Divine Proportion: Simplified Constraint

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold, the second we may name a precious jewel.
–Johannes Kepler

The Trilateral Dynamic
Three vocations unite: the Modulor, Metastaseis and the Philips Pavilion

This thesis shows the findings of an attempt to more clearly understand the relationship between three elements of the Xenakis–Le Corbusier oeuvre: the Modulor, Metastaseis and the Philips Pavilion.  The study persists in uncovering the nature, development and rigour of this trilateral relation, and to see how the balanced rhythm between the different elements enables a richer understanding of each part to its whole.  It is clear chronologically, that the Modulor was first developed from 1942, primarily from Le Corbusier, and from 1953 Xenakis composed Metastaseis, and then the PH Pavilion was created as a collaborative effort from 1957.  What is less clear, is how these relations actually influenced each other.  This thesis draws on the research already available, and attempts to more clearly show evidence of the imagination between these elements and to some extent, to examine the possible strength of forces of such a delicate intuitive dynamic.  The Le Corbusier–Xenakis relation was naturally a dynamic force which enabled collaborations across different fields, in this case music and architecture.  It is true that the composition Metastaseis would still exist without the creation of the PH pavilion, but it is not true of the pavilion.  This was the result of the germ of the ideas within the composition, and both creations claimed the use of the Modulor.  It is true too that the Modulor exists as a system, without its products, found here in Metastaseis and the PH Pavilion.  Yet, through the fluid interchange between these three outcomes, it becomes clear that whilst the chronology of their creation is important to know, the richness of understanding that is further possible is not limited by their order of events.  This is because a post-analysis has the luxury of a larger meta-narrative where relations can be sensed together, examining places where the artist/s may have chosen to conceal, or where the creational process remained inexplicable or elusive due to an order of learned or curated intuition.

Hyperbolic paraboloids were present in the French pavilion in Brussels 1958, where two shallow intersecting shells with edges reinforced by truss beams, webbed with a hyperbolic paraboloid roof.  Treib comments that the spans achieved by the Philips pavilion structure, however, were minuscule, with the shell forms effectively eliminating most planes that could be termed “roof”.  “One assumes that the spatial, rather than the structural, properties of warped structures were what really interested Le Corbusier and Xenakis.  Professional criticism of the French pavilion commented on the discord between the expressive structures of the pavilions and their internal contents. The Philips pavilion, however aimed at an aesthetic unity between the different shell fragments, draped around a warping stomach plan.  “The hyperbolic paraboloid was structurally sophisticated because the strength of its warped surface derived—almost mystically—entirely from straight lines.”

For more information and publications:
Friebel, T. (2007) Masters Thesis: The trilateral dynamic: Metastaseis, the Modulor and the Philips Pavilion. RMIT: Melbourne. [In: Kocatürk, T.Medjdoub, B. (2011) Distributed Intelligence In Design. Allpress, B. “Pedagogical frameworks for digitally networked architecture,” UK: Wiley-Blackwell]

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