So we've looked at paper sizes, proportions, and how it all fits together - now, we're going to look at how ye olde masters like Nicolas Poussin composed his figurative works with geometry.
Check out this Poussin from 1631, Dance before a herm of Pan. It's 39.5 x 56 inches or 100 x 142 centimeters.
Now check out this one below, The Triumph of Pan, from 1636. It's 55 x 57.5 inches or 140 x 146 centimeters, a different proportion. But if I just map each painting by its short side and find the squares or the semi-circles from the center of each edge, I can see how Poussin arranged both pictures using the same method. As a student, this allows me to see that the harmony and beauty of a painting comes as much from the composition as the handling of the paint. The figures describe the harmonic points within the given proportion. So the (dynamic) figures and the (static) proportion itself are in tension with each other - and this, I believe, creates a similar feeling to hearing a melody of sonorous, "correct" notes without discord.
If classical composition interests you, great - keep reading. If classical composition does not interest you - please stop reading. I'm not interested in trying convince anyone that classical proportions are best or right or anything. I think the conservative methods of the academy have been so ignored that my own (academic painter) teachers barely knew anything about them. So I'm writing this because I am mad at my teachers. Maybe you knew about about rigorous classical composition and its direct relation to the harmonic placement of figures within a proportion when you were 20 years old — I did not. I had the vaguest sense of Renaissance framing but nothing so specific as harmonics. When I started assisting painters I discovered that Poussin, Ingres, Degas, and countless other old master painters used these methods - and I flipped out. Why didn't anyone ever show these methods to us back in 7th grade when we were studying short cuts to perspective and other Renaissance tenets? Or at my conceptual art school when I was 20? None of my fancy classes described the political Mexican murals we studied in mathematical terms. No mechanics. All talk.
Look, you can ignore this mapping just like you can ignore learning musical scales, or learning to read sheet music. Yes, artists just "do what looks right" but imagine if that's how they did things at the academy of music. "Okay, just play what sounds right - you don't need to learn how to read sheet music." They learn how to compose by ear and by writing it all out. Learning harmonies, arrangements, and compositional writing skills are all very similar to learning how to draw, paint, and work with color. Most art schools used to teach more basic, less conceptual approaches to making work. Like I said - none of my teachers (from middle school to art school) showed me classical framing methods like Poussin's, because I don't think they knew how to do it. So were they bad teachers? Did they just compose "by ear" or with relatively simple methods like "the rule of thirds?" They taught us perspective and other Renaissance ideas, but never a true study of geometry. They taught us about figure/ground relationships and the picture plane, but never gave a real in-depth look at foundational geometry - which is where all the compositional shorthand that they were parroting comes from. I was so pissed off when I learned about all this stuff - from the abstract painter Dorothea Rockburne - and thought about all the bullshit I would listen to from teachers about studying the old masters. Too bad the teachers telling me this didn't even know how to look or study the masters themselves.
So I'm admittedly a little cagey when it comes to discussing this stuff. It gets into belief systems. Whether or not you feel that an ability like drawing just comes to you - or that it is something that can be taught like music - it is still measurable. We can measure both the "natural" draftsman who composes by eye and the labored and learned draftsman who composes with mapping. It would seem to me that this is like composing music in a certain scale or just free improvisation. But, really, most free jazz musicians know their scales backwards and forwards as Matt Seneca reminded me. Meaning, if you know your scales you can do both - improvise without the restriction of writing it all out (mapping) - let it take form intuitively based on your direct study of scales and chord progressions. So when I wind up discussing all this with a cartoonist friend and that friend resists the idea that an artist should be able to "map" out the harmonic points on a piece of paper or canvas, I just want to strangle them—because they remind me of my teachers who just didn't know any better. Ron Regé got mad at me (in a friendly way) when I started mapping his drawings in front of him. "I don't wanna know! I just know what's there." I laughed, because I was just trying to show him that he intuitively found very complex proportions within his panels.
My teachers were on the right track, I think. They just didn't go far enough for me. They stopped at "head arrangements" essentially. Maybe it was too advanced for general study - but craft and theory got way more play where I went to school than, say, basic geometry and the mechanics of painting. You get a little geometry in art class, a little geometry in math class (taught with the slightest nod to what we were doing in art class), a little geometry in science class, and a lot in architecture class later in art school. No one teacher ever put it together for me until I met Dorothea Rockburne —she opened the door for me. Dorothea is an amazing painter whom I worked for. She talked about math and astronomy and folding time. I was like, "Yeaaaaah, whatever, Dorothea" for awhile, and would sort of ignore her lecturing. But then she came to my studio one day and just sliced me up into a million pieces. My work, to her, was naive. "It's all eye-balled. You don't know how to make it all rhyme together - how to measure tone against shape. Your proportions are off." Dorothea definitely knew her proportions. She was a math wiz on top of being an abstract painter. So I trusted that she knew more about proportions than I did. It really rattled me up. I thought about all the years I'd spent drawing and actually did not know how to measure my own work. I had a good eye, but none of the language for the actual mechanics of painting stripped of its imagery. I had a feel for abstraction but no real understanding of it.
When Dorothea explained the similarities of compositional methods between her abstractions and Poussin's way of placing figures along the same harmonic points - all the little bits of info I'd gathered over a decade or more of drawing all fell into place. I could see specific points along the maps that my eye only felt before. I intuitively found the squares and the diagonals, yes, but there are so many more complex and dynamic arrangements that I, again, now could see what I'd only felt before. It changed my life. I felt like I could see like the matrix of the universe or something. It was like Yoda was sitting there talking to me (use proper voice) "the tree, the rock, the force surrounds you" — a veil had been lifted. All the little bits of visual understanding that were intuitive and learned fused in a way that just let me see the interconnectedness of everything.
Dorothea also introduced me to the workbooks of Robert Lawlor. She suggested I do the exercises weekly, on a day when I didn't have to go to work like Sunday. She explained that the intuitive way of seeing and feeling spatial relationships relates directly to our own physical make-up. The proportions that describe our own bodies are the same proportions that precisely describe branch growth in trees and the movement of the stars. So what we intuitively feel as harmonious is ourselves - like a reflection. And diagramming those proportions and how it all fits together is possible - it's a way of tuning one's own visual perception. Applied to drawing and recording the visual and imaginative world - it becomes an essential method for the student. I think anyways. Lawlor's workbook really provides insights that other books on the subject do not - mostly because Lawlor's workbooks actually show how to construct the proportions being discussed in the text.
Excellent post as usual! The other day I got into an argument with a professional comics artist because I contested the use of perspective on the grounds that it was too limited and non-realistic, to which he disagreed. On the other hand, I find these composition "rules" the most interesting and useful technique used by the Renaissance artists. Maybe your teachers were ignorant of those systems, or maybe they thought geometry was boring. Anyway it sucks.
I hated this kind of attitude so much, I ended up becoming what I hated the most. Now I teach at the same art school where I used to study, and I'm constantly trying to unveil things the way you described. I'll make sure all of these tips and "secrets" get to my students.
That’s funny, about Ron Rege.
Getting inside how things work and analyzing them, specifically with art, I think, got mostly thrown out in the 60's and with the invention of art schools replacing apprenticeships. This is way before my time but I think there was less of a focus on structure and a freer laxness that fostered directionless, spontaneous creation. I think a balance between the two creates the greatest work, the discipline creating limits and the rebelliousness of spontaneity pushing those limits to new places. The push and pull that is found in Picasso, Hitchcock, John Coltrane or Will Eisner, etc. etc.
What could be a more perfect metaphor than Pan? A shepherd and a reckless free spirit rolled into one.
Spontaneously conceived, artificially expressed: This structure, it's killing me.
I think that if people understood these rules of composition, they would feel too trapped by them. I have felt this before(only because my teachers don't explain it thoroughly). My high school art teachers didn't even explain why I should know why people learn to use color wheels, much less perspective lines. This attitude isn't felt by all. M.C. Escher tried to incorporate mathematics into his art. That example is just off the top of my head, I don't think this prevailing attitude that composition rules are dead is exactly correct.
'Maths is so emotional!'
'Ratios breaking down everywhere!'
'A million points of light; a billion lines connecting them!'
This series is super interesting.
I think partially because pre-Modernist ideas about balance and order have not been en vogue for so long.
It's exciting and jarring when a supposedly traditional perspective appears under the guise of subversion! How transgressatory/anti-progressitory, AMIRITE.
What's fascinating to me is thinking about how the geometric conventions in the Renaissance era may have conflated Euclidian geometry with Hellenistic deism. Like, that there's something holy about simplified forms and the kind of order underlying everything as depicted in Frank's illustrations above.
So I think some of the issue is where you identify the divine or the definitive structure of reality. Is it a circle?
Or is it a big splattery mess?
Or is it a big splattery mess containing a circle?
Or is it a circle containing a big splattery mess?
I hope the implied metaphors I'm forcing are painfully obvious here. Anyway, I think a shit in cosmological perspectives especially beginning in the 19th century can account for the discarding of generic (as in general and broadly useful, not as in 'bad') principles in art-making. Not necessarily good or bad, just a historical phenomena.
If you're interested in individual, highly specific, and conditions-based ways of forming perspectives (as I think certain strains of American popular culture have been for 100 years or more), you're going to elevate that which appears disordered, chaotic, and intuitive.
I think it's especially interesting that you, Frank, point out that highly committed craftspeople may tend to unknowingly reproduce structures common to many other artists and common to an inherited tradition. Is that evidence of absolute principles of reality?
Maybe so. Maybe not. Maybe either explanation is compelling.
It could be that the postmodern emphasis on the particular at the expense of the transcendent is waning and that we will experience a new Enlightenment in the face of a decadent Baroque. Totally possible!
I'mmmmmmmmm cool with that.
*a shit = a shift