In this talk, I will explain how to translate basic concepts of music theory into the language of contemporary geometry.  I will show that musicians commonly abstract away from five types of musical transformations, the "OPTIC transformations," to form equivalence classes of musical objects.  Examples include "chord," "chord type," "chord progression," "voice leading," and "pitch class."  These equivalence classes can be represented as points in a family of singular quotient spaces, or orbifolds: for example, two-note chords live on a Mobius strip whose boundary acts like a mirror, while four-note chord-types live on a cone over the real projective plane. Understanding the structure of these spaces can help us to understand general constraints on musical style, as well as specific pieces.  The talk will be accessible to non-musicians, and will exploit interactive 3D computer models that allow us to see and hear music simultaneously.