The quadrivium-the classical curriculum-comprises the four liberal arts of number, geometry, music, and cosmology. It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and cosmology expresses number in space and time. Number, music, and geometry are metaphysical life across the universe investigates them; they foreshadow the physical sciences.
Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series- Sacred Geometry , Sacred Number , Harmonograph , The Elements of Music , Platonic & Archimedean Solids , and A Little Book of Coincidence -it makes ancient wisdom and its astonishing interconnectedness accessible to us today.
Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.
Wooden Books was founded in 1999 by designer John Martineau near Hay-on-Wye. The aim was to produce a beautiful series of recycled books based on the classical philosophies, arts and sciences. Using the Beatrix Potter formula of text facing picture pages, and old-styles fonts, along with hand-drawn illustrations and 19th century engravings, the books are designed not to date. Small but stuffed with information. Eco friendly and educational. Big ideas in a tiny space. There are over 1,000,000 Wooden Books now in print worldwide and growing.
Fascinating. Shows an extraordinary and intriguing beauty and order in the universe. Why, for instance, do musical harmonic intervals show up in planetary orbits? Or why the number of leaves on many species of growing plants can be predicted by one simple sequence of numbers? The universe doesn't appear to be so random. Recommended for artists who don't get science and scientists who don't get art.
This was a lot of fun. I would have given it five stars if it hadn't been for the New Agey stuff that popped in from time to time. But at the same time, this book provided a wealth of information about the world we live in.
I was both fascinated and frustrated by this book. I found much of it interesting, but each topic went from simple to complex quickly, and I needed to read it more slowly to absorb more. The book is has written explanations on the left-side page and illustrations on the right. Often, the illustrations would've been easier to make out if they'd been printed on larger paper: sometimes the captions were too small for me to read even with reading glasses on. But if the point was to pique my curiosity about the Quadrivium, it succeeded: I'd love to understand this better.
Among my collection of books sits “Quadrivium,” so far more of a curiosity than a tome I refer to with endearment. Like the two books on topology, this volume is something I approach with trepidation, the hope of totally understanding its content long since dashed. It’s like trying to understand a cloud- hard to visualize or quantify, yet there, all the same, challenging me to understand much more than its function or existence. And even that is tough sledding.
The easiest place to start is with a description of the form and format. The title is followed by a subtitle: “The Four Classical Liberal Arts of Number, Geometry, Music, and Cosmology,” which pretty much sums up the content. Published by Walker & Company, the 410-page book measures 6” wide by 7.5” tall and 1.5” thick.
“Quadrivium” is part of a series called “Wooden Books.” (Apparently, there are two other books in the series: “Trivium” (covering Grammar, Logic, and Rhetoric), and “Sciencia” (Mathematics, Physics, Chemistry, Biology, and Astronomy.)
Judging by stiff nature of the Quad’s 3/16”-thick cover, it could very well be made of some wood product. But an online search reveals nothing about “Quad’s” construction. Notes opposite the title page do an admirable job of earth-friendly virtue-signaling with the statement that the paper used by Walker & Company consists of “natural, recyclable products made from wood grown in well-managed forests,” and that “manufacturing processes conform to the environmental regulations of the country of origin.” Thank goodness for the reassurance. I sure as hell wouldn’t want to own a book culled from mismanaged forests.
The cover- similar to the book’s standard font color- is dark brown (though the internal font for the body text is closer to sepia. The title and subtitle embody a subtle glow, as if laser-etched, the words surrounded by scores of arcane and geometrical symbols, thus lending the tome an eternal or mystical feel.
As for the internal contents, the choice of sepia is troublesome. While not difficult to read, the graphics tend to be washed-out, at times, lessening their impact. But given the wealth of information presented, it’s a shortcoming we’ll just have to live with. Maybe the color cut down on printing costs.
The contents are divided into six sections, each one originally published at an earlier time; the dates range from 2001-2009, and the collection itself released in 2010. Book I is “Sacred Number” (Miranda Lundy); Book II, “Sacred Geometry” (Miranda Lundy); Book III, “Platonic & Archimedean Symbols” (Daud Sutton); Book IV, “Harmonograph” (Anthony Ashton); Book V, “The Elements of Music” (Jason Martineau); and Book VI, “A Little Book of Coincidence.”
As for the book’s nature and intent, the editor states that it is three things: a rare treasure, immortal, and universal. The foreword informs us that in its original state, the Quadrivium was “first formulated and taught by Pythagoras as the Tetrakyts around 500 BC,” and that it was “the first European schooling structure that honed education down to seven essential subjects.” As I read all of this, I am reminded of why I’ve never gotten too far with the book in previous attempts: it’s a reference book, not exactly the kind of thing you curl up with for an evening of easy reading. But it is what it is.
For the visually-oriented learner, every section is accompanied by one or more illustrations. And the illustrations themselves are interesting, for they represent the old and the new, as well as approaching the respective topic from several different directions to aid in understanding- not that every subject is readily-accessible, despite visual aids.
To delve further into description of Quadrivium’s contents is futile, for it’s similar to giving an overview of a dictionary or encyclopedia- for this is a reference book. That being said, it’s one of the more fascinating examples of a reference book that there is. Where else will one fond a section on games, where the hopscotch diagram shows the starting square as “Earth,” and the final two destination areas as “Heaven,” just past “Hell”? Or instructions for building your own harmonograph? Or yet another attempt to explain the “circle of fifths,” a section of musical theory that continues to baffle me? Then there’s the “Little Book of Coincidence in the Solar System,” a compendium of galactic patterns and parallels that may challenge a reader’s beliefs about the Big Bang theory and evolution as much as it might support them.
As if all of this weren’t enough, the final section is a cornucopia of magic squares, early number systems, symbology incarnate in “Some Numbers of Things” and a “Select Glossary of Numbers,” ruler and compass constructions, scary-looking Platonic Solids formulas, equally intimidating square roots for harmonic constants and equations, and planetary tunings (whatever the hell those are).
After I’d owned the book for a few years, we moved to SoCal. One day I was visiting with Seth, a local transient who was surprisingly well-spoken and educated- not to mention surprisingly well-versed in hygiene, having some secret knowledge of accessible bathing facilities his fellow hoboes were not privy to. (Yes, I said “privy,” so get over it.) The fact that he was also a paranoid schizophrenic- though a high-functioning one- didn’t deter me from inviting him to lunch, one afternoon.
After we spent time over a meal, discussing everything from religion to rock music, it became apparent that he had some cognitive issues that hampered his ability to control his emotions. Having repeatedly assured me that he loathed books- a trait he extended to most humans he came in contact with- his increasingly erratic behavior indicated to me that it was time for him to go. As he headed out the door, I noticed that he had my copy of “Quadrivium” surreptitiously tucked under one arm. I hadn’t seen him grab it, but now I asked for it back. He apologetically handed it over with an unconvincing “How did that get there?” look on his face.
Ever since then, I’ve thought of Seth every time I grab “Quadrivium,” for another go at it. If the tome is good enough for a brilliant, high-functioning schizophrenic, it will always have a place on my bookshelf.
As much as I'd love to, I couldn't quite give this book 5 stars. The first few chapters are beautifully written and illustrated but some of the later stuff is much more dry (though equally as fascinating in some respects). I'd need to give the chapters on music onward another read to truly appreciate it I think.
Still, it's overall an astounding book, highly recommend it to anyone with a general interest in philosophy, science, or music.
Curious person? Then I would suggest reading this book. I mean seriously, who the hell wouldn't want to learn about Epigrams, Phyllotaxis, or Li Symmetries.
Changed from 4-5 after re-reading. I still feel like some of the topics require a lot of research (it is more of a tease, spurring you into looking up more information in places -unless you are already an expert).
Original: Interesting book, which is really four separate books. Some sections where I am strong like Geometry and Numbers felt like there was not enough information, others where I am clueless especially music I felt lost. Probably just me but felt like in some sections I needed way more detail and in others way more explanation. Still, very interesting!
An incredibly fun, well illustrated and densely packed read. Anyone will enjoy, but this isn't for the faint of heart; there's a lot of information packed into these pages and sometimes you'll want to reread the same section or go back to a previous chapter to refresh your memory.
A wonderful look at the classical arts - geometry, arithmetic, music and cosmology, Quadrivium connects dots and expounds on the math and beauty constantly swimming in our world's ether.
Can I give this more than 5 stars?? oh my goodness did I relish in this book. There was a whole hell of a lot I did not understand, but I am more than ready, willing and able to delve into more of this author's work. Bring it on!
Fascinating book on the Quadrivium. I learned a lot from it. At times the book went beyond my ability to understand it (particularly in the geometry and music sections), but it was accessible for the most part. The biggest thing I gained from this, however, was not specific knowledge about the Quadrivium, but a better grasp on the larger point of the Quadrivium and how the Quadrivium is meant to be viewed (or: rather, how the Quadrivium is to reshape our own views and feelings).
At the end of the day, it's more of a "here's a bunch of cool facts about the Quadrivium" book than anything else. But boy are the facts cool. And boy does it do a good job of using the facts to reveal a mindset, and not just present facts for facts' sake.
Nearing 20% of this book (early pages of Book II) and I am , frankly speaking, underwhelmed. This book relates basic numbers and geometries to its use in spirituality, mysticism, music, philosophy- the liberal arts. But 90% of this text is rooted in Abrahamic or western thinking. It is not comprehensive enough to include the use of these in , say, temple art of India and eastern cultures. Or even the seemingly organic Eastern music- which is far more complex than western music. I think such an attempt would be too ambitious. Human mind is complex- and our arts have evolved in so many ways, the permutations are mind-boggling. There are passing references to the contributions of India in coming up with the concept of Zero, or Sunya. And yet, we cannot do without zero in our comprehension of mathematics (or the theoretical sciences) today. Perhaps because its relevance in spirituality is rooted in Indic/Eastern philosophies. The Void conceptually would be blasphemy to the followers of the Abrahamic faiths. How can Heaven be Singularity? And yet, we know now - thanks to Theoretical Astrophysics- that we started from Singularity and then again strive to reach that Singularity.
Reading this book made me think I am reading a pedantic version of the Da Vinci Code.
update 12/29/2021: beautiful, beguiling books with the four minor mathematical arts of the ancient seven liberal arts. Beautiful and fascinating, but a little untrustworthy, like ancient wisdom. I don't blame them, they did their best. Enjoyable in the ingenuity of the ancients in seeing patterns in number, geometry, music, and astronomy. Sometimes they were fooled, but found some nice gems on the way.
Reread 11/26/2025 Covers the four liberal arts of Number, Space (geometry), Time (music), Time and space (Astronomy or the music of the spheres). This is our intellectual inheritance from the ancient world of quadrivium listed above about the cosmos, and the three liberals arts of the polis: grammar, logic, and rhetoric.
4 1/2 stars. Fascinating book. Astronomy section was the weakest which was a shame. The music section was the best. A book to pick up and read a section or two rather than reading straight through.
This book is a single-volume compilation of six books in the Wooden Books catalog, two of which I have read previously (Sacred Geometry, and A Little Book of Coincidence). As is generally true of the books in this series (the ones I have read anyway – I see that some of the more recent additions to their catalog have further ramped up some of the rather unsavory neo-pagan emphases and associations, so some caution is recommended), the presentation is delightful, and the information conveyed is wonderfully dense, fascinating, and invites extended contemplation and revisiting.
The Quadrivium are the four “advanced” members of the Seven Liberal Arts (the other three, the Trivium, being the “fundamental” set: Grammar, Logic/Dialectic, and Rhetoric) which formed the core of the medieval educational curriculum. They might best be thought of in terms of the following brief categorizations:
• Arithmetic – The study of numbers, their features, relationships, symbolic associations, etc. (In this volume: Book I, Sacred Number.) • Geometry – The study of numbers extended into space. (In this volume: Book II, Sacred Geometry; Book III, Platonic and Archimedean Solids.) • Music (Harmonia) – The study of numbers extended into time. (In this volume: Book IV, Harmonograph; Book V, The Elements of Music.) • Astronomy (Cosmology) – The study of numbers extended into both space and time. (In this volume: Book VI, A Little Book of Coincidence.)
A little dry, left-brained and technical for me. There is a great breadth of information here but sometimes it is summed up a little too tersely for my taste. I'll admit that there are portions that I read without consciously absorbing so either it is working on a subconscious level (it took me at least 2 years till now and I still haven't quite finished it), or I'm simply not able to understand parts of it due to its technicality or the need for constant revision.
I love the presentation, it has great illustrations (I can't say for sure how they have been sourced, though they often compliment the text nicely) and of course, the subjects on offer combine for a wonderful compendium to branch everyday science and mathematics into some more esoteric, metaphysical, and spiritual realms.
Sadly it may be just that - a teaser collection to ignite interest in deeper enquiries which necessitate seeking beyond these pages, leaving myself at least a little unsatisfied. It never really hooked my interest on more than a superficial level.
For sure this is more a coffee table book in terms of detail and quality rather than something to really dig into over a month. You can easily pick it up, read a couple of pages, and put it down again.
I came across this attractive volume in the Adler Planetarium's bookshop in Chicago. According to Wikipedia, from the time of Plato through the Middle Ages the quadrivium was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, which consisted of grammar, logic, and rhetoric. The present volume departs somewhat from this definition. It comprises six "books" by various authors, dealing respectively with "sacred number," which includes new-age numerology and several errors of fact (e.g. "five petals form a flower"); "sacred geometry" which includes some interesting constructions; Platonic and Archimedean solids; the harmonograph (a 19th-century mathematical toy that draws curved figures much like a spirograph); the elements of music; and "A Little Book of Coincidence in the Solar System" discussing some numerical ratios but largely ignoring the fact that planetary orbits are ellipses, not circles. Despite the volume's title, there was nothing about cosmology in the modern sense. A very mixed bag, containing some good stuff, but I'm not tempted to buy other books in the series.
Superficial books for superficial times. How to be "deep" without taking the depth. The book touches on multiple ideas and notions mixing mystical elements with science and philosophy but does not treat any of them seriously. More or less like you would be surfing on the internet for cool stuff related to music and astrology. It works great for people who want to sound cool when they talk about their passion for music and pseudo-mysticism. For anybody interested of the real information this book is touching on I would recommend reading Plato, Rodney Collin and P.D. Ouspensky. Mystics treat planets as celestial living bodies, but from there and talking about Venus as "she" and planets "kissing" it is a long way. Sometimes the language used seams borrowed from the popular "healthy smoothy" youtube channels. All in all, better have a look in it at the store then decide if you need it on your shelf. Also it seams to have a great marketing, for every real review posted they have somebody writing a 5 star review to compensate. Just check it for yourself and see if is worth buying it.
Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology by John Martineau is a luminous and exquisitely designed compendium that revives the ancient path of knowledge pursued by philosophers, mystics, and scholars for centuries. Exploring the interwoven disciplines of number, geometry, music, and cosmology, the book reveals a universe ordered by proportion, resonance, and celestial harmony. With elegant diagrams, thoughtful commentary, and a reverence for the mystical beauty of mathematics, Martineau invites readers into a contemplative engagement with the structures of reality. Each page offers insight into how the ancients perceived the cosmos; not merely through science, but through a sacred geometry of meaning.
"To study the Quadrivium is to explore the mind of the universe through the language of harmony."
An exquisite journey into cosmic intelligence and sacred musical wonder!
Has some good information in a rather heterodox package that one still has to approach with a grain of salt. It is a fun book highlighting some of the insights of ancient mathematics, astronomy, philosophy. It covers the topics in the form of Quadrivium the four liberal arts of Arithmetic (the study of number), Geometry (the study of patterns in space), Music (the study of patterns in time), and Astronomy the study (the orbits of planets tracing out patterns in space and time). These are supplemented by the Trivium the arts of Logic, Grammar, and Rhetoric. The Quadrivium is the study out there or the world, and the Trivium is studying of the in here or the mind. Seven Liberal arts of antiquity. We slice it differently today but it is refreshing sometimes to see how our ancient counterparts looked at things.
Really, I'd probably give this more of a 3.5 stars.
Wooden Books has some great, simple books like this that give you the main idea of things without bogging you down too terribly much. Kind of like all those books you see for sale on the tables at Books A Million.
I don't have a strong background in much of anything discussed here, so it doesn't get too terribly complex for somebody who isn't in the know, like myself. I think, to be fair, I read this companies books too quickly (no chapter is over two pages) and end up confusing myself, or just overloading my brain with things like music theory to the point it all gets mushed together.
So, the lower rating is probably partially my fault. These would be a good dip into subjects before you invest time in a longer study.
I really enjoy flipping through this book for inspiration. It touches very briefly on many design concepts, including sacred geometry, the golden spiral, golden proportions, art composition ratios, fibonacci sequence, music and sound wave intervals and ratios, tricks for drawing complex shapes (but light on the details; you have to kind of take the bare bones info and extrapolate), architecture, astronomy, Li symmetries, and more.
It isn't a complete reference of any one subject, but instead it gives a tiny taste of many, many things that show the intimate relationship between math and design. With lots of interesting illustrations.
É muito interessante ver como a matemática se encontra em tudo que vivemos, sinceramente nunca fui uma pessoa boa com exatas, mas depois de ler Quadrivium me deu vontade de focar em aprender haha. O conteúdo em algumas partes pode parecer confuso, ainda mais para quem não é chegado na matemática, principalmente na parte da geometria, mas vale a pena a leitura, eu particularmente fui pesquisar mais sobre a proporção áurea e a sequência de Fibonacci pois me interessei bastante pelo assunto. Por fim, sim, você precisa dar uma chance para este livro!
I really like it as a reference book. However, many of the concepts are addressed too briefly (one page per) and are often described in a way that makes them sound more complicated than they are (i.e. when they first address 'squaring the circle' on the page 'Elevenses'.)
I did buy it because, as I said in the beginning, it acts as quick reference book. Just understand that you will have to do some additional research/digging on your own. It acts more as an outline or guide.
This book follows the classic liberal arts subjects of number, shape, cosmos, and music, and it shows how they all inform each other. It's beautiful, with text on the verso and image on the recto, however, because each spread is a new subject, the text was sometimes too abbreviated. It gives a good overview, but doesn't go in depth enough on anything. It was a great introduction, and I'm interested in learning more.
Fascinating. A wealth of information and wonder at the mysteries of the universe. This does not read like a standard book, but makes more sense as a kind of reference or encyclopedia. There were many things way over my head, but I found it all interesting. The graphics and diagrams on every other page were delightful and well-done. This would be a good introduction to see what the quadrivium can be, but you would need another source to teach these arts.
In a whole different way, this book teaches us a little bit of the beginning from understanding what numbers really are and what do they stand for. Correlating the Mathematics with the inner beauty of Music Theory and Geometry patterns. I use this one as a reference book to get explanations from difficult subjects and breaking them down to demonstrate beginners the exquisite meaning of what we call Mathematics.