In this chapter, our purpose is to generalize some musical properties that the DFT already satisfies in one dimension, such as the Interval content our the Hexachordal TheoremHexachordal Theorem. In fact, most of the properties that are true in one dimension are also satisfied in higher dimensions, which is treated in Terras (Fourier analysis on finite groups and applications. Cambridge University Press, Cambridge, 1999) (Generalization of the DFT in the case of abelian groupsAbelian group): indeed, all the basic theorems can be extended to this case, and here we start by simply recalling some basic facts (inversion and convolution) that we need for our musical applications. Notice that we are doing this for any application \(f: \mathbb {Z}/{t}\mathbb {Z} \times \mathbb {Z}/{p}\mathbb {Z} \rightarrow \mathbb {C}\) , and we will use it in the case of the characteristic map associated with a musical bar \(\mathcal {B} \in Ztp\) .