Mathematics and Musical Entropy

Arts can provide intuitive examples to enhance the understanding of complex mathematical concepts. Also, mathematics can give precise answers to musical questions that can be raised during the analysis of works of art including musical scores. If musical parameters and mathematical objects are seen as belonging to categories, analysis becomes a dialogue and a mapping between them. This paper develops an idea of “open” musicology that exploits suggestions and contaminations with other research areas, first of all from mathematics and the mathematical formalism behind physics. The focus is on the concept of entropy joined with Discrete Fourier Transforms (DFT), that can be extended to the definition of a musical entropy, as an abstract concept, as well as a computational paradigm. The entropy can be seen as the quantification of the degree of disorder throughout the temporal evolution of musical structures of an entire musical piece. Entropy can also be considered with respect to one or more musical parameters. Their temporal evolution acquires an artistic meaning in itself, as well as the variation of its degree. A method to quantitively evaluate the degree of entropy is presented: a new approach to the topic of entropy, that can also open new pedagogical scenarios. (Received September 16, 2019)