before. Whensn¼0, there is no temporal integration—no memory except for
themostrecentevent.Whensn¼1, events at different points in time are com-
pressed into a composite on equal terms.
Evidence for the persistence of tonal activation is clear. A chord sounded for
as short a duration as 50 msec can prime a subsequent chord even if they are
separated by as much as 2.5 sec of silence (Tekman & Bharucha, 1992).Priming
refers to the automatic (i.e., robust and difficult to suppress) expectation for a
target event following a context and is measured by the extent to which the
context increases the speed and accuracy with which the target is perceptually
processed.
The implementation ofsnin a neural net varies among models that have
either explicitly or implicitly adopted a temporal compositing representation
for music. In the MUSACT model (Bharucha, 1987a, 1987b), the persistence of a
previously heard pattern decays exponentially over time. Ifdð 0 ada 1 Þis the
decay rate (i.e., the proportion by which activation decreases per unit time),
and iftis the number of time intervals since the last event, then:
sn¼ð 1 dÞt:Although the duration of each time interval controls the temporal resolution of
the representation,ddetermines the length of the temporal window over which
information is being integrated.
Although activation in the MUSACT model is strictly phasic, it would be
reasonable, in future modeling efforts, to hypothesize a strong phasic response
to the onset of a sound followed by a weaker tonic response. This amounts to
the continuous formation of new composites, even during the duration of a
tone, and is most easily modeled by computing new composites at small and
equal time intervals. A sequence would thus be represented as a composite of a
series of vectors at the ends of successive time intervals. Some time intervals
would include event onsets and others would not. If the time intervals are suf-
ficiently small, this scheme could capture some of the nuances in pitch that are
lost when music is represented as a score of notes. Temporal composites can
also be explored as a way to represent the spectral flux dimension of timbre.
Temporal composites with small time intervals derive some plausibility from
temporal summation in the nervous system. Zwislocki (1960, 1965) found that
thresholds for detecting tones show a trade-off between duration and intensity
(as would be predicted by a temporal composite) and suggests that a combina-
tion of decay and summation of neural activity can account for this.
Some models implement persistence by linking each unit to itself, as shown
in figure 19.4 (Bharucha, 1988; Bharucha & Todd, 1989; Todd, 1988, 1989). Each
Figure 19.4
Implementing a temporal composite with links from each unit to itself.
462 Jamshed J. Bharucha