Papers on dynamical systems, NNs, and music cognition on neuroprose

[Edward Large]

Dynamic Representation of Musical Structure (132 pages)
Edward W. Large
The Ohio State University
PhD dissertation

FTP-host: archive.cis.ohio-state.edu
FTP-file: pub/neuroprose/Thesis/large.diss.ps.Z

ABSTRACT: The problem of how the human brain perceives and represents
complex, temporally structured sequences of events is central to
cognitive science. Music is an ideal domain for the addressing this
issue. Music provides a rich source of data, generated by a natural
human activity, in which complex sequential and temporal relationships
abound.  Understanding how musical structure may be coded as dynamic
patterns of activation in artificial neural networks is the goal of
this dissertation. Implications for other domains, including speech
perception, are discussed. 

This work addresses two questions that are important in understanding
the representation of structured sequences. The first is the
acquisition and representation of structural relationships among
events, important in representing sequences with long distance
temporal dependencies, and in learning structured systems of
communication. The second is the representation of temporal
relationships among events, that is important in recognizing and
representing sequences independent of presentation rate, while
retaining sensitivity to relative timing relationships. These two
issues are intimately related, and this dissertation addresses the
nature of this relationship.

Two research projects are described. The first models the acquisition
and representation of structural relationships among events in musical
sequences, addressing issues of style acquisition and musical
variation. An artificial neural network encodes the rhythmic
organization and pitch contents of simple melodies. As the network
learns to encode melodies, structurally more important events dominate
less important events, as described by reductionist theories of music.
The second project addresses the perception of temporal structure in
musical sequences, specifically the perception of beat and meter. An
entrainment model is proposed. An oscillator tracks periodic
components of complex rhythmic patterns, resulting in a dynamical
system model of beat perception. The self-organizing response of a
group of oscillators embodies the perception of metrical structure.



Resonance and the Perception of Musical Meter (37 pages)
Edward W. Large and John F. Kolen
The Ohio State University
Connection Science, 6 (1), 177 - 208.

Reprint from the recent Connection Science special issue on music and
creativity.

FTP-host: archive.cis.ohio-state.edu
FTP-file: pub/neuroprose/large.resonance.ps.Z

ABSTRACT: Many connectionist approaches to musical expectancy and music
composition let the question of "What next?" overshadow the equally
important question of "When next?". One cannot escape the latter
question, one of temporal structure, when considering the perception
of musical meter. We view the perception of metrical structure as a
dynamic process where the temporal organization of external musical
events synchronizes, or entrains, a listener's internal processing
mechanisms. This article introduces a novel connectionist unit, based
upon a mathematical model of entrainment, capable of phase- and
frequency-locking to periodic components of incoming rhythmic
patterns. Networks of these units can self-organize temporally
structured responses to rhythmic patterns. The resulting network
behavior embodies the perception of metrical structure.  The article
concludes with a discussion of the implications of our approach for
theories of metrical structure and musical expectancy.



Reduced  Memory Representations for Music (39 pages)
Edward W. Large and Caroline Palmer
The Ohio State University
Jordan B. Pollack
Brandeis University

Preprint of an article to appear in Cognitive Science.

FTP-host: archive.cis.ohio-state.edu
FTP-file: pub/neuroprose/large.reduced.ps.Z

ABSTRACT: We address the problem of musical variation (identification of
different musical sequences as variations) and its implications for
mental representations of music. According to reductionist theories,
listeners judge the structural importance of musical events while
forming mental representations. These judgments may result from the
production of reduced memory representations that retain only the
musical gist. In a study of improvised music performance, pianists
produced variations on melodies. Analyses of the musical events
retained across variations provided support for the reductionist
account of structural importance. A neural network trained to produce
reduced memory representations for the same melodies represented
structurally important events more efficiently than others. Agreement
among the musicians' improvisations, the network model, and
music-theoretic predictions suggest that perceived constancy across
musical variation is a natural result of a reductionist mechanism for
producing memory representations.