fifteen variations
on a single theme

• 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
  
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  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