proportion: defining harmony and order in architecture

Chad Alexander Smith | May 4, 2014

Throughout history, architects have proposed theories of proportion as aesthetic rationale for determining choices of design. These geometrys inform the architect in making decisions and in turn unify a visual construction, provide a sense of order, and heighten a sense of continuity. 

A great number of  systems have been developed.  A variety of geometries have been outlined to aid the designer in bringing about beauty from the arrangement of form.  According to Euclid, a ratio refers to the quantitative comparison of two similar things, while proportion refers to the equality of ratios.  Underlying any proportional system, therefore, is a characteristic ratio, a permanent quality that is transmitted from one element to another.  Thus, a proportioning system establishes a consistent set of visual relationships between the parts of a building as well as between the parts and the whole. 

The notion of devising a system for design and communicating its means is common to all periods in history.  Although the actual system varies from time to time, the principles involved and their value to the designer remain the same. 

Mathematical systems of proportion originate from the Pythagorean concept of “all is number” and the belief that certain numerical relationships manifest the harmonic structure of the universe. 


One of the earliest written documents dealing with proportions is Vitruvius The Ten Books on Architecture.  He begins his treatise with the recommendation that temples, in order to be magnificent, should be constructed on the analogy of the well-shaped human body, in which he says there is a perfect harmony between all parts.  In Chapter II, Vitruvius suggests,” Order gives due measure to the members of a work considered separately, and agreement to the proportions of the whole.” 

Vitruvius perceived the human body as the basis for achieving harmony in architecture.  He mentions the height of a well-shaped man is the same as the span of his outstretched arms, these two equal measures yielding a square which encompasses the whole body, while the hands and feet touch a circle centered upon the navel. 

This relatedness of the human body to the circle and the square rests upon the idea of “squaring the circle,” Both shapes were considered perfect and sacred. The circle was recognized as symbolic of the heavenly orbits and the square as a representation of the firmness of the earth.


Renaissance architects, returning to the mathematical systems of antiquity, utilized these geometry’s to develop rules for proportioning the size of rooms and facades in simple mathematical terms.

Palladio in The Four Books on Architecture stated:

“Beauty will result from the form and correspondence of the whole, with respect to the several parts, of the parts with regard to each other, and of these again to the whole; that the structure may appear an entire and complete body, wherein each member agrees with the other, and all necessary to compose what you intend to form.”  -Book I, Chapter I

Architects of the Renaissance, believing their buildings had to belong to a higher order, returned to the Greek mathematical system of proportions.  Just as the Greeks conceived music to be geometry translated into sound, Renaissance architects believed that architecture was mathematics translated into spatial units. Pythagoras discovered that the consonances of the Greek musical system could be expressed in the simple ratios, 1:2, 1:3, 2:3, 3:4.  Applying Pythagoras’s theory of means, ratios developed that formed the basis for the proportions of Renaissance architecture.  These series of ratios manifested themselves not only in the dimensions of a room or facade, but also in the interlocking proportions of a sequence of spaces or an entire plan.

Le Corbusier

During the 20th century, Le Corbusier recognized the inherent potential and richness of the human body and adopted the golden section as a basis for his proportioning system, “The Modulor.”   He stated:

“An inevitable element of Architecture.  The necessity for order . . . a guarantee against willfulness.  It brings satisfaction to the understanding . . .   It confers on the work the quality of rhythm . . .  It is one of the vital operations of architecture.”  -Le Corbusier, Towards a New Architecture

He developed his proportioning system to “the dimensions of that which contains and that which is contained.”  He saw the measuring tools of the Greeks and other civilizations as being “infinitely rich and subtle because they formed the mathematics of the human body. He therefore based his  measuring tool, the Modulor, on mathematics, the aesthetic dimensions of the Golden Section, and the proportions of the human body. 

The principle work of Le Corbusier that exemplified the use of the Modulor was his Unite’ d’habitation at Marseilles, 1946-1952.  It uses measures of the Modulor to bring human scale to the building.

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