- Hardcover: 426 pages
- Publisher: Cambridge University Press; 1 edition (December 11, 2006)
- Language: English
- ISBN-10: 0521853877
- ISBN-13: 978-0521853873
- Product Dimensions: 6.8 x 1 x 9.7 inches
- Shipping Weight: 2 pounds (View shipping rates and policies)
- Average Customer Review: 5 customer reviews
- Amazon Best Sellers Rank: #5,481,817 in Books (See Top 100 in Books)
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Music: A Mathematical Offering 1st Edition
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"Perhaps our children will one day remark on the group symmetries in their favorite music in the way that we now simply note a beautiful tune. They, no less than we, will have much to learn from this delightful book, which sets a new standard of excellence and inclusiveness. Anyone who knows some college-level mathematics and is curious about how it can illuminate music will be richly rewarded by reading Benson's outstanding book."
Peter Pesic, Tutor and Musician-in-Residence at St. John's College, Santa Fe
"... A precise selection of solutions..."
Luigi Carlo Berselli, Mathematical Reviews
"... an excellent introduction to the interdisciplinary subject of music and mathematics (which also involves physics, biology, psycho-acoustics, and the history of science and digital technology). The book can easily be used as the text for undergraduate courses."
The Mathematical Intelligencer
Benson provides a wealth of information for the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the interplay between two ancient disciplines. A must-have book if you want to know about the music of the spheres or digital music and much in between.
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Chapter 4 is where the theory of consonance and dissonance is discussed along with the simple integer ratios of frequencies. Consonance and dissonance are musical terms describing whether combinations of notes sound good together or not. This is a preparation for the discussion of scales and temperaments in Chapters 5 and 6. The emphasis in these two chapters is on the relationship between rational numbers and musical intervals. The fundamental question here is "Why does the modern western scale consist of 12 equally spaced notes to an octave?" Has it always been this way? Are there other possibilities? After the discussion of scales, the book breaks off of its main thread to consider a couple of other subjects where mathematics is involved in music, the first being computers and digital music. Chapter 7 discusses how to represent sound and music as a sequence of zeroes and ones, and again Fourier theory is used to understand the result. Also described is the closely related Z-transform for representing digital sounds, and this is then used to discuss signal processing, both as a method of manipulating sounds and producing them. This leads to a discussion of digital synthesizers in Chapter 8, where we are again confronted with the questionof what it is that makes musical instruments sound the way that they do. The discussion is based around FM synthesis. Although this is an old-fashioned method of sound synthesis, it is simple enough to understand many of the salient features before taking on more complex synthesis methods.
Chapter 9 changes the subject completely and examines the role of symmetry in music. The area of mathematics concerned with symmetry is group theory, and the reader is introduced to some of the elementary ideas from group theory that can be applied to music. The book contains numerous exercises, and the answers to almost all of them are included in the book. It should be noted that the author assumes the reader can read music, as this subject is not approached with the exception of a few entries in the appendices. Thus this book is more of mathematics for musicians rather than vice versa. There is an online version of the book available if you want to browse it before deciding to buy. To me, this is one of the clearest books on the relationship of mathematics to music I have read. The text is accessible and clear, there is a good use of graphics, and the exercises emphasize the understanding of the mathematics presented. I highly recommend it.
I bought the kindle version so feel slightly ripped off! (minus 1/2 star) The kindle version also does not have the answers to the questions at the end of the chapters, so I had to download the free version anyway. (minus another 1/2 star)
The content is good and well written, so hopefully some of the $40 I spent on the kindle version will find it's way back to the author.
Despite all this, I do propose that there needs to be a more elementary treatment of much of this material for those who have not taken major coursework in college-level mathematics. Thus, Benson has left a niche for others, less gifted, to fill.