Classification of complex musical structures by Grassmann schemes
The precise understanding of complex musical structures has made considerable progress in the last 50 years. On the one hand, such structures have been described in a unified way by the use of modern mathematics, in particular by conceptual tools developed in the algebraic geometry of schemes and more generally in topos theory. Both fields were essentially created by Alexander Grothendieck and allow for a conceptual elegance that can capture rather subtle features in music-theoretic thinking.
Mazzola, G. (2011)., Classification of complex musical structures by Grassmann schemes, in S. Russ & J. Liesen (eds.), From Past to Future: Graßmann's Work in Context, Dordrecht, Springer, pp. 401-412.
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