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pieces and of musical styles and genres in general.
Second, the automated description allows more
advanced comparisons between pieces, based on
a comparison between salient structures, instead
of a matching of local structural configurations
that often present less perceptual or musical rel-
evance. We may conjecture also that the motivic
pattern extraction task might be beneficial to music
information retrieval: the automated description
of musical databases allows a reduction of the
size of the search, a focus on the most salient
structures and therefore a probable increase of
the relevance of the results.
The motivic structure is often highly complex.
Detailed analysis of the deeper motivic struc-
tures contained in music has been undertaken
during the 20th century (Reti, 1951). Systematic
approaches have been suggested, with the view
to augmenting the analytic capabilities, both in
quantitative and qualitative terms (Lerdahl &
Jackendoff, 1983; Nattiez, 1990; Ruwet, 1987).
Computational modeling offers the possibility to
automate the process, enabling the fast annotation
of large scores, and the extraction of complex and
detailed structures without much effort.
The pattern discovery system described in this
chapter is applied uniquely to symbolic represen-
tation (such as score or MIDI format). A direct
analysis on the signal level would arouse tremen-
dous difficulties. In fact, even when restricted to
the symbolic level, the pattern extraction task
still remains a difficult challenge. The pattern
discovery task seems therefore too complex for
a direct examination from the audio signal, but
requires rather a prior transcription from the audio
to the symbolic representations, in order to carry
out the analysis on a conceptual level.
This chapter presents an overview of compu-
tational research in motivic pattern extraction,
discusses the main underlying questions, and
suggests a partial answer to the problem. We
will show that the central questions underlying
the topic, concerning the nature of the motivic
structures, the matching strategies and the filter-
ing of the results, have been tackled in alternative
ways by the different approaches. The detailed
analysis of these problems leads to the proposal
of a new methodology developed throughout the
study. Combinatorial redundancy constitutes, in
our view, one major difficulty aroused by the task.
A solution is proposed, through an adaptive filter-
ing based on closed patterns and cyclic patterns.
Important questions that need to be considered
in future works concern, among others, the vali-
dation of the alternative approaches, the taking
into account of complex musical configurations
such as polyphony and the integration of multiple
segmentation factors into one synthetic model.
motIve formalIzatIon
Definition of Motives
The basic principle of
motivic pattern extraction
consists of identifying several short extracts or
subsequences—from one or several pieces—as
instances, or
occurrences
, of a same model called
pattern
. A
motivic pattern
is a succession of
notes that forms a melodic sequence, or motive,
repeated several times in the piece or the corpus.
Each pattern presents two main properties: the
“intentional” property is related to the musical
description common to all its occurrences; the
“extensional” property corresponds to its
class
,
that is, the set of occurrences itself (Rolland,
1999). This dichotomy between intentional and
extensional properties plays a core role since
it implies a Gallois correspondence (Ganter &
Wille, 1999) that offers interesting mathematic
properties, as we will later.
A complete description of the motivic pattern
extraction task requires further specifications: in
particular the explicit formalization of the con-
cept of motive and the description of the match-
ing process. The formalization of motives is of
high importance because it determines the way
pattern occurrences are extracted from pieces.
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