The Math Behind the Music (Outlooks) |  | Author: Leon Harkleroad
Publisher: Cambridge University Press
List Price: $26.99
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Seller: GLOBAL-BOOKS
Rating:  3 reviews
Sales Rank: 486276
Media: Paperback
Pages: 158
Number Of Items: 1
Shipping Weight (lbs): 0.8
Dimensions (in): 9 x 6 x 0.6
ISBN: 0521009359
Dewey Decimal Number: 510
EAN: 9780521009355
ASIN: 0521009359
Publication Date: August 7, 2006
Availability: Usually ships in 1-2 business days
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Product Description
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 Fouries 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.
Book Description
Mathematics has been used for centuries to describe, analyze, and create music. In this book, Leon Harkleroad explores the mathematics related to aspects of music from its acoustical bases to compositional techniques to music criticism. His clear, elementary exposition will be accessible to general readers as well as to mathematicians and musicians of all levels.
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| Customer Reviews:
 An amazing book that links math and music, which have a great deal in common September 8, 2008
Charles Ashbacher (Marion, Iowa United States(cashbacher@yahoo.com))
2 out of 2 found this review helpful
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.
 Good book April 28, 2007
K. Gandhi (Orange County, CA USA)
4 out of 12 found this review helpful
Has a lot of good math theory behind the numbers, and is not that difficult to read, assuming you've had a physics class. Very interesting in some parts, too.
Interesting and informative December 12, 2006
Dr. Lee D. Carlson (Baltimore, Maryland USA)
21 out of 22 found this review helpful
If one is familiar with the physics of sound, with its accompanying use of sophisticated mathematics, such as Fourier series, partial differential equations, and so on, it is not surprising to learn that some mathematicians have tried to give music theory a mathematical foundation. If one studies the historical record one will find that their efforts go back for centuries, and musicians have used their results to varying degrees of success. Philosophers of aesthetics have also attempted to find formal or mathematical theories of art, and in a few cases have completely embarrassed themselves in doing this, primarily because of their misunderstanding of the mathematics. Mathematics can be a powerful tool, and it continues its domination in science, technology, business, and industry, but it must be used where it is relevant, and not distorted to make it fit a particular scenario. This is not to say that a successful theory of mathematical aesthetics could not be developed. Indeed, it is belief of this reviewer that such a theory could be developed and would encompass music, art, and dance, and would add much to the appreciation of all these areas.
In general this short book gives a good overview of what is and has been done in the systematization and composition of music using mathematics. The author has given enough to wet the reader's appetite for more in-depth coverage by perusing the many references at the end of the book. The mathematics is kept at a very elementary level, making the book more accessible to a general readership (elementary group theory plays a central role). Therefore readers with a more sophisticated mathematical background may be disappointed. Musicians, both amateur and professional, would definitely gain an appreciation of just how mathematics can encapsulate musical compositions, and how indeed these compositions can be created using various mathematical constructions. The accompanying CD is of course helpful since it music must be heard in order to be fully appreciated. The book could also be of assistance to those who are interested in fully automated musical composition such as now being done in some research programs in artificial intelligence (some of this research is discussed briefly in the book). Of course, a machine that was able to use the same reasoning patterns to do mathematics as to compose music would signal a major advance in machine intelligence.
Although the book is not one on music theory, the author realizes the importance of understanding the elementary physics behind musical sounds, as well as the various tonal systems, such as the Pythagorean `circle of fifths'. He discusses these concepts early in the book, making it more self-contained. This is followed by a somewhat detailed overview of how to use group theory to create musical compositions. Towards the end of the book one finds an interesting application of L-systems to musical compositions. The book ends with the author's views on how various approaches to mathematical music have failed or have been too ad hoc to be useful.
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