The Mathematics of Music

There is no textbook. All lecture notes will be posted right here. For further information I recommend David Benson's book Music: A Mathematical Offering, which is available for free. The webpage of Daniel A. Russell has a lot of nice animations of acoustic phenomena. My friend Michael O'Connor wrote some great audio demonstrations for this course.
Item Date Information
Introduction Jan 13 - Jan 22 Course Notes
Pythagoras' Observation
Why We Have 12 Notes
Vincenzo's Observation
Frequency and Partials
Helmholtz' Observation
Quiz 1 Tues Jan 27 Solutions
Homework 1 Due: Tues Feb 10 Solutions
Trigonometry Jan 22 - Feb 5 Course Notes
Why Sine Waves?
Hooke's Law
From "jya-ardha" to "sine"
Linear Functions and Matrices
Euler's Formula
Angle Sum Identities
Plomp and Levelt (1965)
Dissonance Curves
Quiz 2 Thurs Feb 12 Solutions
Wave Equation Feb 10 - Mar 5 Course Notes
Vector Fields in R^2
Exponential of a Matrix
The Harmonic Oscillator
The Wave Equation
d'Alembert's Solution
D. Bernoulli's Solution
The Controversy
Homework 2 Due: Thurs Mar 5 Solutions
Quiz 3 Tues Mar 17 Solutions
Fourier Series Mar 17 - Apr 7 Course Notes
Fourier's 1 Weird Trick
Vector Spaces
Inner-Product Spaces
Orthonormal Bases
The Pythagorean Theorem
Parseval's Theorem
Conservation of Energy
Quiz 4 Tues Apr 14 Solutions
Scales & Temperaments Mar 17 - Apr 7 Course Notes
Ptolemy's Epicycles
Planetary Scales
Pythagorean Tuning
Continued Fractions
Just Intonation
Meantone Temperaments
Equal Temperament
Homework 3 Due: Tues Apr 28 Solutions