Music, Math and Mind



Columbia University
Fall, 2019 -- AV4000
Dave Sulzer and Brad Garton

course syllabus


This course is a detailed and hands-on (ears-on) exploration of the fundamental physical and physiological aspects of sound and music. Topics covered include the math and physics of sound waves, pitch, harmonics, and rhythm: animal sound production strategies: sound transduction and perception mechanisms in the ear and brain: and associated neurological disorders. Coursework will include student-led projects.

This course encompasses the physics and neuroscience of music. Topics will include the mathematics by which musical scales, rhythms, and harmonies are derived, a topic that spans the history of math from the monochord of Pythagoras, wave functions, calculus required for equal temperament, through fractal geometry. The perception of music encompasses the physics, anatomy, and neuroscience of the ear and auditory neural pathways, and synaptic mechanisms that occur within the midbrain and cerebral cortex, and there will be attention to what little is known about the physiology of emotion. Additional topics will include physics of sound and physiology and associated behaviors associated with animal sound including songbirds, cetaceans, insects, and bat echolocation. Previous coursework in math and physiology is not required, and it is intended to be useful from diverse backgrounds in science or the arts, including undergrad and grad students.

Some questions the class will address


Textbooks

We don't have a textbook for the course, but my favorite classic on the topic, which is downloadable, is Helmholtz's On the Sensations of Tone. For those very interested in the math of musical scales, check out Harry Partch's Genesis of a Music, also freely downloadable. For inspiration on cortical processing of music, consider Wilder Penfield studies on epilepsy operations, one nice book is Speech and Brain-Mechanisms, but his papers on PubMed are useful. I will mention primary papers during the course of the lecture.