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The REACH project aims to understand, model and develop musical co-creativity between humans and machines through improvised interactions, allowing musicians of all educational levels to develop their skills and increase their individual and social creative potential. Improvisation is at the very heart of all human interactions, and music is a fertile ground for developing models and tools of creativity that can be generalized to other activities, due to the richness of its structures and constraints that foster the emergence of cooperative behaviour and highly integrated courses of action. REACH studies "shared musicality" at the intersection of the physical, human and digital spheres, as an archetype of distributed intelligence, and produces models and tools to better understand and encourage human creativity in a context where it is increasingly intertwined with computation.