A lip-reed is a double continuous system that potentially exhibits several degrees of freedom. Numerical simulations for sound synthesis as well as fitting a model with measurements naturally improve while increasing the number of degrees of freedom that are put into the model. However, this parameter is worth investigating as such. In a first approach, lips are coupled to a Helmholtz resonator whose resonance factor is actively reinforced, as described in Chen and Weinreich [‘‘Nature of lip reed,’’ J. Acoust. Soc. Am. 99, 1227–1233 (1996)]. The dimensionality of the attractor or permanent regime of this nonlinear dynamical system is computed with embedding techniques of the corresponding time-series and information-based measurements [Gershenfeld et al., Time Series Prediction (Addison-Wesley, Reading, MA, 1994)]. Preliminary results indicate a dimension of 1, 2 or 3 for different couplings between the lips and the resonator. The link with the number of freedom of the lip-reed will be discussed. [Work supported in part by CNRS and NSF.]