Mathematics and Music : The Mathieu Group M 12 Emma Ross Year

Despite falling into seemingly contrasting disciplines of art and science, music lends itself surprisingly well to mathematical interpretation and understanding. The appearance of symmetry and repetition of some central theme is extremely common in musical composition and group theory provides us with the ideal tools with which to study this. This project finds its roots in the music composed by Oliviér Messiaen which owes most of its structure to the sporadic group M12. Some context and motivation for studying this exceptional group opens the discussion. The majority of the material covered attempts to build an understanding of the construction of M12 Chapters 2 to 4 exploring in particular detail its relationship with Steiner systems and coding theory. Some interesting properties of the group are presented in the penultimate chapter before returning to Messiaen’s music to close the project. Analysis of one of his pieces in the final chapter serves to demonstrate the mathematics at work in the structuring of music. This project report is submitted in partial fulfilment of the requirements for the degree of MA (Hons) Mathematics.