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tervals have been initiated, the discovery of the
progressive extensions simply requires a matching
of the successive intervals with the corresponding
successive intervals in the pattern.
The four-note pattern of Beethoven's
Fifth
Symphony
(Figure 8) may be considered in this
respect as a concatenation of two specific unison
intervals (or three repetitions of the same note),
followed by a less specific descending contour.
Each new occurrence of the pattern can be easily
perceived due to the high specificity of its three
first notes, which allows an interval-based match-
ing in long-term memory.
approach, in different parametric descriptions
of musical sequences. A prominence value is at-
tached to each of the discovered patterns in order
to prefer most frequently occurring patterns and
in the same time longer patterns and to avoid
overlapping. More precisely, a
selection function
associates a numerical strength value with each
pattern following the formula:
ƒ(L,F,DOL)=L
a
·F
b
/10
c·DOL
where
L
is the pattern length,
F
the frequency of
occurrence of each pattern,
DOL
the degree of
overlapping, and a
, b, c
are constants that give
different weights to the three factors. For every
pattern discovered by the above pattern induction
algorithm a value is calculated by the selection
function. The patterns that score the highest are
considered as the most significant ones. The author
acknowledges the need for further processing that
will lead to a 'good' description of the surface
(in terms of exhaustiveness, economy, simplic-
ity, etc.). It is likely that some instances of the
selected pitch patterns should be dropped out or
that a combination of patterns that rate slightly
lower than the top rating patterns may give a
better description of the musical surface. In order
to overcome this problem, a simple methodology
has been devised, following which no pattern is
disregarded but each pattern (both its beginning
and ending point) contributes to each possible
boundary of the melodic sequence by a value that
is proportional to its Selection Function value.
That is, for each point in the melodic surface all
the patterns are found that have one of their edges
falling at that point and all their Selection Function
values are summed. This way a pattern boundary
strength profile is created (normalized from 0-1).
It is hypothesized that points in the surface for
which local maxima appear are more likely to
be perceived as boundaries because of musical
similarity. The modeling has been subsequently
revised by restricting the definition of the strength
of the pattern boundary profile to the starting
controllIng the
comBInatorIal redundancY
Let us consider now a third central difficulty
encountered by automated motivic algorithms,
related to the control of the complexity of the
results.
review of the filtering strategies
In Conklin and Anagnostopoulou (2001), pattern
discovery is performed by building a suffix tree
along several parametric dimensions. Due to
the large size of the set of discovered patterns,
a subset of the extracted patterns are selected in
a subsequent step, namely those occurring in a
specified minimum number of pieces
k
, and show-
ing sufficient statistical significance. The criterion
of statistical significance of a given pattern is based
on
p
-value, that is, the probability that a random
viewpoint sequences would contain an equal or
higher number of occurrences of that pattern.
In this view the p-value should be lower than a
predefined cut-off value. A further filtering step
globally selected the longest significant patterns
within the set of discovered patterns, by reporting
the leaves of the suffix tree structure.
Cambouropoulos (2006) searched for exact
pattern repetition, using Crochemore's (1981)
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