Mathematical analysis of music started when Pythagoras made his observations about consonant intervals and ratios of string lengths.

**ADDED:**

In the paper **Mathematical Music Theory -- Status Quo 2000**, G. Mazzola, ETH Zu ̈rich, Departement GESS, and Universit ̈at Zu ̈rich, Institut fu ̈r Informatik, available [here][1], we have the following statement: 

*... These models use different types of mathematical approaches, such as—for instance—enumeration combinatorics, group and module theory, algebraic geometry and topology, vector fields and numerical solutions of differential equations, Grothendieck topologies, topos theory, and statistics. The results lead to good simulations of classical results of music and performance theory. There is a number of classifiaction theorems of determined categories of musical structures.*

>>The question is: from the *modern* mathematical point of view, what is **music**?



  [1]: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.2.8716&rep=rep1&type=pdf