Musical Virtuosity and Creativity - Computers and Creativity - page 126

samples to generate novel melodies in a highly constrained context. We consider a
variable-length generation model, but, following Hodgson ( 2006 ), we restrict our
maximum length to 2, an intentionally short value, which ensures an optimal com-
promise between similarity and creativity.
Another problem is related to the case where no solution is found ( NSF here-
after). This happens when the context has not been encountered in the training phase.
This problem, known as the zero-frequency problem has been addressed by many
researchers in Markov modelling (see e.g. Chordia et al. 2010 ), with no general solu-
tion. Here again, we favour an approach based on the observation of bebop practice,
and propose a bebop-specific, simpler solution, described below.
5.4 A Note-Based Jazz Generator
The basic engine in our proposal is a variable-order Markov chain generator, with a
maximum order of 2. This generator, described in the preceding section, is able to
yield the 'next' note, given the last 2 notes (at most) already played. Our experience
has shown that augmenting the memory length does not improve the quality of the
generation.
5.4.1 Pitches for Representation, Beats for Generation
All major decisions for generation are taken at the beat level, and constitute in detail
the intentional score , which is a temporal sequence of beat-level decisions. These
decisions are the following.
At each beat, a rhythm is chosen (arbitrarily in the first approximation) within the
5 possibilities described in Fig. 5.3 (see Fig. 5.9 ). This rhythm in turn determines the
number of notes to produce for the beat (in our case, 1, 2, 3, 4 or 6). Consequently,
there is no need to use durations as training data, as these durations are entirely
determined by this rhythm choice. The velocities of each note are the velocities
played in the training corpus (see below). No harmonic information is used in the
training phase either, as the model used for generation is chosen, for each beat,
according to the current chord, as described below. Higher-level attributes such as
pitch contour, chromaticity, etc. are handled yet at another level as described in
Sect. 5.5.2 . Consequently, the representation used for the Markov model is based
solely on pitch, reducing this basic mechanism to a simple one.
The justification for this choice is based on a long experience with Markov mod-
els for jazz, which convinced us that pitch is the only dimension of music that is
well captured. Although other dimensions can technically be represented as such, it
does not make much musical sense. There are two main reasons for this: firstly, only
intrinsic attributes, by definition, are well adapted to Markov modelling. Pitch is an
intrinsic attribute, but not rhythm, which emerges from the relation between adjacent