Music Expectation by Cognitive Rule-Mapping

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

Toward a Unified Theory of the I-R Model (Part 1): Parametric Scales and Their Analogically Isomorphic Structures

By extensively revising the I-R model of by melody (Meyer, 1973; Narmour, 1984, 1989, 1990, 1991a, 1991b, 1992, 1996, 2000) we can explain the structural functions of many musical parameters. Here I will deal with melodic interval, registral direction, pitch height, scale-step (major and minor), duration (interval, length, rate, speed, and pace), tempo, dynamics (loudness), and texture (saving the other parameters for a later essay). By reconceptualizing the model’s core concept of functional directionality within parametric scales, only three isomorphic structural analogues become cognitively necessary, namely, process (and its variant duplication), reversal, and return. Attached signs (0, ~, - , +) augment the main symbols (P, D, and R) so as to track strength of implication, realization, and denial. A new theory of rhythmic structure is put forth. And with an aim toward theoretical unification, the reconfigured model confronts the combinatorial complexities of parametric interactions and offers convincing interpretations of congruence and noncongruence— the primary sources of musical affects. Works of Brahms, Debussy, Mussorgsky-Ravel, and Schoenberg are analyzed

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

Part 1 briefly recounts the influence of social unrest and the explosion of knowledge in both psychology and the humanities circa 1970-1990. As the sciences rely on explicit top-down theories connected to bottom-up maps and models, and whereas the humanities build on bottom-up differences within malleable top-down “theories” (approaches, themes, theses, programs, methods, etc.), the changes in the sciences during this period contrasted sharply with the changes in the humanities. Part 2 discusses in detail how these two social transformations affected the histories of music theory and cognitive music theory. The former fractiously withdrew from its parent organization (AMS), whereas the latter was welcomed into SMPC. Inasmuch as both music theory and cognitive music theory rely on maps and models, Part 3 examines the metatheoretical importance of these terms for music cognition, music theory, and cognitive music theory. Part 4 speculates about the future—how music cognition, cognitive music theory, and music theory contribute to the structure of musical knowledge. The intellectual potential of this unique triadic collaboration is discussed: psychology provides a commanding empirical framework of the human mind, while music theory and cognitive music theory logically model moment-to-moment temporal emotions and the auditory intellections at the core of musical art

Some Major Theoretical Problems Concerning the Concept of Hierarchy in the Analysis of Tonal Music

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\u27s 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\u27s various levels are rendered into rankings of pitch shown on one level only

The Top-Down and Bottom-Up Systems of Musical Implication: Building on Meyer\u27s Theory of Emotional Syntax

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)

Harmonic Closure: Music Theory and Perception

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

Memetic Perspectives on the Evolution of Tonal Systems

Cohn (1996) and Taruskin (1985) consider the increasing prominence during the nineteenth century of harmonic progressions derived from the hexatonic and octatonic pitch collections respectively. This development is clearly evident in music of the third quarter of the century onwards and is a consequence of forces towards non-diatonic organization latent in earlier music. This article conceptualizes such forces as memetic — drawing a distinction between memetic processes in music itself and those in the realm of music theory — and interprets the gradualistic evolution of tonal systems as one of their most significant consequences. After outlining hypotheses for the mechanisms driving such evolution, it identifies a number of ‘musemes’ implicated in hexatonic and octatonic organization in a passage from Mahler’s Symphony no. 10. Pople’s (2002) Tonalities music-analysis software is used to explore the tonal organization of the passage, which is considered in relation to the musemes hypothesized to generate and underpin it