anglewitheachoftheoriginalvectorsthantheymakewitheachother.Inmore
than two dimensions, the resultant vector is the diagonal of the hyperparal-
lelogram formed by the summed vectors.
The resultant vector can be thought of as acomposite. Composites are super-
imposed patterns. They have some of the properties of prototypes, being per-
ceived as more familiar than any of the original patterns themselves (Metcalfe,
1991; Posner & Keele, 1968). It is fruitful to expand the notion of composite to
include all vectors that result from linear combinations of the original vectors.
A linear combination is the addition of vectors that may have scalar coef-
ficients. In a two-dimensional vector space, all the vectors that lie between two
given vectors are linear combinations—or composites—of them (right-hand
panel of figure 19.3). We can then think of a composite as the result of adding
intensity-scaled versions of several vectors.
F. Compositing Patterns over Time
As a piece of music unfolds, patterns can be composited over time by the ac-
cumulation of activation, creating atemporal composite memory. Suppose, for
example, that the features of interest are pitch classes. When a musical se-
quence begins, the pattern of pitch classes that are sounded at timet 0 con-
stitutes a vector,p 0 , in 12-dimensional pitch-class space. If at a later time,t 1 ,
another pattern of pitch classes is sounded, represented by vectorp 1 ,acom-
posite,c 1 , covering a period of time ending att 1 , can be formed as follows:
c 1 ¼s 1 p 0 þp 1 ;wheres 1 ð 0 as 1 a 1 Þis the persistence ofp 0 att 1. When yet another set of pitch
classesisheardattimet 2 , the resulting composite,c 2 ,is:
c 2 ¼s 2 c 1 þp 2 :When thenth set of pitch classes is sounded attn,thecomposite,cn,is
cn¼sncn 1 þpn;wheresn, the persistence ofcn 1 attn, brings about the diminution of the rep-
resented salience ofcn 1 as it recedes into the past. It controls the relative
weighting of the most recent pattern,pn, relative to the patterns that came
Figure 19.3
Left: Vector addition.ris the sum ofpandq. Right: Composite patterns resulting from linear com-
bination of vectors. All vectors within the angular sweep ofpandqare composites of them.
Neural Nets, Temporal Composites, and Tonality 461