Questions about variation, similarity, enumeration, and classification
of musical structures have long intrigued both musicians and
mathematicians. Mathematical models can be found from theoretical
analysis to actual composition or sound production. Increasingly in the
last few decades, musical scholarship has incorporated modern
mathematical content. One example is the application of methods from
Algebraic Combinatorics, or Topology and Graph Theory, to the
classification of different musical objects. However, these applications
of mathematics in the understanding of music have also led to
interesting open problems in mathematics itself.
The reach and depth of the contributions on mathematical music theory
presented in this volume is significant. Each contribution is in a
section within these subjects: (i) Algebraic and Combinatorial
Approaches; (ii) Geometric, Topological, and Graph-Theoretical
Approaches; and (iii) Distance and Similarity Measures in Music.