The Painter's Secret Geometry: A Study of Composition in Art

390 Pages·2014·26.27 MB·English

by  Charles Bouleau

THE PAINTER’S SECRET GEOMETRY

THE PAINTER’S
SECRET
GEOMETRY
A STUDY OF COMPOSITION IN ART

CHARLES BOULEAU

With a Preface by
JACQUES VILLON

DOVER PUBLICATIONS, INC.
MINEOLA, NEW YORK

Copyright

Copyright © 1963 Éditions du Seuil

Copyright © 1963 Thames & Hudson and Harcourt, Brace & World, Inc All rights reserved.

Bibliographical Note

This Dover edition, first published in 2014, is an unabridged republication of the work, translated from

the French by Jonathan Griffin, and originally published in the U.S. as “A Helen and Kurt Wolff Book” by
Harcourt, Brace & World, Inc., New York, in 1963. The work was originally published in France under the
title Charpentes, La Géométrie secrète des peintres.

Library of Congress Cataloging-in-Publication Data

Bouleau, Charles, 1906–

[Charpentes, la géométrie secrète des peintres. English]
The painter’s secret geometry : a study of composition in art / Charles Bouleau; with a preface by

Jacques Villon.

pages cm.

Summary: “This richly illustrated examination of visual arts in European tradition shows how the great

masters employed the Golden Mean and other geometrical patterns to compose their paintings. Up-to-date
examples include works by Klee and Pollack. Highly sought-after cult classic and vade mecum for
students of art history and artistic composition”—Provided by publisher.

Includes bibliographical references and index.
eISBN-13: 978-0-486-79550-8

1. Painting—Technique. 2. Composition (Art) 3. Painting—History. I. Villon, Jacques, 1875-1963,

writer of supplementary textual content. II. Title.
ND1475.B6813 2014
750.1’8—dc23

2014002161

Manufactured in the United States by Courier Corporation 78040601 2014

www.doverpublications.com

CONTENTS

Preface by Jacques Villon

Introduction

I
Monumental Art

II
The Frame

III
Geometrical Compositions in the Middle Ages

IV
The Musical Consonances

V
Geometry after the Middle Ages

VI
Dynamic Compositions

VII
Compositions in Space

VIII
Picture Framework in the Nineteenth Century

IX
Solutions of the Problem in Contemporary Painting

Conclusion

List of Illustrations

Select Bibliography

Index of Names

PREFACE

In the artistic chaos of these last years, when the absolute liberation of the
individual instinct has brought it to the point of frenzy, an attempt to identify the
harmonic disciplines that have secretly, in every period, served as foundations
for painting might well seem folly.

But this folly is in fact wisdom. It is the way to a kind of knowledge essential

for whoever wants to paint. Essential, too, for whoever wants to look at pictures.
The framework of a work of art is also its most secret and its deepest poetry.

But this study—so important that it is strange it should have been left so long

unattempted—was not an easy undertaking. It is a dangerous quest, one in which
the seeker’s mind must be always on guard against itself. Charles Bouleau has
had need of a great deal of humility; he has taught himself to abandon many of
his initial ideas, to renounce various seductive hypotheses that had given this or
that branch of his researches its first direction, in his determination always to be
true to the reality of the work of art before him.

The aesthetic theories which he expounds in this book are never arbitrary

ones. They are those of the period under discussion: they have always a firm
historical basis. Charles Bouleau does not single any of them out for
partisanship. Advancing step by step through the vast mass of work produced by
the painters, he has had the skill to separate out the new contribution of each
period and each artist. He has carried his analysis through with strict method,
seeking, in the case of each work studied, to recreate the intellectual atmosphere
of its time.

The result of such long and scrupulous reflection is a book that is often highly

original. Though, for example, numerous writers before him have discussed the
golden number, Charles Bouleau’s study of the Renaissance use of musical
proportions in the composition of pictures will come as a revelation to many
readers.

In a word, this book goes a long way towards recovering the spirit of

geometry as Piero della Francesca understood it; it is an attempt to reveal that
secret geometry in a painting, which has been for the artists of every period one

of the essential components of beauty; and the examples which the author offers
from among the works of modern painters, of Mondrian for instance, are a
striking proof of his objectivity.

Jacques Villon.

INTRODUCTION

After gazing for a long time at the Death of Sardanapalus in the Louvre and
making some notes on its composition, I was rash enough to pursue this line,
turning to the Entry of the Crusaders into Constantinople, the Massacre of Scio,
the Women of Algiers. This research and the pleasure it yields had taken hold of
me. After Delacroix came Poussin and Cézanne; then David and Seurat… It was
the beginning of five years spent in questioning hundreds of artists through
thousands of canvases.

This book is not a treatise on painting. It is a study of the internal construction of
works of art, a search for the formulae that have guided, over the centuries, the
distribution of the various plastic elements. The framework of a painting or
carving, like that of the human body or that of a building, is discreet; sometimes,
indeed, it makes one forget its existence; but it cannot be absent, for it is what
gives a work of art those ‘principal lines’ of which Delacroix speaks in his
Journal.

Throughout the book I shall always try to look at the paintings in question in

my capacity as a painter. I shall be searching for the genesis of the work rather
than for the secrets of its formal beauty. I shall try always to resist the temptation
to find the criterion of aesthetic value by applying some favoured formula; not
being either a mathematician or a philosopher, I shall never attempt to prove that
a work of art is a paragon of beauty simply because it may fit some highly
exacting and scientific schema.

Nor is this book a history of composition. I shall take certain liberties with the

time sequence. Due weight must be given to certain resemblances, resulting
from affinities between artists of different periods: as in the case of Cézanne,
Delacroix and Rubens. Conversely, in order to follow the use of geometrical
figures (or of some other compositional device) through the centuries, I shall be
obliged to treat certain painters in several chapters, under different headings. In
spite of all this, the chronological order will often come to the fore, reflecting as
it does the movement of ideas and the fact that every artist is at the start a pupil.

We shall find, as we go along, that there are many valid solutions to the

problem of the distribution of forms within a work; we shall recognize, too, that
artists like change, follow fashions and are subject to currents of taste.

In the midst of all these fluctuations we shall come across fixed points: the books
on painting. The venerable treatises by Cennino Cennini, Piero della Francesca,
Leonardo da Vinci, Alberti, Dürer and Lomazzo, the relevant passages in the
writings of Delacroix and others less well known, will guide us in our search and
will steady us, forcing us constantly to put the artist back into the atmosphere of
his own time.

What is the art of composing a picture, and why, as a student, was one told so
little about it? Is it a matter of instinct and flair? Some people assure us,
nonetheless, that an extremely subtle and secret mathematical science lurks
underneath the apparent spontaneity of the masters. Others, it is true, state that it
is only a false science, a few tricks, a kind of savoir-faire which the budding
artist must make haste to acquire. I found that these questions, when I tried to
answer them, led far afield.

To begin with, the complexity of the subject is great: the organization of

plastic ideas is a response to needs that are not confined to the domain of
painting. The requirements of monumental art have to be taken into account in
any work of large dimensions, in painting and in decorative sculpture as in
architecture. Then there is the effect of the picture-frame on its contents—an
effect which, though it remains very general, has a determining influence on the
way the painted surface is organized, engendering in it geometrical figures that
are often highly complex.

The evolution of ideas and forms in the course of time plays a greater part

than the quite abstract requirements just mentioned. There is a geometry of the
Middle Ages. It has its own peculiar features, and it disappears with the
civilization that was expressed in it. The more and more complicated figures
traced with the compasses are in due course abandoned, and at the beginning of
the Renaissance an aspiration towards simplicity and an intense dislike of
overloading create the conditions favourable to a new enthusiasm—the
enthusiasm for applying to the plastic arts relationships of musical origin, whose
philosophical beauty had already been praised by Plato in the Timaeus. These
relationships were first studied by theorists and then applied by architects; but
the painters were not slow to lay hold on them; and they constitute an essential
element in the style of the Italian Renaissance. There is more than one way,
however, of using musical relationships: starting from them, one can create a

disequilibrium, a swinging movement which, much admired during the Baroque
period, gave them a new life at the very moment when they were about to fall
into disuse. But the Middle Ages were not completely dead—not everywhere.
The taste for geometry persisted, though simplified; circles and arcs of circles,
even the golden section, were still used; and the simple but imperious action of
the rectangular shape of the picture continued to exercise its effect through
changing fashions and styles. This form, of itself, creates a division of the
contents, which may be either a discreet indication or a rigid discipline.

A painting is not simply a plane surface; it undertakes the conquest of space,

and the different stages of its conquest are bound, in their turn, to be expressed in
the composition: there is the conquest by means of geometry in three
dimensions, and also the conquest by means of light and shade. The progress of
this leads to a plastic art of illusion obeying the same laws of stability and
weight as the real.

It is characteristic of contemporary painting that in it each one of these

methods of composition triumphs in its own right, as though all that till now was
jumbled together were suddenly revealed in its pure state.

And to this analytical activity in painting today a book like the present one

surely, in its way, bears witness.

I MONNUMENTAL ART

Church of Saint-Savin-sur-Gartempe: God and Noah. God the Father with the features of Christ appears
many times in the Saint-Savin frescoes; he is always made appreciably larger than the figures who are close
to him and whom he is addressing. (Archives photo graphiques)

First let us look at the artist, whether painter or sculptor, who works within the
framework of a monument, under the direction of an architect; he is not free to
imagine and organize his work as he would do in his studio. To decorate a
monument involves accepting servitudes that are bound to affect profoundly the
distribution of the parts, their proportions, in fact the whole composition. This is
my reason for studying first the characteristics which monumental art imposes
on plastic art.

The monument is that which is bigger than a man, that which dominates him by
its dimensions and mass—and which in consequence calls for an attitude very
different from the simple perception of an object. A monumental work is bound
up with the space which surrounds us. Seen from outside and as a whole, it is
part of the landscape; seen from inside, it is a closed world in which we grow
and move about. Monumental art requires not only vision but movement. A
movement of withdrawal, in order to get a view of the work as a whole in the
midst of its surroundings and to appreciate its unity; and a movement of walking
about, so as to go round it and enter into its various parts. Though monumental
art is no monopoly of architecture, it is closely bound up with it: a statue, in
itself, is a work of architecture; decorative sculpture or mural painting
contributes to a monument its completeness, accentuates or enriches certain
points in it, but must never be detrimental to it.

Monumental art is therefore always bound up with space, and with a space

larger than a man. The movements it imposes, those of withdrawal and of
walking about, give it its distinctive characteristics and produce its main
problems.

A monument looked at from a distance takes on a somewhat unreal

appearance: it cannot be touched; it is hard to judge in relation to oneself; and
the first problem to arise is: how can one know the building’s real dimensions? Is
it very large, or is it quite small?

On the other hand, when one walks through a monument, its forms are

constantly changing: some points of view show it at its best, or better, others are
unfavourable. The artist must always be placing himself in the position of the
visitor, of the user; the place where he will be most inclined to stop is the
sensitive point which demands his utmost care; it is from there that the forms of
the monument must exert their full power over the imagination. This brings us to
the second problem, that of monumental perspective.

Chartres Cathedral: a Queen of Juda. The statue-column arises in obedience to architecture. Its small head,
narrow verticality and fluted folds make it the image of the column: it clothes the column, confirms its
dimensions but does not, like a caryatid, replace it. (Archives photographiques)

The monumental scale

It is on the architectural elements devised for human use, and, above all, on the
representations of figures (statues, frescoes…) that it normally falls to indicate
the dimensions of a building by making possible the comparison with what is
called the human scale.

Man refers everything to himself. Everything exists merely through this
relationship. Primitive man observes the phenomena surrounding him, judges
them to be useful or harmful, and loads them with metaphysics. The art that has
come down to us from remote times is always magical; it is the expression of
what is weaker than man or of forces that surpass him.

In the art of the great political communities, man is still the measure. The gods

are represented by giants. In Egypt the Pharaoh, because he sees himself as of
divine origin, has statues made of him that are ten times, or fifty times, larger
than life.

One must go to Greek civilization to find an art in which the figure keeps the

same size whether a man or a god is being represented. The artist identifies the
divine form with his own. He gives the gods his tastes, his passions and his
beauty. Only in exceptional cases does he dedicate colossal statues to them. He
seeks in his own body the secret of divine beauty and has the courage, in face of
the powers of nature, to proclaim the greatness of man.

The Romans had seen the work of the Greeks, but also of the Egyptians. From

the Greeks they retained the sense of the human, but the Egyptian colossi excited
their vanity as conquerors. They enlarged the Greek models and made colossal
statues of gods or of the Emperor. Then came Christianity. The God of the Jews
had been a terrible God: Jewish law, understandably, forbade his representation.
But Christianity is God made man: the scenes from the life of Jesus return to the
normal stature; only the Pantocrator, in the apsidal recess or in the zenith of the
dome, retains the majestic figure of the giant god.

At that moment Mediterranean civilization suffered inundation by new and

very strange forces. This was no revenge on the part of the Near East, no return
to the feeling for the colossal, but the advent of fresh concepts which came from
the depths of Asia. The human figure lost its proud domination. Yet a new
humanism was soon to be born in the West; and on almost every conceivable
part of the religious buildings there appeared astonishing people—new dwarfs,
new giants—whose subtle relationship with the monument we shall shortly see.
We reckon that an object, or a figure, is on the human scale in so far as it appears
to match man taken as a unit. As I have said, man feels the need to refer
everything to himself. It is characteristic of our intelligence, that faculty of
synthesis and order, that it brings the diverse into unity and measures it against

models, the most immediate of which is the self. By a phenomenon of optical
intelligence1, man takes hold of the figures which he sees some way off upon a
monument, and brings them back to the unity of the self or—more exactly—to
his own dimensions. Optical intelligence takes the form of a rapid, immediate
act: we are not conscious of its working; as soon as we have stood back a little, it
reduces for us the size of any colossal figure so that, whatever the artist may
wish, we can no longer see it as a giant; and in the same way a small figure is
enlarged, so that we shall never take it for a dwarf. The cherubs holding holy
water stoups in St Peter’s, Rome, do not do justice to the immensity of the nave.
It is astonishing to see how a worshipper approaching them seems quite small,
revealing with violent suddenness their colossal dimensions2. The Paul
Delaroche frieze at the Ecole des Beaux-Arts consists of huge figures which we
‘read’ from a distance as men of lifesize, and so they diminish the huge
semicircle. What follows? How does one combat the illusions of optical
intelligence? How can an artist convey size, convey smallness? How can he
make exceptional dimensions felt? Briefly, how can he reconstitute the true
dimensions of the monument?

Saint-Nectaire, capital: Resurrection of St Nectaire. In the Romanesque period sculpture and painting
adapted themselves strictly to architecture. Here the relatively small dimensions of the capital are purposely
stressed by the stockiness of the figures and their large heads. (Archives photographiques)