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).

In previous approaches to repetition discovery in music, the music to be analysed has been represented using strings. However, there are certain types of interesting musical repetitions that cannot be discovered using string algorithms. We propose a geometric approach to repetition discovery in which the music is represented as a multidimensional dataset. Certain types of interesting musical repetition that cannot be found using string algorithms can efficiently be found using algorithms that process multidimensional datasets. Our approach allows polyphonic music to be analysed as efficiently as monophonic music and it can be used to discover polyphonic repeated patterns “with gaps” in the timbre, dynamic and rhythmic structure of a passage as well as its pitch structure. We present two new algorithms: SIA and SIATEC. SIA computes all the maximal repeated patterns in a multidimensional dataset and SIATEC computes all the occurrences of all the maximal repeated patterns in a dataset. For a k -dimensional d...