This course will introduce students to current scholarship in music theory. It will focus in particular on theories that explore the phenomenon of tonality in broad, mathematically rigorous, and perceptually relevant ways. How can we understand tonality not only in European repertoires from circa 1650-1900, but also in earlier periods, 20th-century art, music, and jazz? What musical "spaces" can be developed to model tonal motion and distance beyond the well-known circle of fifths? How can we conceive of triads and seventh chords as special cases in a limitless field of chordal possibilities? How can we develop analytical approaches that are responsive to the multiplicity of tonal perception and experience?
The course will approach these questions through a geometric approach (Tymoczko, A GEOMETRY OF MUSIC) and transformational or algebraic approach (Rings, TRANSFORMATION AND TONALITY). Specialized background in mathematics is not required, but students should be prepared to engage with mathematical ideas and methods in the service of musical insight. The course is intended for students with a solid background in tonal harmony, general musicianship, and score reading.