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Musimathics: 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 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.
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.
482 pages, Hardcover
First published June 16, 2006
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Displaying 1 - 12 of 12 reviews
March 31, 2021
This book is so good. If you're like me, science/math-inclined and musically inspired, but kind of frustrated by arbitrary and seemingly unprincipled rules of music theory, this book is sooo for you.
Get it. You'll get it.
Get it. You'll get it.
August 23, 2011
I started reading this book because I was hoping that I could leverage my mathematics background to learn some music theory. The author does a decent job bringing together information on a very large topic. The writing is casual, and the author builds up both music theory and mathematical theory so that the writing is accessible to most. Being that I have a fairly deep understanding of mathematics, I found most of explanations of mathematics to be a waste of time but if you are reading this book coming from a music background these explanations would probably be very useful.
My main problem with the book is that the flow of the book is not consistent. Numerous times the author uses terms to explain them later in the book, and often the jumps between chapters leave one wondering where the book is going.
This book is a very dense read. It is probably closer to a textbook than a casual exploration of the marriage of mathematics and music.
My main problem with the book is that the flow of the book is not consistent. Numerous times the author uses terms to explain them later in the book, and often the jumps between chapters leave one wondering where the book is going.
This book is a very dense read. It is probably closer to a textbook than a casual exploration of the marriage of mathematics and music.
October 27, 2024
Rating: 4.25/5
To read this book is to be confronted with the idea that music—and therefore mathematics—isn’t something we created, but something we’ve encountered, discovered within the nature of being. It’s an attempt to strip back the veneer of perception and peer into the mechanics, the anatomy, if you will, of reality itself.
Loy reveals it as an emergent phenomenon, governed by the mathematical laws that bind reality together in all its complexity. He covers Fourier transforms, wave theory, and digital synthesis with an intellectual fervor that borders on the obsessive. But the rigor here is not incidental. Loy demands that you grapple with it, that you meet it on its own terms, stripped of any notion of simplification.
Loy’s journey through the mathematics of sound is relentless. It’s dense. And in that density, there is a kind of truth—a recognition that reality, at its core, resists simplification. You may find yourself wrestling with concepts that feel nearly impenetrable. Loy seems to suggest that if you cannot confront the math, then perhaps you are not prepared to truly confront music itself.
It’s not only the technical rigor that strikes me about Musimathics. Loy points toward something transcendent. He offers music as a bridge between the chaos of perception and the order of mathematical structure—a Daoist interplay between the known and the unknown. Loy’s work becomes an invitation to recognize that music, like all ordered phenomena, has a sacred element. It’s a reminder of the fragile balance between chaos and order, where meaning itself is generated. Here, Loy draws on something ancient, something rooted in the deepest traditions of understanding—he’s presenting music as a representation of the sacred, as an encounter with the infinite, structured by the finite.
For those who accept its demands, Musimathics will confront you. Not an easy read—it will demand engagement. It will challenge you to step beyond mere enjoyment of music and consider its place within the fabric of reality itself.
To read this book is to be confronted with the idea that music—and therefore mathematics—isn’t something we created, but something we’ve encountered, discovered within the nature of being. It’s an attempt to strip back the veneer of perception and peer into the mechanics, the anatomy, if you will, of reality itself.
Loy reveals it as an emergent phenomenon, governed by the mathematical laws that bind reality together in all its complexity. He covers Fourier transforms, wave theory, and digital synthesis with an intellectual fervor that borders on the obsessive. But the rigor here is not incidental. Loy demands that you grapple with it, that you meet it on its own terms, stripped of any notion of simplification.
Loy’s journey through the mathematics of sound is relentless. It’s dense. And in that density, there is a kind of truth—a recognition that reality, at its core, resists simplification. You may find yourself wrestling with concepts that feel nearly impenetrable. Loy seems to suggest that if you cannot confront the math, then perhaps you are not prepared to truly confront music itself.
It’s not only the technical rigor that strikes me about Musimathics. Loy points toward something transcendent. He offers music as a bridge between the chaos of perception and the order of mathematical structure—a Daoist interplay between the known and the unknown. Loy’s work becomes an invitation to recognize that music, like all ordered phenomena, has a sacred element. It’s a reminder of the fragile balance between chaos and order, where meaning itself is generated. Here, Loy draws on something ancient, something rooted in the deepest traditions of understanding—he’s presenting music as a representation of the sacred, as an encounter with the infinite, structured by the finite.
For those who accept its demands, Musimathics will confront you. Not an easy read—it will demand engagement. It will challenge you to step beyond mere enjoyment of music and consider its place within the fabric of reality itself.
August 12, 2019
Picked this up and then got sidetracked. Picked it up a couple years later and went through it quickly - very interesting read. Music making dissected from a bunch of different angles. Highlights
- the history of tuning (and its parallels with science) and alternate tunings/microtunings
- quantifications of human perception
- we identify the direction of sound by the way our ear EQs things
- a lot of how an instrument makes sound is the way it transfers energy
- open pipes have different nodes than closed pipes, because of the energy reflection/refraction
- experimental music is not science, since there is no hypothesis to prove
- the history of tuning (and its parallels with science) and alternate tunings/microtunings
- quantifications of human perception
- we identify the direction of sound by the way our ear EQs things
- a lot of how an instrument makes sound is the way it transfers energy
- open pipes have different nodes than closed pipes, because of the energy reflection/refraction
- experimental music is not science, since there is no hypothesis to prove
December 1, 2023
A useful and rather comprehensive overview of various topics connecting music to mathematics and physics. The writing is somewhat awkward and verbose at times, especially the mathematical equations which, in an attempt to be accessible, often avoid using standard formulations/techniques and terminology (like calculus). Nevertheless, the book serves as a useful overview to be supplemented by other texts, such as "Music: A Mathematical Offering" by Dave Benson, which goes into more detail and rigor.
June 17, 2017
If you want to program (or build) synthesizers from scratch, but have massive gaps in your physics, the chapters "Physical Basis of Sound", "Geometrical Basis of Sound", "Introduction to Acoustics" and "Vibrating Systems" could be particularly handy.
Porting parts of chapter 9, "Composition and Methodology" to Ruby and Max/MSP was fun.
There are Suggested Reading sections are the end of most chapters, too!
Porting parts of chapter 9, "Composition and Methodology" to Ruby and Max/MSP was fun.
There are Suggested Reading sections are the end of most chapters, too!
April 20, 2022
overall pretty good. would give 4 or 4.5/5.
March 22, 2013
The first volume of this book is a survey of cherry picked topics in music and math as it relates to music.
There were a lot of errors in the musical notation, which makes me wonder how much of the math and physics have errors. I was not paying close attention to any of the equations. The second volume looks more practical for actually implementing audio algorithms.
The author spends too long on his algorithmic composition chapter at the end. It's like 1/3 of the entire book.
Problems aside, this book is cool because there isn't another book that compiles all this info into one volume.
There were a lot of errors in the musical notation, which makes me wonder how much of the math and physics have errors. I was not paying close attention to any of the equations. The second volume looks more practical for actually implementing audio algorithms.
The author spends too long on his algorithmic composition chapter at the end. It's like 1/3 of the entire book.
Problems aside, this book is cool because there isn't another book that compiles all this info into one volume.
May 6, 2014
This book brought together a great number of threads that I had discovered for myself in a more cohesive way. The math and the physics behind our perception of music has allowed me to approach composition in a completely different way.
June 15, 2015
This book was awesome. Topically, it was exactly what I was looking for, but the math was a little beyond me. But at least it gave me a better sense of what it means when someone says, "Music is so mathematical." I'd love to take a class on this.
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December 15, 2015the big source
Displaying 1 - 12 of 12 reviews