We propose a developmental model inspired by the cortico-basal system (CX-BG) for vocal learning in babies and for solving the correspondence mismatch problem they face when they hear unfamiliar voices, with different tones and pitches. This model is based on the neural architecture INFERNO standing for Iterative Free-Energy Optimization of Recurrent Neural Networks. Free-energy minimization is used for rapidly exploring, selecting and learning the optimal choices of actions to perform (eg sound production) in order to reproduce and control as accurately as possible the spike trains representing desired perceptions (eg sound categories). We detail in this paper the CX-BG system responsible for linking causally the sound and motor primitives at the order of a few milliseconds. Two experiments performed with a small and a large audio database show the capabilities of exploration, generalization and robustness to noise of our neural architecture in retrieving audio primitives during vocal learning and during acoustic matching with unheared voices (different genders and tones).