Victoria Callet-Feltz is a Doctor of Mathematics. She did her PhD at the Institut de Recherche Mathématiques Avancées in Strasbourg and teaches now at the Institut Nationale des Sciences Appliquées in Strasbourg. In her work, she has studied some links between algebraic topology and music analysis: more specifically, her research areas concern the topological analysis of some musical structures and processes using a simplicial tool called persistent homology. She found that combining this approach with the theory of the discrete Fourier transform could produce consistent results in the field of topological musical data analysis, and especially in automatic classification field. She is also a member of the French association Femmes & Mathématiques, which allows her to take part in mediation activities aimed at promoting the place of women in scientific and technical fields.

• 1 Introduction.- Part I The two-dimensional Discrete Fourier Transform.- 2 The DFT for modeling basic musical structures.- 3 Generalization of theoretical results.- Part II Persistent homology on musical bars.- 4 Mathematical background.- 5 Musical scores and filtration.- Part III Musical applications.- 6 The DFT as a metric on the set of notes and chord.- 7 Harmonization of Pop songs.- 8 Classification of musical style.- 9 A different approach: the Hausdorff distance.- 10 Conclusion and perspectives for future research.

Victoria Callet-Feltz is a Doctor of Mathematics. She did her PhD at the Institut de Recherche Mathématiques Avancées in Strasbourg and teaches now at the Institut Nationale des Sciences Appliquées in Strasbourg. In her work, she has studied some links between algebraic topology and music analysis: more specifically, her research areas concern the topological analysis of some musical structures and processes using a simplicial tool called persistent homology. She found that combining this approach with the theory of the discrete Fourier transform could produce consistent results in the field of topological musical data analysis, and especially in automatic classification field. She is also a member of the French association Femmes & Mathématiques, which allows her to take part in mediation activities aimed at promoting the place of women in scientific and technical fields.

• 1 Introduction.- Part I The two-dimensional Discrete Fourier Transform.- 2 The DFT for modeling basic musical structures.- 3 Generalization of theoretical results.- Part II Persistent homology on musical bars.- 4 Mathematical background.- 5 Musical scores and filtration.- Part III Musical applications.- 6 The DFT as a metric on the set of notes and chord.- 7 Harmonization of Pop songs.- 8 Classification of musical style.- 9 A different approach: the Hausdorff distance.- 10 Conclusion and perspectives for future research.

Victoria Callet-Feltz is a Doctor of Mathematics. She did her PhD at the Institut de Recherche Mathématiques Avancées in Strasbourg and teaches now at the Institut Nationale des Sciences Appliquées in Strasbourg. In her work, she has studied some links between algebraic topology and music analysis: more specifically, her research areas concern the topological analysis of some musical structures and processes using a simplicial tool called persistent homology. She found that combining this approach with the theory of the discrete Fourier transform could produce consistent results in the field of topological musical data analysis, and especially in automatic classification field. She is also a member of the French association Femmes & Mathématiques, which allows her to take part in mediation activities aimed at promoting the place of women in scientific and technical fields.

• 1 Introduction.- Part I The two-dimensional Discrete Fourier Transform.- 2 The DFT for modeling basic musical structures.- 3 Generalization of theoretical results.- Part II Persistent homology on musical bars.- 4 Mathematical background.- 5 Musical scores and filtration.- Part III Musical applications.- 6 The DFT as a metric on the set of notes and chord.- 7 Harmonization of Pop songs.- 8 Classification of musical style.- 9 A different approach: the Hausdorff distance.- 10 Conclusion and perspectives for future research.