Motivic Pattern Extraction in Symbolic Domain - Intelligent Music Information Systems: Tools and Methodologies - page 250

Figure 10. Pattern aij, now featuring more occurrences than abcde or abcdefgh (namely, four occur-
rences instead of two), is now explicitly represented.

Figure 11. The rhythmic pattern afghi is less specific than the melodico-rhythmic pattern abcde.

the concept of closed patterns , which are patterns
whose support is higher than the support of the
pattern in which they are included (Zaki, 2005). A
filtering of non-closed patterns is therefore more
selective than a filtering of non-maximal patterns.
In fact, it ensures a more compact representation
of the pattern configuration without any loss of
information .
The model presented in this article looks for
closed patterns in musical sequences. For this
purpose, the notion of inclusion relation between
patterns founding the definition of closed patterns
is generalized to the multidimensional paramet-

ric space of music. A mathematical description
of this operation can be formalized using the
Gallois correspondence between pattern classes
and pattern description (Ganter & Wille, 1999;
Lartillot, 2005). For instance, pattern abcde in
Figure 11 features melodic and rhythmical de-
scriptions, whereas pattern afghi only features
the rhythmic part. Hence pattern abcde can be
considered as more specific than pattern afghi ,
since its description contains more information.
When only the first two occurrences are analyzed,
both patterns having same support, only the
more specific pattern abcde should be explicitly