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Two opposite paradigms have been proposed in
previous works, based respectively on set and
string paradigms.
subsets of points that are translated in that space.
One particular difficulty in this approach is that
it cannot be easily applied—and it has not been
applied yet—to the detection of patterns that
present temporal fluctuations.
Among the configurations allowed by this
broad characterization of motives appears a large
range of structures that do not convey much per-
ceptive and musical relevance.
1
One reason for this
poor selectivity is that no constraint is initially
defined, regarding the relationship between suc-
cessive notes composing each pattern. Hence pat-
terns may be composed of notes taken from very
distinct temporal contexts—for instance one note
from the beginning of a piece and another note
from the end, which is generally counterintuitive.
The solution proposed by the authors consists in
defining the “compactness” of a pattern to be
set-Based formalization
In Meredith, Lemström, and Wiggins (2002;
2003), score are formalized as
sets
of notes, and
motives as
subsets
of the scores. The broad gen-
erality of this approach enables the taking into
account of a large range of musical structures
and configurations—such as polyphony—that
are outside the scope of the more constrained
string-based paradigm, as we will see in the next
subsection. The extraction strategy is founded
on geometrical principles: notes are represented
by points in a multi-dimensional representation
of the score, and melodic patterns are defined as
Figure 1. In the set paradigm, motives are considered as subsets of the notes of the score. Here, the
notes of Twinkle Twinkle Little Star reduced theme (i.e., without pitch repetitions) are circled in the first
theme exposition and the beginning of the first variation in Mozart's theme and variations (K. 300e). The
compactness of each motive is assessed with respect to the corresponding “time segments” (between
crochets), “bounding-boxes” (gray rectangles) or “convex hulls” (black triangles).
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