DFT and Persistent Homology for Topological Musical Data Analysis

There are several works that already exist in the context of persistent homology for Topological Musical Data Analysis, and we can cite [2] and [3] among others: in each one of these works, the main problem is to find how we can associate a point cloud with a musical score, that is a set of points with a metric. This paper proposes to combine persistent homology with a symbolic representation of musical structures given by the Discrete Fourier Transform to answer this question: the points are the musical bars and the metric is given by the DFT in dimension two. We start with the mathematical background, and the main goal of this paper is thus to support the use of the DFT in this context, by extracting barcodes from artificially constructed scores based on Tonnetze, and then recovering topological features.