Musical proportions at the basis of systems of architectural proportion both ancient and modern

Abstract

Throughout the history of architecture there has been a quest for a system of proportion that would facilitate the technical and aesthetic requirements of a design. Such a system would have to ensure a repetition of a few key ratios throughout the design, have additive properties that enable the whole to equal the sum of its parts, and be computationally tractable—in other words, to be adaptable to the architect’s technical means. The repetition of ratios enables a design to exhibit a sense of unity and harmony of its parts. Additive properties enable the whole to equal the sum of its parts in a variety of different ways, giving the designer flexibility to choose a design that offers the greatest aesthetic appeal while satisfying the practical considerations of the design. Architects and designers are most comfortable within the realm of integers, so any system based on irrational dimensions or incommensurable proportions should also be expressible in terms of integers to make it computationally acceptable.