Fourier Approximations and Music

For this module, there are two computer algebra system files for each system. When you click on the button below corresponding to your preferred computer algebra system (CAS), this will launch the CAS and will load a file corresponding to Parts 1-4 of this module. In Part 5, you will have the opportunity to download the second file.

Contents

	1. The nature of a musical sound
	2. Musical notes 2.1 The essential characteristics of a musical note 2.2 Pitch and the naming of notes 2.3 Pure tones 2.4 Harmonics and pure tones 2.5 Harmonics and complex vibrations 2.6 Synthesis of periodic functions
	3. Calculus background
	4. Fourier coefficients for trigonometric polynomials of period 2*pi
	5. Fourier approximations for general functions of period 2*pi
	6. Fourier approximations for general functions of arbitrary period
	7. Approximating a periodic function given as a data set