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exhibiting improvisation generators satisfying the basic rules of the game (detailed
in Sect. 5.2.3 ).
However, the improvisation problem has been only partially solved. Trained jazz
musicians listening to the examples produced by these previous works rarely expe-
rience the feeling of hearing a machine outperforming humans.
In fact, professional bebop musicians are like Olympic sportsmen or chess cham-
pions, reaching a level of technicality which is far beyond the capacities of a begin-
ner. They are usually sought after not so much because they exhibit a general 'ability
to improvise'—children can also improvise—but for their specific display of virtu-
osity. Contemporary jazz improvisers such as John McLaughlin, Al Di Meola, Biréli
Largène (guitar), or Stefano di Battista (saxophone) exhibit a level of virtuosity that
seems to reach beyond the limits of what most humans can do (the expression 'not
human' appears indeed often in commentaries about these performances on social
Web sites). They play intricate phrases at such a speed that even the transcription
of their solos from recording is a challenging task. Deciding which notes to play
at that speed seems indeed impossible, so the virtuosity question can be rephrased
as: How can one perform and execute these musical choices so accurately and so
fast?
Of course, performance as well as timbral dimensions are undoubtedly important
in music, and can themselves be the subject of virtuosity display (Bresin 2000 ), but
these are outside the scope of our study: Following the argument that 'bebop is more
about content than sounds' (Baker 2000 ), we focus here on the melody generation
task. We consider that virtuosity is not only an appealing facet of bebop, but one of
its essential features . This situation bears some intriguing analogy with bird singing
behaviour. Though bebop virtuosity is not only about speed as we will see below,
this analogy suggests a primary role of speed in the attraction for specific melodic
movements.
5.2.1 The Rules of the Game
In this section we define precisely the musical corpus we target: linear improvisa-
tion, which corresponds, roughly speaking, to virtuoso passages of bebop improvi-
sations.
5.2.2 Bebop Phrases
Virtuoso phrases are played fast, typically 1 / 16th notes at 120 bpm or more, which
represent at least 8 notes per second. This speed implies a number of characteristics
for these passages that we call 'linear'. The term linear has been used in the jazz
theory literature (e.g. Ricker 1997 ) to describe phrases built from scales rather than
from chords (i.e. arpeggios), thereby creating a sensation of melodic or horizontal
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