The implication-realization model hypothesizes that emotional syntax in music is a product of two expectation systems-one top down, the other bottom up. Syntactic mismatch or conflict in realizations can occur either within each system or between them. The theory argues that interruption or suppression of parametric expectations generated separately by the two systems explains certain types of recurrent aesthetic strategies in melodic composition and accounts for the most common kinds of musical forms (AAA, AAB, ABB, ABC, and ABA). Disciplines Music | Musicology | Music TheoryThis journal article is available at

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Iterative rules appear everywhere in music cognition, creating strong expectations. Consequently, denial of rule projection becomes an important compositional strategy, generating numerous possibilities for musical affect. Other rules enter the musical aesthetic through reflexive game playing. Still other kinds are completely constructivist in nature and may be uncongenial to cognition, requiring much training to be recognized, if at all. Cognitive rules are frequently found in contexts of varied repetition (AA), but they are not necessarily bounded by stylistic similarity. Indeed, rules may be especially relevant in the processing of unfamiliar contexts (AB), where only abstract coding is available. There are many kinds of deduction in music cognition. Typical examples include melodic sequence, partial melodic sequence, and alternating melodic sequence (which produces streaming). These types may coexist in the musical fabric, involving the invocation of both simultaneous and nested rules. Intervallic expansion and reduction in melody also involve higherorder abstractions. Various mirrored forms in music entail rule-mapping as well, although these may be more difficult to perceive than their analogous visual symmetries. Listeners can likewise deduce additivity and subtractivity at work in harmony, tempo, texture, pace, and dynamics. Rhythmic augmentation and diminution, by contrast, rely on multiplication and division. The examples suggest numerous hypotheses for experimental research. Disciplines Music | Musicology | Music TheoryThis journal article is available at ScholarlyCommons: http://repository.upenn.edu/music_papers/3 Cognitive rules are frequently found in contexts of varied repetition (AA), but they are not necessarily bounded by stylistic similarity. Indeed, rules may be especially relevant in the processing of unfamiliar contexts (AB), where only abstract coding is available.There are many kinds of deduction in music cognition. Typical examples include melodic sequence, partial melodic sequence, and alternating melodic sequence (which produces streaming). These types may coexist in the musical fabric, involving the invocation of both simultaneous and nested rules.Intervallic expansion and reduction in melody also involve higherorder abstractions. Various mirrored forms in music entail rule-mapping as well, although these may be more difficult to perceive than their analogous visual symmetries. Listeners can likewise deduce additivity and subtractivity at work in harmony, tempo, texture, pace, and dynamics. Rhythmic augmentation and diminution, by contrast, rely on multiplication and division. The examples suggest numerous hypotheses for experimental research.Received October 13, 1999; accepted for publication January 12, 2000. psychologists believe that humans apply rules in order to process certain kinds of stimuli. Recent work argues that even infants identify variables, devise symbolic representations, and construct generalizations in order to arrive at contextual linguistic meanings (M...

Music theorists have often disagreed about the material variables that determine the perception of harmonic closure. To investigate this controversial topic, we presented subjects with pairs of selected two-chord progressions. The subjects judged which member of each pair seemed more closed. Preferences varied across pairs of cadences and generally obeyed transitivity. Quantitative reformulation of theoretical harmonic variables permitted correlational analysis of the results. Three or four variables, including one or two that reflect learned stylistic structures, best explained our findings. Conventional harmonic factors of scale step, soprano position, and root position demonstrated surprisingly little explanatory power.

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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.

Level-analysis in the field of music theory today is rarely hierarchical, at least in the strict sense of the term. Most current musical theories view levels systemically. One problem with this approach is that it usually does not distinguish compositional structures from perceptual structures. Another is its failure to recognize that in an artifactual phenomenon the inherence of idiostructures is as crucial to the identity of an artwork as the inherence of style structures. But can the singularity of an idiostructure be captured in the generality of an analytical symbol? In music analysis, it would seem possible provided closure and nonclosure are admitted as simultaneous properties potentially present at all hierarchical levels. One complication of this assumption, however, is that both network and tree relationships result. Another is that such relationships span in both "horizontal" (temporal) and "vertical" (structural) directions. Still another complication is the emergence of transient levels. In this paper, a tentative solution to these problems is offered by invoking a hypothetical theory that relies on the cognitive concepts of return, reversal, and continuation (i.e., similarity) as regards the parameters of melody, harmony, and duration. Applied to the theme of Mozart's Piano Sonata, K. 331, this analytical theory is contrasted with several systemic analyses of the same theme by the theorists DeVoto, Lester, Schenker, and Meyer. In conclusion, the hierarchical analysis of the Mozart theme gives way to a synthesis as the melody's various levels are rendered into rankings of pitch shown on one level only.

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