Aspectsoftonalitycanbethoughtofaspatterncompletion.Theresidualef-
fect of prior exposure found in the responses of Indian listeners hearing Indian
ra ̄gs(Castellano, Bharucha, and Krumhansl, 1984) is evidence of this: a tempo-
ral composite of the underlying mode accounted for variance over and beyond
the variance accounted for by the probability distribution of pitch classes in the
segment. The segment seems to have activated an internal representation of the
mode, which in turn elaborated or filled out the percept. More direct evidence
comes from the priming of an important tone missing from ara ̄g,basedonthe
remaining tones (Bharucha, 1987b). Subjects’ responses in these studies seem to
reflect a composite of the distribution of pitch classes actually heard during the
experiment and an internal representation of the pitch classes that typically oc-
cur in that context. This should not be surprising at all, because the literature in
perception is filled with examples of top-down processing, that is, the influence
of context-dependent expectations based on prior experience.
In an autoassociator, the links between units serve to excite units whose pitch
classes co-occur and inhibit units whose pitch classes do not. This requires just
the right combination of weights on these links, because two pitch classes may
co-occur in one key or mode and not in another. Although this may seem like
an impossible standard for this tangled network to meet, a simple learning
mechanism can lead to this result.
For the purposes of illustration, it is useful to duplicate the units and think of
one copy as representing the stimulus that is actually heard and the other as
representing expectations that are triggered by this stimulus. Figure 19.7 shows
an array of pitch class units that represents, as a temporal composite, what has
been heard (the input) and another array of pitch-class units that represents
expectations based on what has been heard. Each input unit feeds into each
expectation unit. A learning mechanism called thedelta ruleenables the weights
to adjust themselves so each of a number of patterns presented repeatedly to
the input units will reproduce itself at the expectation units. The delta rule
derives from theperceptrondeveloped by Rosenblatt (1962).
Figure 19.7
An autoassociator with pitch-class units or invariant pitch-class units as input and expectation. The
input units constitute a temporal composite, and each input unit is connected to each expectation
unit.
Neural Nets, Temporal Composites, and Tonality 469