- The author proposes a method for constructing a mathematical
function of event-onset expectancy projected over time from a
complex temporal pattern. Given some complex temporal pattern
(i.e., a sequence of time intervals defined by the onsets of
events in a rhythmic pattern), such a function would describe,
for any point in time after the pattern is heard, the degree to
which the listener might expect the onset of an event at that
point in time. The function would be derived by summing a number
of component or "basic" expectancy functions; hence the "complex"
function can be described as "decomposable." Each of the
component or "basic expectancy" functions is projected from the
single time interval bounded by one of the unique (adjacent or
non-adjacent) pairs of onsets in the complex pattern. Given any
method for constructing a basic expectancy function, the complex
function can thus be derived. The author does, however, propose
an approximation of such a basic expectancy function, in which
peaks in expectancy occur at points that define time intervals
that are simple integral multiples or divisions of the given
basic interval, as well as ways in which such a function might be
verified empirically. Finally, the application of the proposed
theory of complex expectancy to such topics as the Gestalt
principle of Good Continuation, meter inducement, rhythmicity and
syncopation, and especially categorical rhythm perception (see Clarke
1987a) is suggested.
**Keywords:**

Rhythm and Meter |
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