Getting involved with mathematical music theory

Abstract

This essay advocates the integration of mathematical reasoning into the teaching of music theory. It offers a didactical pathway through a series of attractive results from well-known algebraic approaches to the study of diatonicity. In particular, strategies are discussed that let the students re-enact processes of investigation and discovery. The content centers around the study of intervals and chords within the diatonic scale. This involves the distinction between generic and specific descriptions, combinatorics of voice leading and chord inversion, as well as the explanatory power of the cycle of fifths. In order to reach its goals, the essay strives towards the introduction of unorthodox media, such as the Tonkreisel, the Rotating Square, or the Diatonic Cord (rope).

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