The Mathematics of Music
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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.
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| 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 Beats 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 |