chord transitions. This corpus roughly represents the transition probabilities
of chord functions in the common practice era, but contains a small proportion
of highly unusual transitions because of the random generation procedure. In
order to encapsulate the potentially large number of possible ‘‘additional con-
text’’ features, one additional context unit was assigned to each sequence as a
place holder for all the contextual information that might help individuate this
sequence.
After repeated presentation of the sequences, the network learned to predict
the first event in each sequence in response to the activation of its additional
context unit and learned to predict each successive event in response to the
temporal composite of chords played thus far plus the activation of its addi-
tional context unit. In a performance model, this would enable the performer to
play the first event. In a perceptual model, it would enable the listener to rec-
ognize whether or not the correct event was played.
After learning, the network was presented repeatedly with two new se-
quences: one consisted entirely of schematically expected (high-probability)
transitions and the other of schematically unexpected (low-probability) tran-
sitions. The schematic sequence was learned in fewer presentations. The net-
work adapted more quickly to the sequence that was typical of the corpus than
to the sequence that was unusual, even though both were novel. This suggests
that the network learned not only the sequences themselves but also the generic
or schematic relationships of the style.
The same network therefore contains information about the two types of
expectations—veridical and schematic—that usually converge but sometimes
diverge. When they diverge, the performer is able to produce, and the listener
to recognize, the correct next event while nevertheless experiencing its unex-
pectedness. The divergence of expectations when an unusual transition occurs
in a familiar piece addresses what Dowling and Harwood (1986) refer to as
Wittgenstein’s puzzle. It also accounts for how expectancy violation, which
Meyer (1956) considers central to our aesthetic response to music, can continue
to occur in a familiar, overlearned piece.
The network reveals these divergent expectations when the activation of ex-
pectation units following the onset of an event is observed over time. We have
thus far considered only spatial summation of activation. The buildup of acti-
vation in a neuron as an event gets under way is the result of temporal sum-
mation. If we consider both spatial and temporal summation, the net input to a
unit can be modeled usingcascadedactivation (McClelland, 1979):
netj;t¼kX
iwijai;t!
þð 1 kÞnetj;tDt;wherekð 0 aka 1 Þrestricts the incremental net input in any given time slice,
Dt, and the second term of the equation carries over net input form the previous
time slice, thereby causing the net input to build up over time.
With cascaded activation, high-probability (schematic) expectations were
generated in less time than low-probability expectations (Bharucha & Todd,
1989). Unique expectations, resulting from chord transition that occurred only
once in the corpus, took the longest. This is presumably because the net-
474 Jamshed J. Bharucha