A classical and dimensionless model of the functioning of single reed instruments such as the clarinet and the saxophone is considered. In this model, the nonlinearity is controlled by two parameters: One linked to the blowing pressure, the other one to the reed opening at rest. Transient commands are applied on this two parameters. In particular, It is shown that a transient decay of the blowing pressure still induces a nonlinear functioning of the system, while a transient decay of the reed opening leads to a free oscillation of the resonator, hence giving a way to estimate the complex frequencies of the impedance peaks. The results are compared to those obtained on natural sounds thanks to a controlled artificial mouth, both in pressure and reed opening. The meaning of the dimensionless control parameters are discussed with respect to the actual command of a musician.