Mathematica est exercitium musicae : la recherche mathémusicale et ses interactions avec les autres disciplines

Abstract : In western tradition, mathematics and music have been deeply connected for more than 2000 years. Despite this long history of the relationship between mathematics and music, the professional interest of mathematicians in this domain is a relatively new phenomenon. Whilst the power of applying mathematics in the description of music has been acknowledged for a long time, it is only thanks to more recent developments that also music begins to occupy a strategic place in the development of mathematics. This fact is supported by the emergence and partially successful solution of an increasing number of “mathemusical” problems, i.e problems which are characterized by the fact that settling an originally musical problem in an appropriate mathematical framework not only gives rise to new mathematical results, but also paves the way to new musical constructions. It is this fruitful double movement, from music to mathematics and backwards, which excites an increasing number of researchers in both domains and which is at the heart of a growing international research activity accompanied by an increasing appearance of international journals, conferences, book series and collaborative projects in this field of study. In this memoir we first present a selection of "mathemusical" problems on which we have been working by showing the results obtained and the questions which still remain open. In the second part we will study in detail three types of interactions between mathemusical research and three main disciplines, namely cognitive sciences, informatics and philosophy.
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Habilitation à diriger des recherches
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Moreno Andreatta. Mathematica est exercitium musicae : la recherche mathémusicale et ses interactions avec les autres disciplines. Mathématiques [math]. Université de Strasbourg, 2010. ⟨tel-00526432⟩

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