PDF Ebook The Math Behind the Music (Outlooks), by Leon Harkleroad
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The Math Behind the Music (Outlooks), by Leon Harkleroad
PDF Ebook The Math Behind the Music (Outlooks), by Leon Harkleroad
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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.
- Sales Rank: #5146966 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2006-08-14
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .67" w x 5.98" l, .0 pounds
- Binding: Hardcover
- 158 pages
- Used Book in Good Condition
Review
"...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.The Math Behind the Musicdoes 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."
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.
"The book can be recommended as a first survey. Those who want to know more can find many suggestions for further study in the extensive bibliography. The book addresses readers who do not have much mathematical knowledge. Everything is explained clearly and at great length, and the theoretical facts are illustrated by many pictures, scores, and the tracks on the accompanying CD."
The Mathematical Intelligencer
"The material is very well presented and well explained, it comes with many (musical and mathematical) examples and illustrations (the book even comes with a CD-ROM from which the reader can listen to the musical examples of the book), and many details side aspects, anecdotes and references are provided."
Christian Krattenhaler, Mathematical Reviews
Most helpful customer reviews
30 of 32 people found the following review helpful.
Interesting and informative
By Dr. Lee D. Carlson
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.
1 of 1 people found the following review helpful.
While not as novel as I expected, there is ...
By Frank
While not as novel as I expected, there is more math involved, clearly explained and presented in appropriate scope and sequence.
5 of 15 people found the following review helpful.
Little insight into why music satisfies or communicates
By B. Bush
This well-written book summarizes topics in music theory that correspond to the mathematics and statistics used in engineering and finance.
What it does NOT do, disappointingly, is give much insight into why music communicates and captures emotions. For that, I believe, one must consider music to be a form of language -- different in different cultures, and heard through a filter of our cultural expectations. We enjoy music when it 'plays with' those expectations -- for example, setting up a simple rhythm and then syncopating, or repeating a melody with a twist at the end. The first book I've found that takes on these deeper issues is Aniruddh D Patel, _Music, Language, and the Brain_ (Oxford, 2008), which is far more technical. To be fair to Harkleroad, there are more unanswered questions than simple answers in this field. And Harkleroad does explain well why it's unsatisfying to listen to computer-generated 'white noise' music or to completely repetitive sound-patterns. So, a good book, but not an ear-opener.
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