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# Numbers & Notes - Table of Contents

Collecchia, Regina. *Numbers & Notes: An Introduction to Musical Signal Processing*. Portland, OR: PSI Press, Inc., 2012. 318 pages.

All images by Sarah Powers and the author.

### Preface

### Contents

### 1 Review of mathematical notation and functions

1.1 Numbers

1.2 Functions

1.3 Calculus

1.4 Notation

2.1 What is sound?

2.2 Simple harmonic motion

2.3 Complex harmonic motion

2.4 Harmonicity, periodicity, and perfect intervals

2.5 Properties of waves

2.6 Chapter summary

### 3 Musical sound

3.1 Rhythm

3.2 Pitch

3.3 Tuning and temperament

3.4 Timbre

3.5 Chapter summary

### 4 Musical instruments

4.1 The piano

4.2 The viol family

4.3 Woodwinds and brasses

4.4 Drums

4.5 Electric guitars and effects units

4.6 Chapter summary

### 5 Auditory perception

5.1 Physiology of the ear

5.2 Psychoacoustics

5.3 Perfect pitch

5.4 Chapter summary

### 6 Digital audio basics

6.1 Sampling

6.2 Compression

6.3 Chapter summary

### 7 The discrete Fourier transform

7.1 The Fourier series

7.2 Euler's formula

7.3 The discrete Fourier transform

7.4 The DFT, simplified

7.5 Examples

7.6 Chapter summary

### 8 Other Fourier transforms

8.1 Discrete-time Fourier transform (DTFT)

8.2 Fast Fourier transform (FFT)

8.3 Short-time Fourier transform (STFT)

8.4 Chapter summary

### A Frequency-selective circuits

A.1 Ohm's Law

A.2 Filtering

A.3 The Z-Transform

A.4 Chapter summary

### B Using computers to do Fourier transforms

B.1 Matlab

B.2 Mathematica

B.3 C

### References

### Glossary

### Index

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