If the input is a tonal composite, this procedure will lead to the formation of
abstract feature detectors for typical composite patterns. The chord and key
units in the MUSACT model (Bharucha, 1987a, 1987b) are thus a direct and
mandatory consequence of self-organization. Pitch classes that co-occur within
a tonal composite that spans the duration of a chord (explicit or implied) will
become associated via the chord detectors that form. Chords that co-occur
within a tonal composite that spans a piece or a key segment will become
associated via the key detectors that form. After these associations are suffi-
ciently strong, hearing one chord will lead to expectations for other chords that
co-occur in the same composite, because activation flows from one chord unit
to parent key units and down to the other chord units in the same composite.
The MUSACT model suggests how the graded activation of chords, mediated
by the multiplicity of their parent keys, and the priming data that provide evi-
dence of this, can be explained by this process (Bharucha, 1987a, 1987b).
Adopting an input representation that is essentially a temporal composite of
invariant pitch-class units, Gjerdingen (1989b) exposed a self-organizing net-
work to works of early Mozart. The network developed categories units (ab-
stract feature detectors) for sequential patterns that characterize the style of the
corpus.
B. Encoding Temporal Composites through Autoassociation
Consider a network in which each unit is connected by unidirectional links
to every other unit and to itself. This network can learn to encode patterns
through autoassociation, that is, by associating them with themselves (J. A.
Anderson, 1970, 1972; J. A. Anderson, Silverstein, Ritz, & Jones, 1977). Why
would one wish to associate patterns with themselves? Neural net autoasso-
ciators have a remarkable property: If after learning a set of patterns, an in-
complete or degraded version of one of the learned patterns is presented to the
network, it will be completed or filled in by the network. Pattern completion is
a general principle of perception that enables us to recognize objects that are
partially masked or occluded and to perceive them as unbroken wholes, with
the concomitant risk of error or illusion. Terhardt (1974) has argued that many
auditory phenomena are examples of this aspect of Gestalt perception.
Figure 19.6
The weight vector (solid line) with the smallest angle to the activation vector (dashed line) repre-
sents the winning category unit. Learning consists of making the angle even smaller.
468 Jamshed J. Bharucha