Mathematical Music Theory and the Musical Math Game - Two Creative Ontological Switches

Mathematical Music Theory (MaMuTh) can be understood as a creative support of the musical ontology, a toolset for composition, or a model for theoretical approaches. Several MaMuTh scholars who are also musicians have asked about the opposed possibility, a Musical Math Game (MuMaGm), namely the creative musical support of the mathematical ontology, setting up conjectures, mathematical theories and eventually helping solve mathematical problems. We discuss this idea and our related proposal of music and mathematics being adjoint functors between (the categories of) formulas and gestures. We illustrate this bidirectional ontological shift of creativity between music and mathematics through the history of counterpoint.