Motivic Pattern Extraction in Symbolic Domain - Intelligent Music Information Systems: Tools and Methodologies - page 255

musical parameters has been taken into account
(Lartillot & Toiviainen, 2007) and all patterns
longer than 3 notes are displayed. These analyses
have been validated through a comparison with
musicological analyses found in the literature.
Figure 16 and 17 shows examples of analysis.
Detailed explanation of these analyses and their
comparison with musicological analyses are de-
veloped in Lartillot and Toiviainen (2007).
Figure 16 shows the analysis of a XIV-century
German Geisslerlied , “Maria muoter reinû maît”.
According to Nicolas Ruwet's analysis (1987), the
piece is composed of a repetition of an eight-bar
phrase A followed by a repetition of a four-bar
phrase B . The algorithm extracts pattern A but
fails to segment pattern B correctly, because the
presence of a suffix of B at the end of pattern A
leads to an incorrect segmentation (represented
by B' ). This segmentation needs to be controlled
using additional heuristics, as suggested in Lar-
tillot and Toiviainan (2007). Pattern b , its melodic
variation b' , and pattern d can also be found in
Ruwet's analysis. A certain number of patterns
proposed by Ruwet are not explicitly represented
in the computational analysis, because they do
not convey additional information concerning
the pattern structure of the piece. Following the
terminology introduced in previous section, these
patterns are non-closed subsequences of others
pattern. In Ruwet's analysis, the selection of these
patterns is based on segmentation processes,
which are not taken into account in our modeling.
On the other hand, the algorithm proposes short
patterns, such as e and f, that have no correspon-
dence with Ruwet's analysis. The assessment of
their perceptual or musical relevance will require
further study.
Figure 17 shows the results of the computa-
tional analysis of the first 14 bars of J.S. Bach's
Invention in D minor BWV 775, which can be
compared with Jeffrey Kresky's analysis (1977).
The opening motive A, with all its occurrences
throughout the piece, has been exactly retrieved

by the machine. The ascending and descending
lines within the motive (gray arrows) have been
detected, too. On the other hand, the inversion
of the motive shape a1 in the second half of mo-
tive A , has not been detected since inversions
are not taken into account in the model yet. The
accompanying figure B has been detected, and is
decomposed into a succession of two successive
and similar shapes c . However, the similarity of
these shapes with motive a1 , suggested by Kresky,
has not been discovered. The first sequence unit
A' is detected and identified as a variation of the
opening motive A , but not exactly for the same
reasons offered by Kresky. The second sequence
unit a3 has been detected and identified as a varia-
tion of the original motive shape a . The successive
repetition of the three-note scale b in bars 11 and
13 is also identified with the first three notes of
the original scale form at the beginning of the
motive shape a . The repeated bass line during
the first sequence is detected ( C ), but cannot be
identified with the motive shape a . Finally, the
descending scale F-E-D-C (first note of bars 7,
9, 11, and 13) has not been detected due to the
incapacity of the algorithm to consider motivic
configurations between distant notes.
The computational analysis also includes
additional motivic structures that do not seem
to offer much musical interest or perceptive
relevance. Pattern D , featuring a succession of a
descending second interval followed by a series of
ascending second intervals, sounds poorly salient
due to its weak position in the metrical structure,
and the limited size of its description. The second
occurrence of pattern D is also considered by the
model as the beginning of a variant a4 of motive
a2 , which is, once again, not very salient due to
the weak position of this motive in the metrical
structure. Pattern E shows similar limitations: it
corresponds to a series of pitches (E5, F5, D5, E5,
F5) starting offbeat. In order to filter patterns D
and E , a higher-level metrical representation may
be integrated in future works that would show the