Music and Computers

A Theoretical and Historical Approach

Phil Burk,
Larry Polansky, Department of Music, Dartmouth College
Douglas Repetto,
Mary Roberts
Dan Rockmore, Department of Mathematics, Dartmouth College

Questions/comments/corrections? Please contact: douglas at


Preface to the Archival Version (Spring, 2011)
Preface and Acknowledgments
How to Use the Web Site
The Vision of Mathematics Across the Curriculum
Scanned copy of the Teaching Guide (8.4MB pdf file)

Chapter 1   The Digital Representation of Sound, Part One:
Sound and Timbre
1.1 What is Sound?
1.2 Amplitude
1.3 Frequency, Pitch and Intervals
1.4 Timbre
Chapter 2   The Digital Representation of Sound, Part Two:
Playing by the Numbers
2.1 The Digital Representation of Sound
2.2 Analog v. Digital
2.3 Sampling Theory
2.4 Binary Numbers
2.5 Bit Width
2.6 Digital Copying
2.7 Storage Concerns
2.8 Compression
Chapter 3   The Frequency Domain
3.1 The Frequency Domain
3.2 Phasors
3.3 Fourier and the Sum of Sines
3.4 The DFT, FFT and IFFT
3.5 Problems with the FFT/IFFT
3.6 Some Alternatives to the FFT
Chapter 4   The Synthesis of Sound by Computer
4.1 Introduction to Synthesis
4.2 Additive Synthesis
4.3 Filters
4.4 Formant Synthesis
4.5 Introduction to Modulation
4.6 Waveshaping
4.7 Frequency Modulation
4.8 Granular Synthesis
4.9 Physical Modeling
Chapter 5   The Transformation of Sound by Computer
5.1 Sampling
5.2 Reverb
5.3 Localization/Spatialization
5.4 The Phase Vocoder
5.5 Convolution
5.6 Morphing
5.7 Graphical Manipulation