What do you think?
Rate this book
The Math Behind the Music
Mathematics has been used for centuries to describe, analyze, and create music. In this book, Leon Harkleroad explores the math related aspects of music from its acoustical bases to compositional techniques to music criticism, touching on • overtones, scales, and tuning systems • the musical dice game attributed to Mozart and Haydn • the several-hundred-year-old style of bell-playing known as ringing the changes • the twelve-tone school of composition that strongly influenced music throughout the 20th century and many other topics involving mathematical ideas from probability theory to Fourier series to group theory. He also relates some cautionary tales of misguided attempts to mix music and mathematics. Both the mathematical and the musical concepts are described in an elementary way, making the book accessible to general readers as well as to mathematicians and musicians of all levels. The book is accompanied by an audio CD of musical examples.
158 pages, Paperback
First published May 1, 2006
5 people are currently reading
79 people want to read
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 6 of 6 reviews
August 18, 2015
Ever since I took classic guitar lessons about 20 years ago, I've been very curious about how music works. The Math Behind the Music does an excellent job of explaining this, helped immensely by the CD that accompanies the book.
Now I know more but: It is So Complicated that I don't think I will study this very much further.
If there is such a thing as a mathematical composer, then Bach, Beethoven and Mozart must be the highest of all practitioners. They fully understood all this; I do not and will not. Lucky for me, all I have to do is put on a CD, listen to what they did, and then I'm happy.
Now I know more but: It is So Complicated that I don't think I will study this very much further.
If there is such a thing as a mathematical composer, then Bach, Beethoven and Mozart must be the highest of all practitioners. They fully understood all this; I do not and will not. Lucky for me, all I have to do is put on a CD, listen to what they did, and then I'm happy.
May 31, 2017
Interesting chapter on campanology.
May 8, 2025
informative, concise, and endlessly expanding.
September 15, 2015
An amazing book that links math and music, which have a great deal in common
It is no coincidence that the three areas of human endeavor where there are child prodigies are mathematics, music and chess. Success in each requires a similar form of mental reasoning, with music and mathematics being the two that are most related.
Harkleroad has written an amazing book, after the base introduction in chapter one, chapter two covers the concept of pitch, in other words the fundamentals of how sounds are different. Chapter three then uses this idea to describe how different sounds can either clash or reinforce each other. In chapter four, you learn how to vary a theme mathematically; it is here where group and subgroup operations are used to alter tunes to make new ones that still sound pleasing. Chapter five covers bell-ringing, where groups and their cosets are used to describe the permutations in the order of bell-ringing. Creating music by using random processes is the topic of chapter six, while it seems odd to think of random processes creating noise having a pleasing structure; some composers have been able to do it. Chapter seven deals with some of the patterns found in music, chapter eight, which is called “Sight Meets Sound”, starts with an explanation of “millimetrization.” This is the process where the rises and falls of a tune are used to trace out a graph and vice-versa. Composer Heitor Villa-Lobos used photographs of scenes such as mountains and skylines to construct the graph, from which he would compose his music. The ninth and last chapter has the title “How Not to Mix Mathematics and Music.” In it, attempts to do things like using numeric sequences such as the Fibonacci numbers to compose music are explored and the reasons why they failed explained. A CD containing the musical pieces referenced in the text is included with the book.
Although I played the saxophone in elementary school and am a regular attendee at the local symphony, I make no claim to being knowledgeable in music. Yet, I was able to read and follow this entire book and truly came away with an appreciation for how mathematics can be used to explain the structure of musical pieces.
This review also appears on Amazon
It is no coincidence that the three areas of human endeavor where there are child prodigies are mathematics, music and chess. Success in each requires a similar form of mental reasoning, with music and mathematics being the two that are most related.
Harkleroad has written an amazing book, after the base introduction in chapter one, chapter two covers the concept of pitch, in other words the fundamentals of how sounds are different. Chapter three then uses this idea to describe how different sounds can either clash or reinforce each other. In chapter four, you learn how to vary a theme mathematically; it is here where group and subgroup operations are used to alter tunes to make new ones that still sound pleasing. Chapter five covers bell-ringing, where groups and their cosets are used to describe the permutations in the order of bell-ringing. Creating music by using random processes is the topic of chapter six, while it seems odd to think of random processes creating noise having a pleasing structure; some composers have been able to do it. Chapter seven deals with some of the patterns found in music, chapter eight, which is called “Sight Meets Sound”, starts with an explanation of “millimetrization.” This is the process where the rises and falls of a tune are used to trace out a graph and vice-versa. Composer Heitor Villa-Lobos used photographs of scenes such as mountains and skylines to construct the graph, from which he would compose his music. The ninth and last chapter has the title “How Not to Mix Mathematics and Music.” In it, attempts to do things like using numeric sequences such as the Fibonacci numbers to compose music are explored and the reasons why they failed explained. A CD containing the musical pieces referenced in the text is included with the book.
Although I played the saxophone in elementary school and am a regular attendee at the local symphony, I make no claim to being knowledgeable in music. Yet, I was able to read and follow this entire book and truly came away with an appreciation for how mathematics can be used to explain the structure of musical pieces.
This review also appears on Amazon
August 18, 2017
This is one of my favourite books ever. I have loved it. The typesetting is beautiful, it is very well written and its content is accessible both for mathematicians with little knowledge of music and for musicians with little knowledge of mathematics. Everything is very clearly explained, the maths are introduced with easy examples (even for abstract topics as group theory).
This book illustrates one of my favourite quotes:
"A good attitude to the preparation of written mathematical exposition is to pretend that it is spoken. Pretend that you are explaining the subject to a friend on a long walk in the woods, with no paper available; fall back on symbolism only when it is really necessary." (Paul Halmos)
If you are a mathematician curious about music, or a musician curious about mathematics, this book is for you.
This book illustrates one of my favourite quotes:
"A good attitude to the preparation of written mathematical exposition is to pretend that it is spoken. Pretend that you are explaining the subject to a friend on a long walk in the woods, with no paper available; fall back on symbolism only when it is really necessary." (Paul Halmos)
If you are a mathematician curious about music, or a musician curious about mathematics, this book is for you.
August 29, 2014
Main sections:
- pitch
- tuning
- how to vary a theme mathematically
- bells and groups
- music by chance
- patterns
- sight meets sound
- how not to mix mathematics and music
The last chapter had an interesting discussion on how various people have tried to find Fibonacci series in various compositions, with unconvincing results. Mentions Richard Guy's paper "The Strong Law of Small Numbers", pointing out that "there aren't enough small numbers to meet the many demands made of them". The upshot is that if you find Fibonacci sequences, it is likely a coincidence unless there is an underlying reason for their presence.
- pitch
- tuning
- how to vary a theme mathematically
- bells and groups
- music by chance
- patterns
- sight meets sound
- how not to mix mathematics and music
The last chapter had an interesting discussion on how various people have tried to find Fibonacci series in various compositions, with unconvincing results. Mentions Richard Guy's paper "The Strong Law of Small Numbers", pointing out that "there aren't enough small numbers to meet the many demands made of them". The upshot is that if you find Fibonacci sequences, it is likely a coincidence unless there is an underlying reason for their presence.
Displaying 1 - 6 of 6 reviews