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Resonance and the Perception of Musical Meter
 CONNECTION SCIENCE
, 1994
"... Many connectionist approaches to musical expectancy and music composition let the question of "What next?" overshadow the equally important question of "When next?". One cannot escape the latter question, one of temporal structure, when considering the perception of musical meter. We view the percep ..."
Abstract

Cited by 93 (3 self)
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Many connectionist approaches to musical expectancy and music composition let the question of "What next?" overshadow the equally important question of "When next?". One cannot escape the latter question, one of temporal structure, when considering the perception of musical meter. We view the perception of metrical structure as a dynamic process where the temporal organization of external musical events synchronizes, or entrains, a listener's internal processing mechanisms. This article introduces a novel connectionist unit, based upon a mathematical model of entrainment, capable of phase and frequencylocking to periodic components of incoming rhythmic patterns. Networks of these units can selforganize temporally structured responses to rhythmic patterns. The resulting network behavior embodies the perception of metrical structure. The article concludes with a discussion of the implications of our approach for theories of metrical structure and musical expectancy.
Mixed memory Markov models: decomposing complex stochastic processes as mixtures of simpler ones
, 1998
"... . We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combinationor mixtureof simpler dynamical models. The parameters in these models admit a simple ..."
Abstract

Cited by 62 (1 self)
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. We study Markov models whose state spaces arise from the Cartesian product of two or more discrete random variables. We show how to parameterize the transition matrices of these models as a convex combinationor mixtureof simpler dynamical models. The parameters in these models admit a simple probabilistic interpretation and can be fitted iteratively by an ExpectationMaximization (EM) procedure. We derive a set of generalized BaumWelch updates for factorial hidden Markov models that make use of this parameterization. We also describe a simple iterative procedure for approximately computing the statistics of the hidden states. Throughout, we give examples where mixed memory models provide a useful representation of complex stochastic processes. Keywords: Markov models, mixture models, discrete time series 1. Introduction The modeling of time series is a fundamental problem in machine learning, with widespread applications. These include speech recognition (Rabiner, 1989), natu...