It is possible to recognize abstract structures lying behind music. Some music's features can be naturally described borrowing a largely used and well known set of tools in mathematics. In the first part of this "math-music" journey, after a preliminary introduction about music theory, we will show how the Tonnetz (an abstract graph which represents the interaction among notes) can be a useful, low-dimensional representation of some basic musical objects as triads, and how it is possible to achieve a generalization of the standard Tonnetz, inducing a geometrical and topological structure on the graph.