Harmonograph: A Visual Guide to the Mathematics of Music. by Anthony Ashton

I didn't know what quite to expect with this book; I wasn't familiar with the term "harmonograph" before getting this text. This is a small book with about 25 topics, each discussed on 1 or 2 pages. It links together many concepts from our past (including the 19th century harmonograph) and the mathematics underneath them. This is one book which satisfyingly explains the concept of an even-tempered scale -- something I had been pondering for a long time. You could say this book is a group of different stories about the vibrations in music, and the relationship between those vibrations. Vibrations are important for us to understand: our bones float; our bodies are springy and resilient. The math and physics of vibrations -- scientists call it "simple harmonic motion" -- can get rather tricky. Most of use stop our math classes before they get to this point. On the other hand, there are many topics in this field that are understandable without all of those complicated scribbles; this book lovingly explores many of them. My main gripe is that there are few links for the DIY types to go try this stuff hands-on. There must be some websites which have virtual harmonographs; the author should have found these. And it's a darn shame that so few of these machines are around. I make it a point of seeing lots of science museums; I've never seen a harmonograph. We forget how many wonderful things before we had computers. Things like the harmonograph have a delightful physicality; that's something we've lost in our "modern" society. I highly recommend this book to a young high-school student. There are hidden delights in the drawings and historical references. For such a small book, there is a surprising depth of detail. I can't wait to explore the rest of this series.

I found this book to be extremely helpful. I'm a music teacher and have been interested in the physics of music for years, but I've never seen the physics of frequency explained so clearly and concisely. I'm really impressed with how well the Pythagorean Comma was handled. This book, in a format where chapters are almost always one page long, gets into some pretty difficult concepts and explains them better than I thought possible. This is the book I loan high school kids who are thinking about doing a science project with music. They love it.

This is a great book - not only is it absolutely beautiful, but it actually does the job. After years of struggling with Pythagorean Commas and Syntonic Commas and all the other tricky little bits in music I was given a copy of Anthony Ashton's little book and the pieces finally fell into place. A simply delightful book with truly awesome images and clear concise mathematics. I have given copies to every musician friend I have and they all love it too. Well done Wooden Books - clarity, brevity and beauty combined. More please.

This is an excellent little book on harmonics and sound, encompassing science and music. It is a much needed counter weight to the effervessence of other recent titles on temperament and harmonics. It is such a beautifully visual book, with graphic depictions of sound waves, you will simply want to look at the illustrations for hours. It hints at the mystical without falling off the edge into either New Age or Cultural Supremacy.

I discovered the the Wooden Books series less than a year ago through some serendipitous bookstore browsing, and soon purchased them all. Each volume is compact, well-written, beautifully illustrated, and most of all informative. I'm reading my copy of Harmonograph along with Stuart Isacoff's book Temperament (also recommended), and couldn't imagine a more perfect pairing of books. Being musically challenged, I rely on Harmonograph to make better sense of the intervals Isacoff discusses in his book, and it does so in a brilliant, unique way. You won't be disappointed in this little gem.