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future trends
rithm could be applied. The additional factors of
combinatorial explosion resulting from this gen-
eralized framework will require further adaptive
filtering mechanisms. Patterns of chords might
also be studied in future works.
objective validation and
comparison Between approaches
The analyses produced by the different compu-
tational models are evaluated for the moment
in a mostly qualitative manner: the results are
searched for the most important motives of the
piece, and the additional unexpected structures
proposed by the algorithm are rated intuitively.
In future works, the computational results need
to be compared each other and with analyses
available in the music literature. A more precise
and refined validation of the results will require
the establishment of a “ground truth”: a corpus
of pieces of diverse style will be collected, on
which manual motivic analyses will be carried
out by a board of musicologists. The comparison
of the manual analyses and the computational
results will enable a more precise determination
of the precision and recall factors offered by the
different models.
articulating global patterns and
local discontinuities
As explained in the introduction, this study is
focused on the extraction of repeated patterns.
Another important heuristic for motivic analysis
is based on local discontinuities of the sequential
structure of music along its different dimensions,
which imply the inference of segmentations
(Lerdahl & Jackendoff, 1983). The strength of
each segmentation depends on the size of the cor-
responding discontinuities. A local maximum of
pitch and/or temporal interval amplitude, or the
accentuation of one particular note, are common
examples of such local discontinuities. These seg-
mentations result in a rich structural configuration.
The multiple principles ruling these segmenta-
tions, such as Lerdahl and Jackendoff's Grouping
Preference Rules (Lerdahl & Jackendoff, 1983),
can be ordered relative to their perceptive salience
(Deliège, 1987).
Local discontinuities impose some important
constraints on the pattern extraction process.
Hence pattern extraction needs to be studied
in interaction with local segmentation. Lerdahl
and Jackendoff (1983) have proposed a coupling
of the two principles, and Temperley (1988) has
suggested a computational formalization. But
in these approaches, as acknowledged by their
authors, pattern extraction (called here “parallel-
ism”) is theoretically considered without actual
systematic modeling. Cambouropoulos (2006)
proposed a way of modeling the interaction
between the two principles. In a first step, both
local segmentation and pattern extraction are
performed in parallel, but only the boundaries of
the segments and motives are taken into consid-
generalization of the string
approach to polyphony
String-based approaches are currently limited to
the detection of repeated monodic patterns. Music
in general is polyphonic, where simultaneous
notes form chords and parallel voices. Research
carried out in this topic (Dovey, 2001; Meredith
et al., 2002), generally focuses on the discovery
of exact repetitions along different separate di-
mensions, following the set-based paradigm. On
the other hand, the string-based approach may
be generalized to polyphony, if the polyphony
is first decomposed into monodic stream and if
the pattern detection is applied to each stream
(Cambouropoulos, 2006). More generally, as
explained previously, these different streams may
be intertwined, forming complex “syntagmatic
graphs” along which the pattern discovery algo-
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