Harmonograph: A Visual Guide to the Mathematics of Music

Wooden Books

by Anthony Ashton

Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this magical subject. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Genres: Music, Mathematics, Science, Nonfiction, Art, Reference, Design

64 pages, Paperback

First published May 1, 1999

Reviews

[Qonita]

Welp i didn't understand that one bit HAHAHA. But i enjoyed the pictures (bukunya satu halaman tulisan satu halaman gambar gitu so there's a lot) and who knows that when translated to graphs, music has such an outstanding organization to them. Pretty cool and adds nuance to the world. The technical rambling is an otherworldly total nonsense for me it sounds poetic lmao. I had an episode of crying under the overtones too (tmi) so this book is not without some sentimental value. The production's super pretty so i'm so collecting this series in the future. 3.5/5

[Einsamkeit]

I couldn't imagine of reading a book like this before, but I don't regret about have done it.

This book is about how the harmonograph showed beautiful music patterns. As a music teacher I was teaching my students about the relationship between Music, Science, Arts and Language and after reading this book I felt a little more interested about the topic and I would like my students could read the book as well.

It was so catching how it introduces the evolution of simple harmonic theory.

Now I must mention the beautiful drawings you find in its pages. It's a definitely WOW! 🤯

And at the end it describes how to build a harmonograph. 🤩

This book is highly recommended for those who are musicians, artists, mathematicians, designers, or even all people who feels really attracted by this beautiful instrument. 😌

[Aris S.]

3,5/5*

[Deana]

This was a really cool book. My mom gave it to me many years ago, and I just not got around to reading it. Basically, it's about this really cool machine called the "harmonograph". If you've ever heard of tuning forks, this will make sense to you. If not, go here. So, a long time ago, someone set up two tuning forks at right angles to one another some distance apart. Using mirrors, a light was shone at one tuning fork, bounced off toward the second, and then finally the light bounced off that one and onto a dark surface. Very pretty and interesting patterns emerged when both tuning forks were set into motion, and of course different patterns emerged depending on the ratios of the vibrations.

These movements were too small and too fast for someone to record, so the harmonograph was invented. It uses the same principles except it uses pendulums swinging at different ratios to simulate the movements of the tuning forks. Pendulums can be made to swing in much longer and slower motions than tuning forks. By attaching pens and paper to the pendulums, beautiful patterns could be drawn tracing out their travels. Check out the cover of the book for one example, although trust me - the others are far more beautiful and intricate than that one.

[Mafalda]

didn't understand anything but the images were pretty

[Rev. Christopher Arnold]

Harmonograph is far more than a book about music. Anthony Ashton reveals that harmony is not merely something we hear, but something woven into the fabric of creation itself. As the Psalmist writes, "The heavens declare the glory of God" (Psalm 19:1), and this book illustrates how mathematics, sound, and form echo that same order. Claude Debussy observed that "Music is the arithmetic of sounds as optics is the geometry of light," while Pythagoras saw the cosmos itself as governed by harmony. In an age captivated by algorithms and artificial intelligence, Harmonograph reminds us that the deepest patterns are timeless, inviting us to listen not only with our ears, but with our minds and spirits. Small in size, yet profound in its vision of a universe ordered by beauty, proportion, and meaning.

[Dan Becker]

Writing this review a couple months after finishing this brief, but information-rich book, as I keep thinking about the concepts it illustrated.

The book serves as visual evidence and visual explanation of how music's physical manifestation is mathematical. I appreciate the author's determination and success at documenting the strange, and strangely informative, harmonograph.

I found the images themselves harmonograph produces attractive in the same sort of formal way that the engineered geometry of a suspension bridge or railway station can be - as an illustration of physical forces in the structure made to carry them. I wouldn't want a tattoo of one, but I could see them being used as architectural motifs at a concert hall.

[Praveen Sinha]

A lovely collection of methods and techniques used in early days or in other words were discovered by observing the musical harmony and notes. The illustrations illustrate the beauty of the numbers and patterns and ease with which we can find them around us via different media.

[Matthew Bird]

Pleasant read with beautiful illustrations. A little more time spent on the basics of music theory and its connection to frequencies and harmonics would have been appreciated as ratios were being thrown about all over the text with minimal introduction.

[Ineke]

I think it just needed an extra page or two at the front explaining the ratio stuff that most of the book then used. If I'd understood that I think I'd have really enjoyed it all, as it was, I enjoyed bits, but definitely felt like it was too clever for me.

[Len]

Great book, but could have used more detailed construction pictures and plans.

[Joseph Young]

Spirograph, the book. A neat visual guide to various harmonies, with assorted mathematics. History of how these rhythmic machines work and are built, and instructions on how to build them included.

[Carys]

3.5 🌟 Super interesting, even if do I have very little knowledge of music theory!

[Adi]

A fun, quick read on topics including the Chladni patterns and kaleidophones. I found it a little difficult to follow terms from Western music systems.

[Andy]

So informative and inspiring.

[G Garland]

fun pictures, lots of words and numbers
brain goes brrr i wish i was intelligent enough to understand everything

[Steve]

Brilliant

[Alexis Reyna]

very interesting and beautiful diagrams.

[Rohan Jha]

Visual music

[Emory]

Fascinating read, despite grammatical errors and some other minor inaccuracies

[Kirsty Park]

This is a really beautiful little book. Looking at the diagrams (of which there's plenty) and realising how these patterns and shapes are created by musical sounds left me amazed.

It is pretty heavy on the music theory though. If you're not quick at discerning between your major thirds or minor sevenths then it might feel a bit dense if you're reading all in one go.

It is very short too, so I'm not including it in my reading challenge.

[Scott]

This is a cool little book that discusses and illustrates relationships between music and mathematics. Like all of the Wooden Books, it's brief.

[Matt Webb]

I still don't understand how ratios between vibrations lead to different tones, but I have now spent a good deal of time making Chladni patterns. A happy discovery in the Wellcome bookshop.

[Maxwell]

! ! !

[Snufkin]

Very beautiful