Non-verbal communication enables efficient transfer of information among people. In this context, classic orchestras are a remarkable instance of interaction and communication aimed at a common aesthetic goal: musicians train for years in order to acquire and share a non-linguistic framework for sensorimotor communication. To this end, we recorded violinists' and conductors' movement kinematics during execution of Mozart pieces, searching for causal relationships among musicians by using the Granger Causality method (GC). We show that the increase of conductor-to-musicians influence, together with the reduction of musician-to-musician coordination (an index of successful leadership) goes in parallel with quality of execution, as assessed by musical experts' judgments. Rigorous quantification of sensorimotor communication efficacy has always been complicated and affected by rather vague qualitative methodologies. Here we propose that the analysis of motor behavior provides a potentially interesting tool to approach the rather intangible concept of aesthetic quality of music and visual communication efficacy.