ral units, as in spreading activation network models (J. R. Anderson, 1983;
Collins & Quillian, 1969). The underlying mechanism could well be the re-
sponse strength of a group of neurons rather than an individual neuron (Hebb,
1949). For this reason we shall use the termunitinstead ofneuronin the context
of a model, reserving the latter term for units that are known to be individual
neurons.
Numerous mechanisms have been used to model changes in activation over
time. These include phasic versus tonic responses, oscillating circuits, temporal
composites, and cascaded activation. The first two will be summarized briefly
in this section, and the last two will be covered more extensively in later
sections.
In the cochlear nucleus and beyond, tones elicit bothphasicandtonicre-
sponses. A phasic response is a response to change (usually the onset or offset
of a tone); a tonic response is sustained throughout the duration of a tone. Most
neurons in the cochlear nucleus show a strong phasic response to the onset of a
tone, followed by a weaker tonic response over the sustained portion of a tone
(Kiang, 1975). Some neurons (the so-called octopus cells) show only a phasic
response to onsets. This enhancement of onsets may serve to draw attention to
a new event and may play a role in segmenting the musical stream. Phasic
activation can account for the salience of harmonic rhythm (Bharucha, 1987a).
Some neurons switch from tonic to phasic as intensity increases (Gulick,
Gescheider, and Frisina, 1989); thus both onset and intensity are to some extent
coded by a phasic response. This helps explain how chord changes can compete
with high-intensity percussive sounds in establishing the meter. (In rock music,
for example, the highest intensity percussive sound is often on a weak beat, and
it is presumably the chord changes that establish the meter).
Activation can be modulated cyclically over time by oscillatory circuits.
These circuits give the activation an isochronous pulse, and have been used by
Gjerdingen (1989a) to model meter. Phasic activation and oscillatory circuits
are consistent with the idea, proposed by Jones (1989), that meter is temporally
focused attention: phasic responses draw attention to the onsets of tonal
changes, and oscillatory circuits are implementations of attention via the mod-
ulation of activation.
D. Vector Spaces as Formal Depictions of Neural Representations
The representations and computations in a neural net can be understood in
terms of linear algebra. Consider, for simplicity, an environment with exactly 2
features,f 1 andf 2. Each possible pattern in the environment consists of some
combination of intensities of these two features and can therefore be repre-
sented as a point in a Cartesian space whose axes aref 1 andf 2 .Clearly,pat-
terns that contain only one of the features will be represented as points along
one of the axes. For simplicity, we shall limit the discussion in this chapter to
the first quadrant, that is, to feature intensities that are either zero or positive,
never negative.
Patternp, depicted on the left in figure 19.2, contains both features, butf 1 is
about twice as intense asf 2 .Patternqlies on the straight line passing through
the origin andp. All points on this line (in the first quadrant) represent pat-
terns that contain the two features in the same proportion of intensities. These
Neural Nets, Temporal Composites, and Tonality 459