This essay explores the use of generative AI systems in cocreativity within musical improvisation, offering best practices for this paradigm. Using practice-based research in the interdisciplinary fields of scientific and artistic exploration, this study documents the author's artistic collaboration with an experimental music ensemble. This partnership resulted in a studio album and will continue with international concerts and workshops. The research is supported by observations and surveys on computational creativity and co-creativity in Human-Computer Interaction (HCI), along with reflections on musical improvisation from scientific, cognitive, and musicological perspectives. These insights form the foundation of the article, which later specifically examines the cocreative system for improvisation, Somax2, developed within the European project REACH (Raising Co-Creativity in Cyber-Human Musicianship). The analysis situates Somax2 in a new context, detailing generative agent models, the taxonomy of interactive systems between player and instrument paradigms, and cognitive behaviors in improvised music. This research confers on Somax2 a novel multifaceted identity, offering artists new perspectives on its use and positioning it as an optimal case for defining the new proposed framework of Environmental or Ecological Referent in HCI contexts of music improvisation.