Klein Concert: A Report from a Math-Musical Classroom Experience

Can music help mathematical education? Can some shapes, that challenge visual imagination, be translated into music? I present a pedagogical application of my interdisciplinary research. This concerns a cycle of seminars about mathematics and music I gave in Italy at the Music Conservatory of Palermo and that, in a shortened version, I also gave at Ca’ Foscari University in Venice, at the Conservatory of Livorno, and in the UK, at the University of Greenwich. Seminars included a theoretical section and a workshop. Mathematical concepts helped students formalize their musical knowledge, and music provided an intuitive understanding of mathematical concepts, such as the dualism continuous/discrete, the concept of envelope, and the abstraction of categories. Then, the students were given the Klein bottle, and they translated it into music. The resulting musical compositions were different but they shared general structures highlighting the bottle’s features: e.g., counterpoint represented multiple simultaneous paths on the bottle, and quadraphony recreated a feeling of an additional dimension through spatialization and time variations. Musical cyclicity and inversions rendered the non-orientability of the Klein surface. The final output was a string orchestra concert.