Conclusion and perspectives

This brief journey has deliberately left out a number of traditional concepts (such as scale and temperament constructions, chord notation, rhythmic segmentation, Schenkerian analysis, voice-leadings, etc.), which some readers may have expected to see. I chose to focus on the most accessible fundamental tools that are essential for understanding contemporary publications in mathematics and music. It was certainly frustrating (it was for the author) not to address the next level (group actions, refined algebraic structures like rings, quotients, modules, metric spaces, topology, polynomials, matrices, categories, etc.), but the purpose of this book was to open doors, not to impress or scare people away. As it stands, it was already a delicate exercise.