Summary
We investigate numerically the basins of attraction of a simple model of single-reed musical instruments with a time- varying parameter. More precisely, the main control parameter – the blowing pressure γ – is linearly increasing and saturating to account for attack transients, which are known to be of particular importance in a musical context. In the space of initial conditions of the state variables and initial value of γ, we compute the boundary between the so-called dynamical basins using a machine learning technique, namely an explicit design space decomposition method combined with a support vector machine classifier. This allows for the systematic investigation of the effect of attack transients on the observed regime among the coexisting stable solutions. Our results show that, depending on their duration, attack transients might have a dramatic impact on the playability of the different stable regimes.
