Hearing in Time: Psychological Aspects of Musical Meter

This is the first logically precise, computationally implementable, book-length account of rational belief revision. It explains how a rational agent ought to proceed when adopting a new belief - a difficult matter if the new belief contradicts the agent's old beliefs. Belief systems are modeled as finite dependency networks. So one can attend not only to what the agent believes, but also to the variety of reasons the agent has for so believing. The computational complexity of the revision problem is characterized. Algorithms for belief revision are formulated, and implemented in Prolog. The implementation tests well on a range of simple belief-revision problems that pose a variety of challenges for any account of belief revision. The notion of 'minimal mutilation' of a belief system is explicated precisely for situations when the agent is faced with conflicting beliefs. The proposed revision methods are invariant across different global justificatory structures (foundationalist, coherentist, etc.). They respect the intuition that, when revising one's beliefs, one should not hold on to any belief that has lost all its former justifications. The limitation to finite dependency networks is shown not to compromisetheoretical generality.This account affords a novel way to argue that there is an inviolable core of logical principles. These principles, which form the system of Core Logic, cannot be given up, on pain of not being able to carry out the reasoning involved in rationally revising beliefs.The book ends by comparing and contrasting the new account with some major representatives of earlier alternative approaches, from the fields of formal epistemology, artificial intelligence and mathematical logic.Our sense that a waltz is "in three" or a blues song is "in four with a shuffle" comes from our sense of musical meter. Hearing in Time explores the metric aspect of our musical experience from a psychological point of view. Musical meter is taken as a musically-specific instance entrainment, that is, our more general ability to synchronize our actions to the rhythms around us. As such, musical meter is subject to a number of fundamental perceptual andcognitive constraints. These constraints are the cornerstones of Hearing in Time's account of musical meter. Hearing in Time also takes into account the fact that listening to music, like many other rhythmic activities, is something that we do a lot. It also approaches musical meter in the context of music asit is actually performed, with nuances of timing and dynamics, rather than as a theoretical ideal.Hearing in Time's approach to meter is not based on any particular musical style or cultural practice, and so it discusses musical examples from a wide range of musical styles and cultures-from Beethoven and Bach to Brubeck and Ghanaian (Ewe) drumming. In taking this broad approach a number of fundamental similarities between a variety of different metric phenomena-such as the difference between so-called simple versus complex or additive meters-become apparent.Hearing in Time is written for musicians, musicologists, music theorists and psychologists who are interested in rhythm and meter. Only a modest ability read a musical score is presumed, and most musical examples are taken from familiar popular and classical repertory.