Melodic expectation

Abstract: The cognitive representation of harmonic and tonal structure in Western music is investigated using a tone-profile technique. In this method listeners rate how well single tones (any one of the 12 tones of the chromatic scale) follow a musical element such as a scale, chord, or cadence. Very stable rating profiles reflecting the tonal hierarchies in major and minor keys are obtained, which, when intercorrelated and analyzed using multidimensional scaling, produce a four-dimensional spatial map of the distances between keys. The keys are located on the surface of a torus, in which the circle of fifths and the parallel and relative relations between major and minor keys are represented. In addition, single chords (major, minor, diminished, and dominant seventh) are found to be closely associated with the major and minor keys in which they play harmonic functions. The developing and changing sense of key during sequences of chords is traced by obtaining probe tone ratings following each chord in 10 different sequences, 8 of which contain modulations (changes) between keys. Modulations between closely related keys are found to be effected more immediately than are modulations between relatively distant keys. In all cases beyond the initial chord, the sense of the prevailing key is stronger than that produced by the last heard chord in isolation. Thus, listeners integrate harmonic functions over multiple chords, developing a sense of key that may need to be reevaluated as additional chords are sounded. It is suggested that the perceived relations between chords and keys and between different keys are mediated through an internal representation of the hierarchy of tonal functions of single tones in music. Music consists of tones varying in pitch, serve to highlight rhythmic patterns, further duration, loudness, and timbre, but the per- emphasize phrase structure, and distinguish ception of music extends well beyond the between tones constituting the primary meregistration of these physical attributes of lodic line and tones serving more ornamental the musical stimulus. Indeed, music contains or harmonic functions. Timbral characterconsiderable structure even in the relations istics may additionally provide important that obtain among the individual tones. For cues for the overall structure of the musical example, the durations are such that metri- composition.

Abstract: Eugene Narmour formulates a comprehensive theory of melodic syntax to explain cognitive relations between melodic tones at their most basic level. Expanding on the theories of Leonard B. Meyer, the author develops one parsimonious, scaled set of rules modeling implication and realization in all the primary parameters of music. Through an elaborate and original analytic symbology, he shows that a kind of "genetic code" governs the perception and cognition of melody. One is an automatic, "brute" system operating on stylistic primitives from the bottom up. The other constitutes a learned system of schemata impinging on style structures from the top down. The theoretical constants Narmour uses are context-free and, therefore, applicable to all styles of melody. He places considerable emphasis on the listener's cognitive performance (that is, fundamental melodic perception as opposed to acquired musical competence). He concentrates almost exclusively on low-level, note-to-note relations. The result is a highly generalized theory useful in researching all manner of psychological and music-theoretic problems concerned with the analysis and cognition of melody. "In this innovative, landmark book, a distinguished music theorist draws extensively from a variety of disciplines, in particular from cognitive psychology and music theory, to develop an elegant and persuasive framework for the understanding of melody. This book should be read by all scholars with a serious interest in music."--Diana Deutsch, Editor, Music Perception

Abstract: Models of pitch space have been developed in music psychology to account for perceived proximity among pitches, chords, or regions. This article introduces a different model that (1) treats pitches, chords, and regions within one framework, (2) correlates with the experimental data, and (3) connects in interesting ways with a variety of music theories.

Abstract: The Implication-Realization (IR) theory (Narmour, 1990) posits two cognitive systems involved in the generation of melodic expectations: The first consists of a limited number of symbolic rules that are held to be innate and universal; the second reflects the top-down influences of acquired stylistic knowledge Aspects of both systems have been implemented as quantitative models in research which has yielded empirical support for both components of the theory (Cuddy & Lunny, 1995; Krumhansl, 1995a, 1995b; Schellenberg, 1996, 1997) However, there is also evidence that the implemented bottom-up rules constitute too inflexible a model to account for the influence of the musical experience of the listener and the melodic context in which expectations are elicited A theory is presented, according to which both bottom-up and top-down descriptions of observed patterns of melodic expectation may be accounted for in terms of the induction of statistical regularities in existing musical repertoires A computational model that embodies this theory is developed and used to reanalyze existing experimental data on melodic expectancy The results of three experiments with increasingly complex melodic stimuli demonstrate that this model is capable of accounting for listeners’ expectations as well as or better than the two-factor model of Schellenberg (1997)