Music and the Circular Functions (UMAP)

A unit that relates circular functions to the topic of music. This module represents a simplified version of how sounds is generated and transmitted as well as key definitions from music. The properties of vibrations that determine pitch, loudness, and tone quality are examined in terms of simple harmonic motion and its equations. The unit concludes with an intuitive presentation of Fourier's Theorem and harmonic analysis.

Table of Contents:

1. MATHEMATICS AND MUSIC
1.1 Introduction
1.2 The Generation and Transmission of Sound

2. PICTURES OF SOUNDS
2.1 The Oscilloscope
2.2 Sample Problem
2.3 Definitions and Terms

3. TONE QUALITY
3.1 Beats
3.2 Timbre

4. HARMONIC ANALYSIS
4.1 Fourier's Theorem
4.2 Sample Problem

5. SAMPLE EXAM

6. ANSWERS TO EXERCISES

7. ANSWERS TO SAMPLE EXAM