Automatic Exercise Generation for Exploring Connections between Mathematics and Music

Abstract

Abstract Mathematics and Music are closely connected and their multifaceted relationship has been explored since ancient times. Pythagoras was one of the first who discovered and formalized one of those connections by studying the arithmetic of musical intervals, expressing them by numerical ratios and relating ratios to consonance/dissonance notions, being the Pythagorean tuning and scale based on arithmetic principles. Another interesting link between Mathematics and Music is the geometric approach to musical composition. Geometric patterns are present in different musical style compositions and some composing techniques, such as the 12-tone technique, use geometric transformations, involving also applications of modular arithmetic and set theory to Music. The aim of this work is to present existing relations between Mathematics and Music and to propose automatic exercise generation for exploring and studying those relations. The exercises are generated using the system MVGEN and the LaTeX package MusiXTeX. The generation process and the automatically generated exercises can be used for creating learning and assessment materials for education in Mathematics and Music, linking Science and Art.