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We describe the Tonnetz web environment and some of the possible applications we have developed within a pedagogical workshop on mathematics and music that has been conceived for high-school students. This web environment makes use of two geometrical representations that constitute intuitive ways of accessing some theoretical concepts underlying the equal tempered system and their possible mathematical formalizations. The environment is aimed at enhancing “mathemusical” learning processes by enabling the user to interactively manipulate these representations. Finally, we show how Tonnetz is currently being adapted in order to lead computer-based experiences in music perception and cognition that will be mainly carried at universities. These experiences will explore the way in which geometrical models could be implicitly encoded during the listening process. Their outcome may reinforce educational strategies for learning mathematics through music.

The Tonnetz Environment: A Web Platform for Computer-aided “Mathemusical” Learning and Research