The Math Behind the Music (Outlooks)

Features

• Cover Type: Hard Cover with 158 pages
• Published by: Cambridge University Press; Har/Cdr edition August 14, 2006
• Written in: English
• ISBN 10 Number: 0521810957
• ISBN 13 Number: 978-0521810951
• Book Dimensions: 9.2 x 6.2 x 0.7 inches
• Weighs: 15.2 ounces

Product Review
"The Math Behind the Music does not require advanced understanding of either mathematics or music: in fact most of the text could be easily understood by an interested high school student."
Math DL

"a text which relates music and mathematics in a manner accessible to many individuals, and provides a bibliography of further readings on each chapter's topics, so the best use of this book may be as a jumping-off point for further examinations of whichever topic interests and individual reader."
Sarah Boslaugh
MAA Reviews

"Leon Harkleroad has written a concise and accessible survey of some of the interesting mathematics of music, and he has done so in a way that requires a minimum of preparation on the reader's part in either music or mathematics."
Gareth Loy
Gareth, Inc.

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 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.

Reader Reviews
This review is from: The Math Behind the Music (Outlooks) (Paperback) 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. Comment | | (Report this)