Geometry of Triadic Harmony

This paper explores the intersection of geometry and music, investigat- ing how mathematical structures shape musical theory, composition, and perception. It begins by examining the geometric foundations of pitch organization, including the circular representation of pitch classes and the tonal space. We then explore rhythmic structures through symmetry, analysing how patterns in time are geometrically conceived. Finally, the study examines more recent developments in computational music theory, such as the use of topological data analysis to model musical transformations and voice leading.