Matemática e música: análises, contextos e padrões em escalas musicais e sequências

Abstract

This work deals with mathematics and music, more specifically in relation to patterns belonging to the musical scale, intervals, times of figures, and sequences. It is an interdisciplinary work which objectively provides ways to study some objects of knowledge covered in secondary and higher education. Its development was based on research in books, articles, monographs, dissertations, etc. Thus, by approaching the philosopher Pythagoras as one of the main scholars responsible for the development of the musical scale based on an instrument called monochord, the work suggests some analyzes and possible contextualizations about these two areas of knowledge aiming to contributing to the methodological and spreading the possibilities of dialogue between both areas of knowledge. When it comes to the mathematical context involved, there are approaches and analyzes on harmonic series, modular congruence, combinatorics, Indian mathematics and a proposal for a didactic sequence on geometric progression. All of this related to the musical scale, intervals, times of the figures, measures, etc. Therefore, it is also possible to state that one of the ideas of the work is to discuss the scope of the theme, involving it in order to understand the extent to which it is possible to connect it from a logical, historical and cultural approach, within the different possibilities of the teaching and learning mathematics from different perspectives.