spiritual significance (because of the generally recognized limitation on repertoire still in force at the time, he did not need to argue issues of canonization). Meyer does go much further than Lerdahl in ascribing cultural significance to music and its expressivity, though always in the context of a history of style. He develops these ideas extensively elsewhere, but in Explaining Music, his book on musical analysis he restricts himself to effects and relationships; these are four: hierarchic organization, and implicative, conformant, and ethetic relationships. Critical analysis (as he calls it) is primarily concerned with the first three, and expressivity is primarily a matter of the setting up of expectations and their subsequent dousing or realizing.
Meyer's "implicative" is identical to David Bordwell's term "gap," in the latter's similarly Gestaltist theory of film narrative. Meyer, however, uses "gap" for a specific class of melodic process. He gives most of his attention to melody, using both rhythm and harmony (but more the former than the latter) as contributors; he builds a catalogue of melodic processes, all of which are implicative, and among which the "gap-fill" melody is perhaps the most prominent. Under a Meyer-style scrutiny, the melodies of D779n13 become quite complex: an amalgam of overlapping types that just barely yield at last to a hierarchy of scale (the process that covers the distance of the whole piece sits at the top of the hierarchy).
The gap-fill model works in miniature in the opening eight-note motive (see graphic below), but the continuation gives the effect of a bilevel melody (Meyer's term for what is also called "polyphonic melody," a single melodic line that clearly contains two separate voice-leading parts – here, of course, the two parts are indeed separate voices). The symmetry of a complementary melody encompasses the first phrase (mm. 2-9), as the initial E-F# figure is answered by the F#-E 6-5 figure over the tonic at the end of the phrase (level b). The same initial figure can simultaneously imply continuation with a rising series of steps and so encompasses the first strain through its realization in the cadence figure (level c). Finally, the suspensions of the alto voice are strongly linear, but descending (level d). Taken together, levels c and d give the effect of a "diverging" melody – again, recognizing that these really are two separate parts. Meyer recognizes "convergence" as a type – two strands of (typically) linear melody that converge on a single tone. Here the effect is not of a wedge closing, but of one opening (to the octave).
The next graphic shows large-scale implicative processes (those that cover the whole piece). The C#-E interval of the opening suggests an arpeggio whose continuation is realized with the concluding A5 (level a), but this pattern continues through the C#-major section to E6 in the reprise (m. 33). Level b shows a complementary pattern in the second strain, while level c shows how level b's first component can be understood as completing a gap-fill process initiated in the first strain.
The final graphic gathers the larger-scale elements (labelled "x") in a summary of the processive hierarchy; the linear pattern ("a") is placed in the lower staff.
Tomorrow's post will comment on these analyses.
References.
Meyer, Leonard B. Explaining Music: Essays and Explorations. Berkeley: University of California Press, 1973.
Bordwell, David. Narration in the Fiction Film. Madison: University of Wisconsin Press, 1985.
