Musimathics The Mathematical Foundations of Music Volume 2

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 this volume, 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. The topics are all subjects that contemporary composers, musicians, and musical 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.

The second volume of a commonsense, self-contained introduction to the mathematics and physics of music, focusing on the digital and computational domain; essential reading for musicians, music engineers, and anyone interested in the intersection of art and science.

"Music and mathematics enjoy many points of intersection. Just think of musical scales and number theory, or the impact of computers - both analog and digital - on the composition and creation of musical sounds. The second volume of *Musimathics* ably covers these and many other instances of this happy union: Fourier and wavelet transforms, natural and artificial reverberation, and much more."--Manfred Schroeder, Professor of Physics, University of Goettingen, Germany

"Musimathics is destined to be required reading and a valued reference for every composer, music researcher, multimedia engineer, and anyone else interested in the interplay between acoustics and music theory. This is truly a landmark work of scholarship and pedagogy, and Gareth Loy presents it with quite remarkable rigor and humor."
—Stephen Travis Pope, CREATE Lab, Department of Music, University of California, Santa Barbara

"From his long and successful experience as a composer and computer-music researcher, Gareth Loy knows what is challenging and what is important. That comprehensiveness makes Musimathics both exciting and enlightening. The book is crystal clear, so that even advanced issues appear simple. Musimathics will be essential for those who want to understand the scientific foundations of music, and for anyone wishing to create or process musical sounds with computers." -- Jean-Claude Risset, Laboratoire de Mécanique et d'Acoustique, CNRS, France The MIT Press

The second volume of a commonsense, self-contained introduction to the mathematics and physics of music, focusing on the digital and computational domain; essential reading for musicians, music engineers, and anyone interested in the intersection of art and science.

“It will be obvious by now that this is a book wholeheartedly to be recommended for a wide readership. As definitive as is possible, certainly the leading resource in the field, it will meet many needs. Those with school algebra and physics who are performers, engineers, composers, listeners will almost inevitably get much from MusimathicsàThe two volumes of this book, then, must be considered as the place to start any exploration of this field. Entertaining, secure, comprehensive, clear, authoritative, timely, up-to-date, well wrought in every way, these are for every music lover's shelves.”
— Mark Sealey, Classical Net: The Internet's Premier Classical Music Source“Music and mathematics enjoy many points of intersection. Just think of musical scales and number theory, or the impact of computers—both analog and digital—on the composition and creation of musical sounds. The second volume of Musimathics ably covers these and many other instances of this happy union: Fourier and wavelet transforms, natural and artificial reverberation, and much more.”
—Manfred Schroeder, Professor of Physics, University of Goettingen, Germany“Musimathics is destined to be required reading and a valued reference for every composer, music researcher, multimedia engineer, and anyone else interested in the interplay between acoustics and music theory. This is truly a landmark work of scholarship and pedagogy, and Gareth Loy presents it with quite remarkable rigor and humor.”
—Stephen Travis Pope, CREATE Lab, Department of Music, University of California, Santa Barbara“From his long and successful experience as a composer and computer-music researcher, Gareth Loy knows what is challenging and what is important. That comprehensiveness makes Musimathics both exciting and enlightening. The book is crystal clear, so that even advanced issues appear simple. Musimathics will be essential for those who want to understand the scientific foundations of music, and for anyone wishing to create or process musical sounds with computers.”
—Jean-Claude Risset, Laboratoire de Mécanique et d'Acoustique, CNRS, France

"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.

Mathematics can be as effortless as humming a tune, if you know the tune, writes Gareth Loy. In

Gareth Loy is a musician and award-winning composer. He has published widely and, during a long and successful career at the cutting edge of multimedia computing, has worked as a researcher, lecturer, programmer, software architect, and digital systems engineer. He is President of Gareth, Inc., a provider of software engineering and consulting services internationally.