Music, Math and Mind



Columbia University
Fall, 2021 -- AV4000
Thursdays, 6:10 PM -- 8:00 PM, room 320H Prentis Hall
Dave Sulzer and Brad Garton

course syllabus


This course encompasses the physics and neuroscience of music and sound. Previous course work 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.Topics include the physics of sound waves (explained with grad school level math), pitch, harmonics, and rhythm: sound transduction and perception mechanisms in the ear and brain: sound, and music and hearing by other species including songbirds, cetaceans, insects, and bats: associated neurological disorders: and what little is known about the physiology of emotion. We will study 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, 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. There will be guest scientist. and musician presentations. Coursework will include student-led projects. Brad Garton of the Computer Music Center is co-instructor.


Textbooks

There is no required text for the class, but Dave wrote the book Music, Math and Mind based on this class (if you use the code "AUTH" you can get 20% off!).

Other books you might find useful include my favorite classic on the topic, which is downloadable, 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.