The development of musical improvisation partners is an important issue in the domain of computationally creative systems. While there have been several attempts to develop musically engaging systems, they are challenged by certain preconceived notions of what partnerships mean with machines. Here, I argue for the study of creative partnerships through the experiences that are engendered in such situations. The experience of creative partnerships is felt through the interaction with co-creators, and is termed co-experience. With a computational co-creator, the focus shifts towards the abilities of computational system to engender co-experiences through interaction. The position articulated in this paper is that musical co-experiences arise through the design of interaction behaviors that are responsive to human co-creators. Reports from music studies are drawn to support this position. The potential to further research in the domain of creative computational musical partnerships is highlighted through the position developed in this work.