primes the target. Priming thus reveals the extent to which one stimulus evokes
another. Priming tasks are well suited to studying music cognition because of
their robustness across levels of formal expertise. Because of the premium on
speed, there isn’t time for musical experts to use analytical strategies; and if the
true/false decision is one that novices can make, priming can reveal associa-
tions that the novice may be unable to express verbally.
Priming studies demonstrate that musical events that typically co-occur in a
musical culture become mentally associated. For Western listeners, for exam-
ple, chords that have high transition probabilities in Western music prime each
other, even though they may share no frequencies (Bharucha, 1987b). For In-
dian listeners, tones that typically co-occur in a particulartha ̄tprime other
tones in thetha ̄t(Bharucha, 1987b).
Tonal and modal composites can account for these results if they are encoded
for later retrieval. Pitch classes or invariant pitch classes that co-occur in a
temporal composite can become mentally associated if the composite is stored
in memory. The long-term encoding of composited information can be accom-
plished by neural nets that adjust the connections between units, and is the
subject of Sections II,A and II,B.
Although it may seem that the temporal integration in tonal or modal com-
posites results in a complete loss of information about the serial order of events,
serial order can indeed be recovered, as needed for the recognition and perfor-
mance of pieces of music, if the context is unambiguous. Section II,C deals with
the long-term encoding and recovery of sequences using modal composites.
II. Neural Association and Learning
This section deals with how a neural net can learn temporal composite patterns
so that they function as schemas and as sequential memories. (Some of these
mechanisms may be limited to modal composites for most of the population
but may extend to tonal composites for absolute pitch possessors.)
A neural net (equivalently, a connectionist or parallel distributed network)
consists of units connected by links. Links have weights associated with them,
representing the strengths of the connections between units. Thenet inputto a
unit at any given time is a weighted sum of activations received through the
links that connect to it (spatial summation), integrated over time (temporal sum-
mation). We will deal only with spatial summation first and then introduce
temporal summation later. Spatial summation can be modeled as follows. The
net input,netj,tounitj,is
netj¼X
iwijaiwherewijis the weight associated with the link from unitito unitj,andaiis
the activation of uniti. The summation is over all unitsithat connect toj.
Links may be unidirectional or bidirectional, or may conduct different kinds
ofinformationindifferentdirections.Althoughsynapsesinthebrainaretypi-
cally unidirectional, departures from strict unidirectionality in a neural net
model are not neurophysiologically implausible, because separate sets of syn-
apses could underlie different directions of information flow.
Neural Nets, Temporal Composites, and Tonality 465