Raising co-creativity in cyber-human musicianship Digital cultures are increasingly pushing forward a deep interweaving between human creativity and autonomous computation capabilities of surrounding environments, modeling joint human-machine action into new forms of shared reality involving "symbiotic interactions”. In the artistic, cultural or educative fields, co-creativity between humans and machines will bring about the emergence of distributed information structures, creating new performative situations with mixed artificial and human agents. This will disrupt known cultural orders and significantly impact human development. Thanks to the computation of semantic structures from physical and human signals, combined with (deep or statistical) generative learning of symbolic representations, we are beginning to comprehend the dynamics of cooperation (or conflicts) inherent to cyber-human bundles. To this end the REACH project aims at understanding, modeling, and developing musical co-creativity between humans and machines through improvised interactions, allowing musicians of any level of training to develop their skills and expand their individual and social creative potential. Indeed, 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, as in music the constraints are among the strongest to conduct cooperative behaviors that come together into highly integrated courses of actions. REACH will study shared musicianship occurring at the intersection of the physical, human and digital spheres as an archetype of distributed (natural / artificial) intelligence, and will produce models and tools as vehicles to better understand and foster human creativity in a context where it becomes more and more intertwined with computation.