Proceedings IX CIM 1991, Genova, November 13-16 - AIMI

dynamics of contextual similarity such that tones get their meaning within the tonal context
The difficult point to understand is, how the context can be determined by elements whose own
meaning is determined by the context. We believe that the same situation occurs, at least to some
extend, in natural language processing 11 : A sentence can indeed be considered as the context
within which words, that constitute this sentence, get their proper meaning. Like tones, words have
there proper meaning that builds up a context which then determines their actual meaning or
contextual meaning.
The dynamics can also be understood in terms of attractor-dynamics. The tonal context can be
considered as an attractor point to which nearby perceptions are forced. Formulated this way, we
can say that the attractor can be disturbed by input. The fluctuations can ultimately cause a
transition towards a new stable point of perception. A transition of a stable state happens for
example with modulation: tones that are strange to the tonal center cause a fluctuation that leads to
a transition of the system towards a new tonal center, which gives a quite different contextual
meaning to the same tones.
It should be added also that this interpretation of tonal semantics is not so new. Fetis (Fetis, 1844)
already interpreted harmonic processing is terms of tension and relaxation which comes very close
to the concepts of complex dynamic systems (p. iij) :
"[...] fai donc vu que toute l'harmonie reside dans ces necessites alternatives: repos, tendance
ou attraction, et resolution de ces tendances dans un repos nouveau."
5. Time-dependent information processing and invariants.
One of the central problems which we have not solved in the provious accounts of the theory, and
which is relevant for the automatic recognition of tonal centers as well, is concerned 'with the way
in which time-dependent information may give rise to the emergence of these perceptual schemata.
This can in essence be reduced to the question of how a (tonal) context is builded up.
As mentioned, we believe that a tonal context might be interpreted as an perceptual invariant.
According to Gibson, invariants are extracted from the spatio-temporal information flow. They
correspond with constancy properties of the environment, which the brain can detect The method
we have used to obtain the invariants is by (temporal) integration. This assumes a mechanism by
which the information flow is integrated in the activation of neurons. In other words, the memory
is capable of holding information for a short time. This short-term memory seems to play an
essential role for building up a mental context of the surrounding world.
6. Integration and neural synchronisation.
We found some support in the work of Poppel (efr. Poppel et al., 1990; Poppe!, 1989). According
to PoppeI the temporal experience of humans can be described by a hierarchic classification of
subjective temporal phenomena such as (i) simultaneity, non-simultaneity (asynchrony), (ii)
succession, (iii) the subjective present (now) and (iv) duration.
11. For the rest we are very sceptical to compare natural language processing with musical processing, since musical
processing is much more perceptualy based.
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