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eration. These boundaries are summed together,
leading to a segmentation curve, and global seg-
mentations are performed at local maxima of the
curve. The resulting segments are then classified
based on similarity measurement, following the
paradigmatic analysis approach (Cambouropoulos
& Widmer, 2000).
Ahlbäck (in press) has elaborated a set of Ge-
stalt theory-based principles for melodic grouping.
The core of this model is the classification of the
different grouping principles according to the role
they play in the cognition of grouping structure
in melody. The model postulates that groups can
be formed by implication based on properties of
grouping determined by primary grouping prin-
ciples, reflecting the general coherence principle.
Secondary grouping principles refer to group-
ing by good continuation, which involves both
selection of grouping and implicative grouping
by means of periodicity and symmetry. A third
class, tertiary grouping principles, is defined
as involving perceptual and cognitive selection
of grouping, reflecting principles of cognitive
economy, significance and intelligibility.
conclusIon
This chapter presented the state of the art in
motivic pattern extraction, and has shown that,
however simple the task may appear according
to its basic purpose, its computational realization
remains a very difficult challenge. The review of
the different approaches and underlying difficul-
ties suggests the idea that the question cannot be
answered using solely mathematic or geometric
heuristics and classical engineering tools inspired
from artificial intelligence, but requires also a
detailed understanding of the multiple constraints
derived by the cognitive situation of the process.
This philosophy implies a vision of the question
of pattern extraction that is tightly interdependent
with other issues such as pitch spelling, rhythm
quantification or stream segregation. This is,
in our vision, the price to pay in order to reach
a complete and sound automation of this chal-
lenging task.
acknoWledgment
motives of motives
This work has been supported by the European
Commission (NEST project “Tuning the Brain for
Music,” code 028570). Some ideas presented in this
paper emerged after fruitful conversations with
my colleague Petri Toiviainen. Their formaliza-
tion have also benefitted from valuable feedback
offered by reviewers of this chapter and reviewers
of our previous publicatios as well.
Throughout the chapter, motives have been
defined as series of notes that feature particular
invariants related to the relative configurations
between the successive elements of these series.
Several approaches propose to accept as building
blocks of these series not only elementary notes,
but also motives themselves. This recursive defi-
nition would enable in particular a multi-leveled
hierarchical construction of motivic structures.
Previous works in music cognition have studied the
structural particularities of successive repetitions
of patterns (Deutsch & Feroe, 1981). The recent
development of Conklin and Anagnostopoulou's
project (2006) is dedicated to the formalization
of interval relationships between successive
motives.
references
Agrawal, R., & Srikant, R. (1995). Mining sequen-
tial patterns. In Proceedings of the International
Conference on Data Engineering (pp. 3-14).
Ahlbäck, S. (2007). Melodic similarity as deter-
minant of melody structure. Musicae Scientiae ,
Discussion Forum 4A, 235-280.
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