peaks creates substantial overlap between the representations of patterns that
differ only slightly in their tuning. The latter is enabled because the maxima of
the peaks are unchanged and can be recovered if necessary by sharpening the
peaks through lateral inhibition.
B. Abstract Feature Tuning
Although frequency detectors have been the most widely studied feature de-
tectors in the auditory system, evidence exists for detectors of more abstract
features. Pantev, Hoke, Lu ̈tkenho ̈ner, and Lehnertz (1989) argue that the tono-
topic representation in the primary auditory cortex is of pitch, not frequency.
Weinberger and McKenna (1988) have found feature detectors for contour.
Frequency detectors must therefore map onto higher order neurons in such a
way as to extract pitch and contour from complex spectra. This suggests a hi-
erarchy of feature detectors: elementary features are detected at the sensory
periphery, and entire patterns of these features are detected by abstract feature
detectors, which in turn form patterns that are detected by even more abstract
feature detectors. This conception of neural architecture has already received
strong support for the visual system (Hubel & Wiesel, 1979; Linsker, 1986;
Marr, 1982).
Deutsch (1969) suggested how feature abstraction might occur in a neural
net. For example, if frequency detectors whose characteristic frequencies are an
octave apart connect to the same neuron, and if no other frequency detectors
connect to this neuron, then it is effectively an octave-equivalent frequency de-
tector. The circuits Deutsch proposed anticipate the circuits that develop auto-
matically as a result of learning, although these methods were not available at
that time.
The neural connections that make a unit an abstract feature detector may in
many cases have developed through evolution, in which case they are innate.
Yet it seems obvious that humans are capable of learning new patterns, and if
abstract feature detectors are necessary for pattern learning (as most neural net
models tacitly assume), then humans must be capable of acquiring abstract
feature detectors through learning. We understand how this can be done
(Fukushima, 1975; Grossberg, 1970, 1972, 1976; von der Malsberg, 1973), and in
thecaseofmusic,itseemsreasonabletoadoptapresumptionoflearning.
Neural net models assume an array of units whose feature-detecting prop-
erties are given. The network then acquires either new associations or new
abstract feature detectors through learning. These two types of learning are
commonly referred to as pattern association and self-organization, although the
latter can be thought of as a special case of the former. Both types of learning
are surveyed in Section II.
The most commonly assumed feature detectors in models of music that learn
are pitch or pitch-class (i.e., octave-equivalent pitch) detectors whose tuning is
spaced at semitone intervals (e.g., Bharucha, 1987a, 1987b, 1988, 1991; Bhar-
ucha & Todd, 1989; Laden & Keefe, 1989; Leman, 1991; Sano & Jenkins, 1989,
Todd, 1988). We already have evidence of pitch detectors in the brain (Pantev
et al., 1989). Pitch-class units can be postulated on the assumption of a circuit
like the one proposed by Deutsch (1969), which if not innate, can be learned
by the self-organization of harmonic spectra. The semitone spacing of their
Neural Nets, Temporal Composites, and Tonality 457