A definition is given of expectancy of events projected into the future by a complex temporal sequence. The definition can be decomposed into basic expectancy components projected by each time interval implicit in the sequence. A preliminary formulation of these basic curves is proposed and the (de)composition method is stated in a formalized, mathematical way. The resulting expectancy of complex temporal patterns can be used to model such diverse topics as categorical rhythm perception, clock and meter inducement, rhythmicity, and the similarity of temporal sequences. Besides expectancy projected into the future, the proposed measure can be projected back into the past as well, generating reinforcement of past events by new data. The consistency of the predictions of the theory with some findings in categorical rhythm perception is shown.
Many incompatible theories about temporal perception and memory exist, which explain a number of phenomena well, but fail to predict others. A common theoretical basis for such work would be desirable. Connectionism might be an attractive paradigm in the search for such a basis, but most of its models lack compositionality. This means that the model as a monolithic whole might perform well, but it is impossible the decompose its complex behaviour into meaningful smaller parts. Chandrasekaran (1990) argues that the composability is a condition for successful cognitive modelling, even in the connectionist paradigm. In Desain (1990) the behavior of a sub-symbolic (connectionist) model of temporal quantization was described such that it could be compared with an incompatible symbolic model from the traditional AI paradigm. The paper concluded with an abstraction of the behavior of the quantizer in the form of an 'expectancy of events' with a temporal pattern as prior context. Expectancy turned out to be (de)composable which makes it possible to base a theory of perception of complex stimuli on a simple model for the perception of their constituting components. Because the expectancy concept seems to explain the dependency of perception of rhythmic structure on global tempo, the influence of context on categorical perception and other complex phenomena I propose to use it as a common basis for theories about temporal perception and memory. It is noteworthy that Povel (1984, 1985) has already remarked that high level cognitive judgements like rhythmicity might be based on, or be a byproduct of, low level rhythm perception processes that deal with quantization and tempo tracking.
"The experience of rhythmicity is supposed to result from the process that updates the internal clock in the light of the incoming stream of events. It may be noted that this process makes part of the normal process of listening to music in which the listener constantly adjusts his internal clock (metrical frame) to local temporal irregularities and tempo variations" (Povel,1984)
In this paper I will focus on the explanation and formalization of the theory and the composability of the definition of expectancy. The interpretation of the resulting curves, their possible use, and their relations to other research aimed at a higher level of rhythm perception, will be dealt with in Desain (in preparation). Although the theory looks attractive enough, I have to warn the reader that this paper is an account of recent work and it has yet to be empirically verified.