Neural Correlates of Processing Syntax in Music and ... - PubMan

Music Perception 13
Krumhansl and Schmuckler (see Krumhansl, 1990) constructed an algorithm that
matches the tone duration in the sample to the tonal hierarchies (Krumhansl & Kessler,
1982). Later, Shmulevich and Yli-Harja (2000) proposed an extension to this algorithm
directed at smoothing local oscillations in key assignments.
Another influential approach to key-finding was based on modelling with neural networks.
Leman’s (1995) neural network model takes acoustic information as input which
enters a self-organizing network that consists of cognitive schemes for pitch structures
including a schema for tone-centre perception that has resulted from long-term learning.
However, this model focus’ on chords and on tonal centres but does not account for the
relationships between tones, chords, and keys.
Bharucha’s (1987) connectionist model of key membership (a self-organizing map,
SOM; Kohonen, 2006) is organized in three layers (corresponding to tones, chords, and
keys). In spite of some simplifications, the model provides a relevant framework for
understanding how musical knowledge may be mentally represented and how this
knowledge, once activated by a given musical context, may influence the processing of
tonal structures. However, the model was based on music theoretic constraints; neither
the connections nor their weights resulted from a learning process. In this respect, the
model represented the idealized end state of an implicit learning process.
Tillmann, Bharucha, and Bigand (2000) demonstrated how implicit knowledge of tonal
structure may be acquired, namely that such knowledge can result from neural selforganization
following mere exposure to tone sequences structured according to particular
regularities. A SOM, comparable to Bharucha’s (1987) connectionist model, was
used. It was trained in two steps: First, the layer representing the major and minor
chords was learned to detect the tones belonging to these chords. Then, the layer representing
the major keys was trained with chord sequences. Four different learning simulations
were set up: During the training of the chord layer the input was defined by
either a sparse coding (the pitch classes) or a psychoacoustically richer coding scheme
(a weighted sum of subharmonics corresponding to the pitch classes, according to Parncutt,
1988). Then, during the training of the key layer, either simple harmonic material
(sets of three major and three minor chords for each key presented in random order) or
more realistic chord sequences (with the same chords but relying on a probability distribution
of these chords in tonal music) were used. The differences in the input coding
were essentially for the feed-forward activation while comparable activation patterns
were found when the abstracted “knowledge” (i.e., the connection weights) exerted its
influence by top-down processes. The model could simulate empirical data from a large
number of studies. Taken together, it was possible to model the acquisition of the highly
sophisticated regularities of the Western tonal system by an implicit learning process.