Musimathics, Volume 2: The Mathematical Foundations of Music (Mit Press)
"Mathematics can be as effortless as humming a tune, if you know the tune," writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music--a commonsense, self-contained introduction for the nonspecialist reader.Volume 2 of Musimathics continues the story of music engineering begun in volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short time Fourier transform, and the wavelet transform. These subjects provide the theoretical underpinnings of today's music technology. The material in volume 1 is all preparatory to the subjects presented in this volume, although either volume can be read independently. Cross-references to volume 1 are provided for concepts introduced in the earlier volume, and additional mathematical orientation is offered where necessary. The topics are all subjects that contemporary composers, musicians, and music engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Additional material can be found at a companion web site.
Why Read This Book
You will gain an intuitive, musically grounded tour of digital signal processing that translates abstract math into audible examples and practical algorithms. Loy explains sampling, Fourier analysis, filtering, STFT and wavelets with clear visuals and listening-oriented demonstrations so you can both understand the theory and apply it to audio, speech, and other DSP problems.
Who Will Benefit
Engineers, audio programmers, and graduate students with some math background who want a concept-driven, application-focused grounding in DSP as it applies to music, audio/speech, and broader signal-processing tasks.
Level: Intermediate — Prerequisites: Basic algebra and trigonometry, comfort with complex numbers and sinusoidal functions, and some exposure to calculus (derivatives/integrals) or linear algebra will help you get the most from the book.
Key Takeaways
- Understand digital sampling, quantization, aliasing, and how to choose sampling and bit-depth for audio and measurement systems.
- Apply the Fourier transform, DFT/FFT, and short-time Fourier transform to analyze and visualize spectral content of audio and nonstationary signals.
- Design and reason about convolution, FIR/IIR filters and resonance models for synthesis, equalization, and system modeling.
- Implement time-domain and frequency-domain signal processing workflows including FFT-based convolution and spectral analysis.
- Use the wavelet transform and time–frequency tradeoffs to analyze transient and multi-scale signal structure relevant to speech and music.
- Relate DSP building blocks to real-world acoustical systems, sound synthesis techniques, and to signal-processing problems in communications and sensing.
Topics Covered
- Digital audio basics: sampling, quantization, and binary representation
- Complex numbers, phasors, and sinusoidal signals
- Fourier series and the continuous Fourier transform
- Discrete Fourier transform and the FFT
- Convolution, impulse responses, and filtering
- Resonance, poles & zeros, and simple filter design
- The wave equation and acoustical systems
- Sound synthesis and physical modeling
- Short-time Fourier transform, spectrograms, and time–frequency analysis
- Wavelet transforms and multi-scale analysis
- Practical spectral analysis: windows, leakage, and resolution
- Applications and listening demonstrations: from musical timbre to speech
Languages, Platforms & Tools
How It Compares
Compared with Oppenheim & Schafer's Discrete-Time Signal Processing (more formal and mathematically rigorous) and Steven W. Smith's The Scientist and Engineer's Guide to DSP (more textbook-style and tool-focused), Musimathics emphasizes musical intuition and listening-based explanations to make DSP concepts tangible.
