  Paced finger tapping is one of the simplest tasks to study sensorimotor
synchronization. The subject is instructed to tap in synchrony with a periodic
sequence of brief tones, and the time difference (called asynchrony) between
each response and the corresponding stimulus is recorded. Despite its
simplicity, this task helps to unveil interesting features of the underlying
neural system and the error correction mechanism responsible for
synchronization. Perturbation experiments are usually performed to probe the
subject's response, for example in the form of a "step change", i.e. an
unexpected change in tempo. The asynchrony is the usual observable in such
experiments and it is chosen as the main variable in many mathematical models
that attempt to describe the phenomenon. In this work we show that although
asynchrony can be perfectly described in operational terms, it is not well
defined as a model variable when tempo perturbations are considered. We
introduce an alternative variable and a mathematical model that intrinsically
takes into account the perturbation, and make theoretical predictions about the
response to novel perturbations based on the geometrical organization of the
trajectories in phase space. Our proposal is relevant to understand
interpersonal synchronization and the synchronization to non-periodic stimuli.
