Analyzing Form and Measuring Perceptual Content in Mozart's Sonata K. 282: A New Theory of Parametric Analogues

Abstract

Hierarchic analysis in music necessarily separates form from content. However, in active listening, the two are indivisible. To illustrate this, I first analyze in Part 1 the opening movement in Mozart's Sonata K. 282 from the top down, using traditional methods in music theory. Arriving at the manifest level, I then dissect the music from the bottom up, relying on the implication-realization model (Narmour, 1977,1989,1990,1991a, 1992). The contrasting perspectives reveal in great detail some of the movement's richly complex structuring. More generally, they confirm the inextricable feedback between parametric content and the meaning of form, specifically with respect to the contrary functions of closure and nonclosure. Following these analyses, Part 2 forges a synthesis by developing an implicative theory of analogical structures for melody, harmony, duration, and meter. Because, in terms of bottom-up processing, the analytical symbology for tracking structures is commensurable, we can, in all four primary parameters, weight similarity (aa), difference (ab), closure (stability), and nonclosure (implication) with comparable numbers. Further, by adding in some essential stylistic properties from the top down (scale step, diatonic pitch set, tonal cadential closure), we are able to represent the overall rhythmic shape of the first phrase in a single twodimensional graph. Thereby, we recapture from hierarchic analysis the perceptual sense that, in on-line listening, form and content are synthetically one.

A Model of Melodic Expectation

“…Although his implicationrealization theory successfully articulates many of the factors at play in melodic expectancy, it cannot be a complete theory, if only because of its omission of expectational assessments of many, and in some cases most, events in each melody. (Narmour, 1996).…”

Tracking musical patterns using joint accent structure.

“…Lengthened tones lead to closure and tend to be heard as end accents (e.g., Narmour, 1996) 2 . For these reasons we rely on distinct silences to convey beginning t accents.…”

Our Varying Histories and Future Potential: Models and Maps in Science, the Humanities, and in Music Theory

“…This is why I call the theory the "implication-realization model": its target of study is mostly melody, although I have claimed (Narmour 1990, Targets) becomes operational provides feedback interprets completes (not isomorphic) bottom up introspective (initiated from personal experience) rationalistic (certain concepts are privileged) phenomenological (certain observations asserted as mental objects, functioning as factual content in the theory) pragmatic (designed to facilitate the theory) empirical (if designed to be tested) often symbological (rule-driven nexus) implicative (pointing to "downstream" social practice) 1996) that the theory has the potential to deal with all musical parameters in any style. But that remains to be modeled (or mapped).…”

“…Numerous textbooks augmented these scholarly essays at the undergraduate level (e.g., Butler, 1992; Dowling and Harwood, 1986; Hargreaves, 1986;Sloboda, 1985, and others). During the same period, a number of music-theoretic books specifically directed toward music psychology shaped the field (e.g., Gjerdingen, 1988;Lerdahl & Jackendoff, 1983;Narmour, 1990Narmour, , 1992Parncutt, 1989). Solo books by scientists were also a regular and important occurrence (e.g., Krumhansl, 1990;Serafine, 1988;Sundberg, 1987).…”

“…As an example, consider the metatheoretical path chosen to formulate the implication-realization model (Narmour, 1990(Narmour, , 1992. I began by: (1) listing my intuitive, contemplative, and introspective speculations about melody; (2) devising postulates, grounds, axioms, and hypotheses for the theory; (3) making clear definitions of abstract (theoretical) and concrete terms, properties, and attributes (those to which people will normally assent); (4) writing a set of hierarchical statements (major and minor premises) in order to formulate (5) how the theory's construction can be systematically operational in terms of a symbological system and (6) how the theory is to be empirically evaluated in terms of principles, logical consistency, coherence, and parsimony.…”