  When musicians perform in an ensemble, synchronizing to a mutual pace is the
foundation of their musical interaction. Clock generators, e.g., metronomes, or
drum machines, might assist such synchronization, but these means, in general,
will also distort this natural, self-organized, inter-human synchronization
process. In this work, the synchronization of musicians to an external rhythm
is modeled using the Impulse Pattern Formulation (IPF), an analytical modeling
approach for synergetic systems motivated by research on musical instruments.
Nonlinear coupling of system components is described as the interaction of
individually propagating and exponentially damped impulse trains. The derived
model is systematically examined by analyzing its behavior when coupled to
numerical designed and carefully controlled rhythmical beat sequences. The
results are evaluated by comparison in the light of other publications on
tapping. Finally, the IPF model can be applied to analyze the personal
rhythmical signature of specific musicians or to replace drum machines and
click tracks with more musical and creative solutions.
