Introducción a las matemáticas musicales: conjuntos, grafos y cadenas de Márkov

Abstract

In this paper was carried out a research about four mathematic areas that have been demonstrated, on the course of the XX and XXI centuries, to be essential on music theory, compositional and analytical production. The investigation was developed through literature research of eminent mathematicians and musicians theorists who have dedicated their studies in logic, set theory, graph theory and Márkov chains. The reason why this study is important, is that it includes a need to create a text that teaches to the music students the theoretical axes of current relevance by approaching each theme, at first, with its musical application, without disregarding the mathematical basis and enunciation. Furthermore, all the topics discussed show musical examples of musical literature of the XX and XXI centuries, as well, prior to the twentieth century literature. The result of this research is an academic-pedagogical sourcebook for all types of audiences who are interested in the intrinsic relationship of these two knowledge and will serve as prefatory material to mathematical pillars of contemporary music and it proposes, on the other hand, new theoretical notions that, in any case, complement the studied.