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Computer Music

The Mathematical Foundations of Music

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 examples given are all practical problems in music and audio. Additional material can be found at

Downloadable instructor resources available for this title: file of figures in the book

The Mathematical Foundations of Music

“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. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science.

In Volume 1, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Calling himself “a composer seduced into mathematics,” Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The examples given are all practical problems in music and audio.

Additional material can be found at

Downloadable instructor resources available for this title: file of figures in the book

This comprehensive handbook of mathematical and programming techniques for audio signal processing will be an essential reference for all computer musicians, computer scientists, engineers, and anyone interested in audio. Designed to be used by readers with varying levels of programming expertise, it not only provides the foundations for music and audio development but also tackles issues that sometimes remain mysterious even to experienced software designers. Exercises and copious examples (all cross-platform and based on free or open source software) make the book ideal for classroom use. Fifteen chapters and eight appendixes cover such topics as programming basics for C and C++ (with music-oriented examples), audio programming basics and more advanced topics, spectral audio programming; programming Csound opcodes, and algorithmic synthesis and music programming. Appendixes cover topics in compiling, audio and MIDI, computing, and math. An accompanying DVD provides an additional 40 chapters, covering musical and audio programs with micro-controllers, alternate MIDI controllers, video controllers, developing Apple Audio Unit plug-ins from Csound opcodes, and audio programming for the iPhone.The sections and chapters of the book are arranged progressively and topics can be followed from chapter to chapter and from section to section. At the same time, each section can stand alone as a self-contained unit. Readers will find The Audio Programming Book a trustworthy companion on their journey through making music and programming audio on modern computers.

Designing Sound teaches students and professional sound designers to understand and create sound effects starting from nothing. Its thesis is that any sound can be generated from first principles, guided by analysis and synthesis. The text takes a practitioner’s perspective, exploring the basic principles of making ordinary, everyday sounds using an easily accessed free software. Readers use the Pure Data (Pd) language to construct sound objects, which are more flexible and useful than recordings. Sound is considered as a process, rather than as data--an approach sometimes known as “procedural audio.” Procedural sound is a living sound effect that can run as computer code and be changed in real time according to unpredictable events. Applications include video games, film, animation, and media in which sound is part of an interactive process. The book takes a practical, systematic approach to the subject, teaching by example and providing background information that offers a firm theoretical context for its pragmatic stance. [Many of the examples follow a pattern, beginning with a discussion of the nature and physics of a sound, proceeding through the development of models and the implementation of examples, to the final step of producing a Pure Data program for the desired sound. Different synthesis methods are discussed, analyzed, and refined throughout.] After mastering the techniques presented in Designing Sound, students will be able to build their own sound objects for use in interactive applications and other projects

An Introduction to Psychoacoustics
Edited by Perry R. Cook

How hearing works and how the brain processes sounds entering the ear to provide the listener with useful information are of great interest to psychologists, cognitive scientists, and musicians. However, while a number of books have concentrated on individual aspects of this field, known as psychoacoustics, there has been no comprehensive introductory coverage of the multiple topics encompassed under the term. Music, Cognition, and Computerized Sound is the first book to provide that coverage.

The book begins with introductory chapters on the basic physiology and functions of the ear and auditory sections of the brain, then proceeds to discuss numerous topics associated with the study of psychoacoustics, including cognitive psychology and the physics of sound. The book has a particular emphasis on music and computerized sound. 

Perspectives in Software Synthesis, Sound Design, Signal Processing, and Programming

Created in 1985 by Barry Vercoe, Csound is one of the most widely used software sound synthesis systems. Because it is so powerful, mastering Csound can take a good deal of time and effort. But this long-awaited guide will dramatically straighten the learning curve and enable musicians to take advantage of this rich computer technology available for creating music.

Written by the world's leading educators, programmers, sound designers, and composers, this comprehensive guide covers both the basics of Csound and the theoretical and musical concepts necessary to use the program effectively. The thirty-two tutorial chapters cover: additive, subtractive, FM, AM, FOF, granular, wavetable, waveguide, vector, LA, and other hybrid methods; analysis and resynthesis using ADSYN, LP, and the Phase Vocoder; sample processing; mathematical and physical modeling; and digital signal processing, including room simulation and 3D modeling.

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