Book Review – Quadrivium

Ratings

  • Writing: 5
  • Illustrations: 5
  • Math Level: 3
  • References: 4
  • Overall: 5

(For a detailed explanation of the rating system, see the end of the review.)

Review

Introduction

Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology (Wooden Books) may possibly be the most efficient little book I’ve ever purchased.  By this I mean that the amount of information, illustration, and insight packed into its 416 6″x7″ pages is mind blowing. Another in the series of Wooden Books (I previously reviewed Platonic and Archimedean Solids, another in this series), it is, in fact, an artful compilation of six (!) of their other books, each of which sell for a similar price. So, in a way, it’s like hitting a six-for-the-price-of-one sale!

About the Title

Quad-what?!  I’m sure most of you are wondering, as I did, what the word “quadrivium” means. The term arises from ancient Greece, and refers to four (“quad-“) areas of studies related to Number. The foreword of the book explains this better than I can:

The Quadrivium arises out of the most revered of all subjects available to the human mind – Number. The first of these disciplines we call Arithmetic, the second is Geometry or the order of space as Number in Space, the third is Harmony which for Plato meant Number in Time, and the fourth is Astronomy, or Number in Space and Time.

This is a fascinating way of conceiving of these areas of study. What this book does is to assemble six other Wooden Books that together cover these four areas in great detail (geometry and music are each covered in two books, hence six books instead of four!).

Walkthrough

There is so much information in this book that a complete walkthrough would take many, many paragraphs.  Instead, let me walk you through it by listing the six “sub-books” and a little description of what each one covers.

[NOTE: All images below are courtesy of and © Wooden Books.]

Book I: Sacred Number (Miranda Lundy)

This book discusses the study of numbers as it has evolved in many cultures over many centuries. In essence, it approaches numbers from a philosophical or mystical point of view, musing on what each number represents, symbolizes, or embodies in the larger world. For example: one = unity, two = duality and opposites, three = the trinity, four = the elements (air, fire, water, earth), etc. Although very different from our modern “scientific” view of numbers, it offers a rich, beautiful, and intriguing exploration of the world of numbers.

Book II: Sacred Geometry (Miranda Lundy)

This book “charts the unfolding of number in space” as the introduction puts it. Starting from basic concepts of point, line, vertex, circle, and so on, it works up through arrangements of circles, then three dimensional solids and regular tesselations, all the time relating these back to their “sacred” connotations throughout history, as well as their use in the designs of church windows, sacred stone circles, Celtic spirals, Islamic tilings, etc.

Book III: Platonic & Archimedean Solids (Daud Sutton)

This book (the second “geometry” book) is a thorough tour of these groups of solids. See the full review here for more details.

 

 

Book IV: Harmonograph (Anthony Ashton)

This book is aptly subtitled “A Visual Guide to the Mathematics of Music.” In particular, the vast majority of the book features beautiful spiral-like pictures (think Spirograph) representing different musical intervals as drawn by a device called (you guessed it!) a harmonograph. The illustrations here are utterly captivating, and for the truly ambitious, there are even instructions on how to build a harmonograph of your own!

Book V: The Elements of Music (Jason Martineau)

This book (the second “music” book) is a comprehensive overview of the fundamental elements of musical structure – melody, harmony, and rhythm – with a special emphasis on the mathematical underpinnings of each of these elements. As usual for Wooden, it covers a remarkable amount of territory in a short space, including scales and modes, overtones and timbre, construction of melody and chord progressions.

Book VI: A Little Book of Coincidence (John Martineau)

This book discussed astronomy, but from a very particular and atypical point of view.  Rather than the usual litany of  information about the science behind the formation of planets and stars, this book focuses almost exclusively on the “music of the spheres” or, in other words, the many fascinating mathematical relationships between the timing and distances of the various planets’ and moons’ orbits, diameters, and the like. The more of these “little coincidences” the author relates, the more you wonder whether something more fundamental is really hidden in all the numbers…

Highlights

As with every Wooden Book I’ve ever picked up, I’d have to give the nod to the plentiful and wonderful illustrations.  Part of how they are able to pack so much information into these little gems is by including beautiful, information-rich illustrations on (literally) every other page of the book.  You could not read a single word and still have a wonderful time and glean a lot of what the books have to say!

Conclusion

Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology (Wooden Books) is an incredible treasure trove of information on these four ancient areas of study, packed into an incredibly compact book for an incredibly reasonable price. I can’t recommend it highly enough for anyone interested in these areas and their interrelationships.

Feedback

Please let me know what you think about this review – the rating scales, the format, the content, anything!  I want to make sure these reviews are as useful and informative as possible, and only you can help me do that! Thanks. :-)

Rating Format

To keep things consistent, I have decided to give each book I review a rating from 1-5 stars on each of several scales, pertaining to their usefulness and desirability for the library of someone interested in geometric art. Here are the rating scales I will be using:

  • Clarity of Writing: Is it easy to understand? [1 = Poorly written, 5 = Excellently written]
  • Quality of Illustrations: Is it beautiful to look at? [1 = Few/boring/monochrome illustrations, 5 = Many/beautiful/color illustrations]
  • Math Level: Is a lot of prior math knowledge needed? [1 = Basic/high school level, 5 = Very Advanced/Graduate level]
  • Depth of References: Are there references to other interesting sources? [1 = None, 5 = Many]
  • Overall Rating: How would I rate the book overall? [1 = Skip It, 5 = Must Have]

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About Phil Webster

Phil is the creator of GeometricArts.com. You can reach him on the Contact page.
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