Musical Virtuosity and Creativity - Computers and Creativity - page 119

in principle, an analysis performed on the whole chord sequence. Chord sequence
analysis was shown to be a non-trivial task in general (Steedman 1984 ). In practice,
however, simpler forms of analysis are used, which consist in using ready-made
associations between chords and scales. Such associations are routinely available in
harmonic treatises, e.g., in Aebersold ( 2000 ). For instance, on a minor 7 ( 5b ) chord,
say D minor 7 ( 5b ), one can use a harmonic minor scale one minor third above the
root (here, F harmonic minor ).
5.2.3.2 Continuity
Jazz beginners often improvise by playing arpeggios corresponding to each chord:
this simple technique satisfies local harmonic satisfaction by definition, but pro-
duces obviously uninteresting, unmelodic phrases. Producing a 'sense of melody'
is difficult to define precisely. Continuity is a good approximation and is easier to
define. We will see that low-order Markov processes exploiting carefully chosen
scales guarantee a form of natural continuity.
Melodic continuity is a difficult challenge for a human when playing fast, as
it requires the ability to find quickly short paths between the note currently be-
ing played and the next ones, which may be in a different scale. This ability is
referred to as chord change negotiation, stressing its inherent problem-solving di-
mension.
Note that continuity does not necessarily imply brownness , in the sense of (Voss
and Clarke 1978 ), i.e. the sole use of small intervals. It rather implies that notes
are glued together smoothly, and not made up of isolated elements or patterns, con-
catenated without care. For instance, the phrase in Fig. 5.7 contains several large
intervals but is perfectly continuous.
The One-Step-Max Theorem There is a factor that helps address the continu-
ity challenge: the one-step-max theorem . The scales used in jazz (minor, major or
diminished, in first approximation) contain an interval of maximum 3 semitones
(in the harmonic minor scale). Consequently, any note is always within 1 semitone
maximum (up or down) to a note of any possible scale, i.e. a 'good' note. We will
see below how this theorem can be used as a rescue mechanism when the basic
generator fails to find a solution.
5.2.4 Playing Outside and Side-Slipping
The bebop language is deeply grounded in tonal harmony. However, like all lan-
guages, bebop evolves. One important development was caused by a paradoxical
force that pushes musicians to escape the constraints of harmonic satisfaction, once
they know how to satisfy them perfectly: playing out in jazz jargon. Playing out is
not to be confused with free jazz , a radical way to escape the laws of tonal harmony,