Gareth Loy: Musimathics: The Mathematical Foundations of Music, Vols. 1-2 (2006)

“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. Musimathics is carefully structured so that new topics depend strictly on topics already presented, carrying the reader progressively from basic subjects to more advanced ones. Cross-references point to related topics and an extensive glossary defines commonly used terms. The book explains the mathematics and physics of music for the reader whose mathematics may not have gone beyond the early undergraduate level. Calling himself “a composer seduced into mathematics,” Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously.

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.

Foreword by John Chowning
Publisher MIT Press, 2006, 2007
ISBN 0262122820, 9780262122825 (Vol 1)
ISBN 0262122855, 9780262122856 (Vol 2)

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Doron Swade: The Difference Engine: Charles Babbage and the Quest to Build the First Computer (2001)

In 1821 an inventor and mathematician named Charles Babbage was reviewing a set of mathematical tables. After finding an excess of errors in the results, he exclaimed, “I wish to God these calculations had been executed by steam.” Thus began Babbage’s lifelong enterprise to design and build a mechanical calculating engine-the world’s first computer. Drawing on Babbage’s original notes and designs, Doron Swade recounts both Babbage’s nineteenth-century quest to build a calculating machine-the Difference Engine-and Swade’s own successful attempt to build a replica for the bicentennial of Babbage’s birth. Set against the tantalizing background of Victorian science and politics with a colorful cast of characters, The Difference Engineis a saga of ingenuity and will-and the dawning of a new age.

Publisher Penguin Books, 2001
ISBN 0670910201
342 pages

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Michele Emmer (ed.): The Visual Mind II (2005)

“Mathematical forms rendered visually can give aesthetic pleasure; certain works of art—Max Bill’s Moebius band sculpture, for example—can seem to be mathematics made visible. This collection of essays by artists and mathematicians continues the discussion of the connections between art and mathematics begun in the widely read first volume of The Visual Mind in 1993.

Mathematicians throughout history have created shapes, forms, and relationships, and some of these can be expressed visually. Computer technology allows us to visualize mathematical forms and relationships in new detail using, among other techniques, 3D modeling and animation. The Visual Mind proposes to compare the visual ideas of artists and mathematicians—not to collect abstract thoughts on a general theme, but to allow one point of view to encounter another. The contributors, who include art historian Linda Dalrymple Henderson and filmmaker Peter Greenaway, examine mathematics and aesthetics; geometry and art; mathematics and art; geometry, computer graphics, and art; and visualization and cinema. They discuss such topics as aesthetics for computers, the Guggenheim Museum in Bilbao, cubism and relativity in twentieth-century art, the aesthetic value of optimal geometry, and mathematics and cinema.”

Published by MIT Press, 2005
ISBN 0262050765, 9780262050760
699 pages

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