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Fig. 5.14
Phrase #1 in C
minor
Fig. 5.15
Phrase #2 in C minor
Fig. 5.16
Phrase #3 in C minor
The example given above suggests a constrainton the training phrase: to ensure
continuity (and avoid NSF cases), each Markov model should contain all pitches.
This is a sufficient condition, by definition, but not a necessary one. Our repair
strategy handles graciously the cases where no solution is found. Other more subtle
constraints can be deduced from the desired nature of the improvisations to gener-
ate, dealing with longer patterns. For instance, the density of the Markov network
determines the nature of the generated phrases: the more choice there is for a single
note, the more possibilities there are for controlling the phrase. If a single note has
only one possible continuation, there is a risk of producing repeated patterns when
reaching this particular note. Note that this is a current situation with human play-
ers, who sometimes learn only a small number of escape solutions, when reaching
particular notes or passages (on guitar, this is often true for notes played in the top
of the neck). A static analysis of the Markov model can reveal such bottlenecks, and
be used to suggest new phrases to learn to create new branching points.
To illustrate the generation of phrases from the training phrases, we describe a
part of a Markov model, specifically designed to represent a 'classical' bebop player,
with no particular stylistic influence. We give here the complete set of phrases used
in the minor scale. These phrases are played in the key of C, and then transposed in
the 11 other keys. The interested reader can find the corresponding database for the
other scales in C (major, diminished, seventh and whole tone) on the accompany-
ing web site ( http://www.csl.sony.fr/Virtuosity ) . These other databases are similarly
transposed in the 12 keys.
The following six phrases (Figs. 5.14 - 5.19 ) were designed (by the author) to
contain basic ingredients needed to produce interesting jazz melodies in C minor.
Of course, they do not contain all the patterns of this style, as this would be an
impossible task, but they can be enriched at will. As can be seen, not all pitches are
present in the database (at least for all octaves). This is intentional to show how the
mechanisms we present here interact with each other.
Figure 5.20 shows a phrase generated on a chord sequence consisting only of a
C minor chord. The various segments of the training phrases are indicated, showing
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