The Mathematical Foundations of Music
Volume I: Musical Elements
Volume II: Musical Signals
by Dr. Gareth Loy
There is a PDF version of Musimathics floating around the web. If you see these PDFs posted, please let me know so I can post a take-down request to the website owner. It took me ten years to write these books, working late into the night most days to get it published. I also respond to readers questions and errata notices. Please don't post the PDF version on the open internet; please either buy the paper books or buy the ebook, but don't just rip me off. You can reach me at errata > a t < musimathics.com if you have questions or concerns.
Reprint editions are now available for both volumes that correct (almost) all errata from the first printings. You can tell which print version you have by looking at the numbers at the bottom of the copyright page, which count down from 10. If the series stops at 1, you have the original printing. If the series stops with 2, you have the second printing, etc.
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Educators: follow this link to Request Exam/Desk Copy of Musimathics.
"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.
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, digital systems engineer, expert witness, and generally as a provider of software engineering and consulting services internationally.
You can visit my professional home page at
You can visit my personal home page at http://www.GarethLoy.com.
"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