Music Math and Mind

Columbia University
Fall, 2017 -- AS4000
Dr. David Sulzer, Professor of Psychiatry, Neurology, and Pharmacology at Columbia University Medical School; Sound Arts in the School of the Arts
Co-instructors: Ethan Edwards, Brad Garton and Ben Holtzman

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

• 1) Sound waves are in three space dimensions (and time). What shape are they, how big and fast? how are sound waves different under water, through the earth?
• 2) why do instruments sound different from each other? why do larger instruments play lower pitches?
• 3) we have two eardrums and two ears, how can we distinguish so many different simultaneous sounds?
• 4) neurons fire maybe as fast as 200 times a second (Hz). We can hear frequencies up to 20,000 Hz: how is that possible?
• 5) do sound and anti-sound waves cancel each other out? (trick question)
• 6) what is the Doppler effect on ambulance sirens?
• 7) how can we tell the direction a sound is coming from?
• 8) what sounds seem in tune and out of tune and how can a musical scale be made? Is it true that scales are really never in tune?
• 9) related issue: what do Pythagorean ratios like 3/2 for a perfect 5th really mean?
• 10) what are sum and difference tones?
• 11) what is a sin? what’s a log? what is a Fourier transform?
• 12) what is the math definition of noise and different kinds of noise?
• 13) how does the brain understand what it is listening too? warning; this does not yet have a really satisfying answer
• 14) how are emotions carried by music?: ditto
• 15) what kind of disorders are there for hearing sound and music?
• 16) how do other animals hear and make sound differently?
• 17) how do microphones and speakers work, and how is sound encoded on records and digitally?
• 18) what are overtones and harmonic sounds and how are they different?
• 19) how might a musician use math to come up with unusual forms and structures?

• Audacity -- a sound-editing and analysis program
• SPEAR -- a sound analysis and manipulation program
• Raven -- an interactive sound analysis progam (note: on the Raven Downloads page, scroll down to find the free versions. You will need to request a license [instructions on the page])
• NEW!   LearningSound.app.zip -- zip archive of the app we developed for this class to explore different aspects of sound and tuning
  
  we will be putting other software links here as the term progresses -- keep checking!