organization of the detected key centres that reflects the harmonic distances between keys
(as on the cycle of fifths) with the distances on the map. Leman’s work provided evidence
that higher order units of Western music (i.e. tonal centres) can be learned via passive
exposure to a rich acoustic input. These models focused on the learning of tonal centres,
but did not account for relations between tones, chords, and keys. Gjerdingen^84 proposed
to simulate a more complex aspect of musical learning: the perception of musical style. An
ART network19,20was trained to categorize and memorize stylistic features of Mozart
pieces and the learned feature patterns were compared to music theoretic concepts.
Perceiving musical structures
In order to be compelling, a cognitive model of Western music should not only simulate the
internalization of Western pitch regularities via mere exposure, but should also simulate the
behaviour of listeners after having adapted to Western tonal music. Numerous connection-
ist models in music have not been developed to reflect cognitive processes and their predic-
tions are not directly tested with behavioural data observed with human listeners. In Leman’s
work,^72 for example, musical pieces were presented to the network and tonal centre activation
was compared with music theory analyses. In Ref. 83, a context followed by a chord was pre-
sented to the network and changes in activation patterns were correlated with probe-chord
judgements of human listeners.^36 The activation changes simulated indirectly the differences
in subjective judgements, but the network was not able to generate predictions for the
chords themselves. A different approach to compare performance of network and human
listeners has been proposed by Stevens^85 and Stevens and Latimer.86,87A network was
trained to distinguish musical excerpts (standard) from modified excerpts. Results of simula-
tions were compared with performance of human listeners and the influence of musical
expertise was modeled by length of training. However, the model was explicitly restricted to
a recognition task without the goal to simulate other tasks or a more general representation
of tonal knowledge. Krumhansl et al.^80 compared performance of human listeners and SOM
networks for the specific case of melodic expectation in Finnish spiritual folk hymns.
Expertise was simulated by contrasting two SOM networks trained with either hymns or dif-
ferent finish folk songs. Activation patterns of the hymn SOM correlated more strongly with
melodic continuation judgements of human expert listeners and suggested that this SOM
became sensitive to tone distributions and tone transitions underlying the Finnish hymns.
In Tillmann et al.,^31 the HSOM network was tested for its capacity to simulate a variety
of empirical data about perceived relations between and among tones, chords, and keys in
Western tonal music. Simulations were run with the experimental material used in the
empirical studies. The underlying rationale of the simulations was to test activation (spread-
ing through a representation of tonal knowledge) as a mechanism unifying a range of cog-
nitive tasks. The experimental material was presented to the model and the activation levels
of network units were interpreted as levels of tonal stability.aThe more a unit (i.e. a chord
115aFor event sequences, activation due to each event is accumulated and weighted according to recency. (^73) The
total activation of a unit is thus the sum of the stimulus activation, the phasic activation accumulated during
reverberation and the decayed activation due to previous events.