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Description
The Math Behind the Music [With CDROM]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
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.Binding Type: Paperback
Publisher: Cambridge University Press
Published: 08/01/2006
ISBN: 9780521009355
Pages: 143
Weight: 0.75lbs
Size: 9.00h x 6.00w x 0.40d
Review Citations: Univ PR Books for Public Libry 01/01/2007 pg. 1 - Strongly Recommended
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★★★★★ 5
Dogs love these!
Pros: keeps the dog entertained both solo and tug of war.
Super entertaing to watch the dog beat itself half to death with a big grin on it face.
Cons: dog will beat everything else to death too. You're basically giving your dog a wrecking ball. Similar to giving rubber nunchucks to a hyper 8yr old kid.
If you dont own much nice stuff or you keep it all out of reach you should be fine.
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Reviewed in the United States on November 1, 2023
★★★★★ 1
Worst Toy Ever
Rope broke in one use of tug a war with my dog and I. It literally pulled apart, didn't even last 5 minutes. Not a strong toy at all.
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Reviewed in the United States on February 7, 2026
★★★★★ 5
Small
A little small but my dog loved them. Does not hold up to a shredder though. Perfect for typical toy lovers
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Reviewed in the United States on January 18, 2026
★★★★★ 5
Well made, sturdy toys
Color: 3 Pack Donkey Goat Dog
So cute! Sturdy too, great for tugs of war.
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Reviewed in the United States on May 8, 2026
★★★★★ 5
None of the stuffing pulled out
I have 3 dogs. 1 is very gentle w/ stuffed toys. 1 is new to us and very anxious and kept stealing things like water bottles to gnaw on. And 1 destroys every stuffed toy we have ever brought into the house. We bought these for the anxious one. She was recently adopted and very people shy and afraid of the world around her. She doesn't know how to play with people and she's terrified if you try to throw a ball or if you squeak a squeaker, but we also needed something durable enough for her chewing that would be safe for her and could also withstand the toy destroyer possibly getting hold of it. They've been playing with these for a few months now and the most damage is that some of the rope necks are a bit frayed and a lot of the fuzz on the outside is gone, but none of them have been torn open. And the squeakers are in there in a way that it's hard to make them squeak if not doing so intentionally. The 1 dog can have plush toys again, the 1 dog can gnaw and chew to reduce her anxiety and the 3rd can chew and attack it without me having to clean up stuffing all the time
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Reviewed in the United States on August 6, 2022