The music theorist Thomas Noll, currently a guest at the Max Planck Institute for Mathematics, will give a public lecture about his research on the relation between music and mathematics.

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**Abstract:** Music theorists emphasize the historical anchors of their field and trace the history of ideas as a substantial part of their collective knowledge. Mathematical investigations offer a complementary approach, where mathematical redefinitions of historically grown concepts are studied with respect to their logical interdependencies. Within the last three decades a fruitful dialogue between the two types of investigation emerged. In my talk, I will share some instances where central elements of traditional knowledge appear in a promising new light after mathematical investigation. For instance, the decomposition of the dorian mode d-e-f-g-a-b-c-(d) into a species of the fifth (tone semitone tone tone) and a species of the fourth (tone semitone tone) suggests the consideration of an automorphism f(a) = abaa, f(b) = aba of the free group F2 over the generators a and b. Starting from such a definition, various music-theoretically relevant issues around diatonicity can then be re-interpreted on the basis of known facts from algebraic combinatorics on words. But also fundament progressions, a main subject in harmonic tonality, can be revisited in this context. In addition to the illustrative role of these examples I will attempt to position them within ongoing projects in mathematical music theory. The applied mathematical concepts include group actions, monoid actions, algebraic combinatorics on words, formal concept analysis, and discrete Fourier transforms.

**Thomas Noll** (Germany/Spain) works in mathematical music theory as his main research area. He studied mathematics (diploma) in Jena and semiotics (PhD) at the TU Berlin. From 1998 - 2003 he was the leader of an interdisciplinary research group on mathematical and computational music theory at that same university. After two years of teaching in theoretical informatics at the TU Berlin he works since 2005 as a lecturer in music theory at the Escola Superior de Musica de Catalunya in Barcelona. He was co-editor of the "Journal of Mathematics and Music" (2006 - 2012) and serves as reviewer for several journals and conferences in the field. He also is active in popularizing mathematical music theory for a wider audience. He is currently a guest at the MPIM collaborating with guest Thomas Fiore (Topology).

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