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The flow of p into f is the virtual counterpart of the sonic interactions that are
taking place between performers. In a dynamical system, p could become a state
alongside x , with the difference that the dynamics of p are driven by the outside
world, whereas the dynamics of x are enacted by a map. Interaction fits naturally
within the dynamical systems approach, unlike reasoning and machine learning al-
gorithms which are normally constructed as closed systems. The variety of possible
inputs would have to be specified by the designer in a rule-based system, and in
a learning system, response is dependent on the comprehensiveness of the test set.
The dynamical systems approach offers a more robust alternative. Finally we note
that an extremely large number of alternative outputs (the size of H ) can be easily
implemented in a dynamical system.
6.4 Live Algorithms in Context
This section considers aspects of Live Algorithms that cannot be directly pro-
grammed. Improvisers are characterised by individual behaviours which are the re-
sult of learning and playing music in a social and cultural context. We speculate that
a Live Algorithm might also participate in these contexts. The section looks at some
behaviours, and then discuses the social and cultural dimensions of improvisation.
6.4.1 Live Algorithm Behaviour
Young and Bown ( 2010 ) identify four distinct behaviours that might be exhibited
by a Live Algorithm: shadowing, mirroring, coupling and negotiation. These be-
haviours give some indication of the capacities systems in Fig. 6.1 E-G would need
to demonstrate.
The behaviours are expected to be emergent, rather than directly programmed.
In general it is better to set overall goals and let a system develop its own behaviours
in order to that accomplish these goals. A top-down approach is rigid and relies on
a complete analysis of the problem; a bottom-up approach is more robust. The per-
formance goals for a Live Algorithm are not well understood; Sect. 6.3.4 advocates
the study and codification of the observed function F of human improvisors.
6.4.1.1 Shadowing
Shadowing involves a synchronous following of what the performer is doing,
mapped into a different domain. Systems E-H in Fig. 6.1 could produce this, al-
though only E or F are necessary. A pitch shifter in both the audio or MIDI domain,
or any synchronous audio or MIDI effect, are very simple examples. In such cases,
shadowing reduces to the configuration shown in Fig. 6.1 E, with or without a human
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