Physics in the Arts Lecture S10 Musical Instruments Sound Perception Gregory Uhlmann Extra Stars Reminder Course Evaluations Hopefully you enjoyed this class and learned a lot Please please please participate in course evaluations Without your input we won t know what worked and what didn t Your feedback matters and will be taken into account for future versions of this class Example Square Wave Superposition of partials 0 5 1 0 1 5 time s 2 0 time s 1 0 0 5 0 5 1 0 The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 1 0 0 5 0 5 1 0 0 5 1 0 1 5 time s 2 0 Square wave sound time s The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 0 5 1 0 1 5 time s 2 0 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 1 0 0 5 0 5 1 0 The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 0 5 1 0 1 5 time s 2 0 1 0 0 5 0 5 1 0 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 First partial The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 0 5 1 0 1 5 time s 2 0 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 1 0 0 5 0 5 1 0 The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 0 5 1 0 1 5 time s 2 0 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 1 0 0 5 0 5 1 0 First third partial The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 0 5 1 0 1 5 time s 2 0 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 1 0 0 5 0 5 1 0 The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 First third fth partial 1 0 0 5 0 5 1 0 0 5 1 0 1 5 time s 2 0 The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 0 5 1 0 1 5 time s 2 0 time s 1 0 0 5 0 5 1 0 The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave Superposition of partials 0 5 1 0 1 5 time s 2 0 time s 1 0 0 5 0 5 1 0 Hundreds of partials The more partials we include the closer we get to a true square wave and the harsher the tone sounds Example Square Wave sin 360 f1 t 1 Fourier spectrum of a square wave sin 360 3f1 t 1 5 sin 360 5f1 t 4 3 All the odd harmonics like a closed pipe e d u t i l p m a 1 2 1 0 0 8 0 6 0 4 0 2 0 0 2 4 6 8 multiples of 10 fundamental frequency Example Sawtooth Wave 1 0 0 5 0 5 1 0 0 5 1 0 1 5 time s 2 0 Example Sawtooth Wave 1 0 0 5 0 5 1 0 Sawtooth wave sound 0 5 1 0 1 5 time s 2 0 Example Sawtooth Wave 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 First partial 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 Example Sawtooth Wave 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 First two partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 Example Sawtooth Wave 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 First three partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 Example Sawtooth Wave 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 First four partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 Example Sawtooth Wave 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 First 100 partials 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 Example Sawtooth Wave Fourier decomposition of a sawtooth wave sin 360 3f1 t sin 360 f1 t 1 2 sin 360 2f1 t 1 3 2 0 5 0 5 1 0 1 0 1 5 1 5 time s 2 0 2 0 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 First 100 partials Example Sawtooth Wave 1 0 1 0 0 5 0 5 0 5 0 5 1 0 1 0 First 100 partials 0 5 0 5 1 0 1 0 1 5 1 5 2 0 2 0 time s 0 6 Fourier decomposition of a sawtooth wave sin 360 3f1 t sin 360 f1 t 1 2 sin 360 2f1 t 1 3 2 All the harmonics like an open pipe e d u t i l p m a 0 5 0 4 0 3 0 2 0 1 0 0 2 4 multiples of fundamental frequency …