fifteen variations
on a single theme

the theme and the variations
- my "fifteen variations on a single theme" were produced between 1934 and
1938 and i have decided to publish them in their present form only because
i feel that a great many of those who are interested in art have no clear
idea of how works of art are created and are without any clear understanding
of the internal and external construction of such works.
although it is possible to like our creations without fully understanding
them, one is scarcely able to extract from them all the pleasure they can
give without at least a little insight into the methods by which they have
been evolved. the purpose of this brief introduction is to give a glimpse
of what a group of these methods consist of and to give anyone who takes
the trouble to look at the plates the opportunity of following certain operations
by mean of the examples shown on them. this introduction, therefore, draws
attention to a certain number of relationships which show themselves both
in the theme and in the fifteen variations and which, indeed, bind all the
variations together.
as there exist within these narrow and clearly defined limits such a large
number of variations, the fact that a single theme - that is to say a single
fundamental idea - leads to fifteen very different developments can be considered
the proof that concrete art holds an infinite number of possibilities. such
constructions are developed only on the basis of their given conditions
and without any arbitrary attempt to modify them for reasons of proportion.
with this method once the basic theme has been chosen - whether it be simple
or complex - an infinite number of very different developments can be evolved
according to individual inclination and temperament. this method of thus
developing and transforming a fundamental idea - a theme - into a variety
of expressive forms derived from the theme itself is used by various artists
in the realm of concrete art. knowledge of these methods ought to enable
the observer to discern the methods by which other works of art have been
created. a number of these last are essentially more complex than the "fifteen
variations on a single theme" although superficially they may look simpler.
even for the person who has some knowledege of the subject the underlying
constructive thought is often difficult to distinguish because the bias
of the personal element in the composition comes more to the surface not
only in the general presentation of the work but also in its opposition
to the system of variations in its individuality, and also because personal
interpretations are more possible and permissible that in the case of a
group of variations on a construction worked out without compromise.
everything which is not strictly a part of the "construction" theory outlined
above is omitted in the following analysis. all the personal considerations
which were responsible for the choice of the figures have also been omitted
- that is with the exception of the methods by which the figures have been
evolved from each other. it must also be pointed out that it would be posssible
to develop other variations on the same theme and that no attempt has been
made to reverse or develop the theme itself or to combine the variations
with each other or to try other colour combinations. these possibilities
have been omitted here in order to keep the drawings as clear as possible
and to eliminate all these developments which would lead to constructions
of a too personal nature and which would only tend to make the explanations
more confused.
it is possible that some, on reading these notes, may find nothing in the
"fifteen variations on a single theme" other than a mere amusement of a
pseudo-mathematical or geometrical nature. although the exact placing of
the spaces and surfaces of these figures was obviously done by geometrical
methods, the controlling idea which produced the figures was neither mathematical
nor geometrical. what is brought out in the "fifteen variations on a single
theme" is the pure play of form and colour freed from the compulsion of
being something other than it really is, of which the sole aim is to give
pleasure by the fact of its own independent existence.
max bill
zurich november 1938
1935-1938
Fifteen Variations on a single Theme
16 lithographs 12" x 12 5/8".
(30.5 x 32 cm)
Paris: Editions des
Chroniques du Jour, 1938