Strange attractor 24.41/14.81/9.44
T H E T R I L A T E R A L D Y N A M I C
T. Friebel PH Pavilion 5 models compared
The three apex points, governing the height and aesthetic of the pavilion.
THREE VOCATIONS UNITE: THE MODULOR, METASTASEIS AND THE PHILIPS PAVILION
Fibonacci (notice form is uncontained) 21/13/8
TAMARA FRIEBEL Supervisor: Brent Allpress Fibonacci 34/21/13
The more abstract the truth you want to teach, the more you must seduce the senses to it.1 Nietzsche This thesis shows the )0#102* of an attempt to more clearly understand the relationship between three elements of the Xenakis le Corbusier oeuvre: Modulor, Metastaseis and the Philips Pavilion. This study focuses on uncovering the nature, development and rigour of this trilateral relation to see how the balanced rhythm between the different elements enables a richer understanding of each part to its whole. In a number of different sources that Xenakis has edited or written, he has stated that there is a symbiotic relation between the Modulor and its outcomes in Metastaseis, and that his composition, in turn, 103$.0,.# the design of the pavilion. There is no explicit statement regarding the use of the Modulor in the PH Pavilion, except by way of its inclusion through Metastaseis. This study follows the research which currently exists on the relation of these three elements and reveals, to the writer’s knowledge, the )&*+ more concrete explanation of the use of the Modulor in the PH Pavilion, that is, independent of its presence through the Metastaseis diagrams. Each aspect of the trilateral dynamic is explored in relation to itself, and in turn how it influences the other elements.
Strange attractor average 32.3/23.3/20
DIAGRAMMATIC ARCHITECTONICS: CATIA AS AN AESTHETIC GENERATOR TO STUDY PROPORTIONAL SYSTEMS The pursuit of the Modular and the extent to which it could be held responsible for certain finite constraints, thereby engendering the design of the PH Pavilion, was a diagrammatic tectonic aspect of this study. Through a process of postdiagramming the pavilion in the parametric software CATIA, it was demonstrated that the collected trial design schemes of the pavilions rigorously employed the Modular to help define the aesthetic form and the engineering balance of the final built form.
!"#$%"&'(')&*+'*,-./. 17/13/11
Xenakis’s translation from his composition Metastaseis into the PH Pavilion can be understood at different levels. The graphic translation of the hyperbolic curve is clear. This study modelled the explicit use of the Modular 1 for the l’estomac planning proportion, and for the three apex points, governing the height and formal aesthetic impact of the pavilion. This was verified by comparing the development from Scheme 1 to Scheme 2. Both of these variants employed the use of the Modular 1 to define the apex points. The PH Pavilion models allowed a comparison of the fine effects of the differences between Modular 1 and 2, the Fibonacci series, and a system extrapolated from a strange attractor selected after randomly searching that showed a remarkable similarity to the Fibonacci and Modular series.
T. Friebel STL prototype models of Variations
Modulor 1 second scheme 21/18/13
The design work on the PH Pavilion consisted of an architectural design methodology revealed as one of the earliest engagements with parametric variation. The possibilities that Xenakis and le Corbusier painstakingly achieved through trial and error, in drawings and maquettes, were further trialled in this post diagrammatic exercise with STL models, with the help CATIA, making visually legible the place that rigorous constraints held within this particular bound field of parametic design. 1
Modulor 1 accurate 21.6/17.5/13.3
Friedrich Nietzsche, Beyond Good and Evil, Fourth Part: Maxims and Interludes, section 128 (1886)
Xenakis sketch(25m/40m), PH Pavilion l’estomac, Modulor 1: 25.06/40.55 vs. (Modulor 2: 27/43.2) Le Corbusier, Excerpt Modulor 1
Explicit use of the Modulor 1 for the l’estomac planning proportion. Modulor 1 built form 20.5/18.5/13
Modulor 2 14/11.3/8.6
Andre Baltensperger, Deutung der Gesamtform, Meaning of the entire form
Metastaseis, meaning before/after states, seeks a dialectical transformation. It has a Macro form which moves from order to complexity to disorder, before returning to order.
Modulor2 22.5/18.3/14 The causal chain of ideas that lead to the PH Pavilion, from I. Xenakis Formalised Music.
“... my inspiration was pinpointed by the experiment with Metastaseis. Thus I believe that on this occasion music and architecture found an intimate connection.” Xenakis
Bars 309314 and 317333 scaled according to harmony
In analysing the diagrams according to their same harmonic scale one can see the entirety of the range of breadth of sound.
T. Friebel PH Pavilion 5 models compared in PLAN & ELEVATION sections
T. Friebel Proportions compared
Bars 309314 and 317333 scaled according to time
The proportion of the diagrams, when related by their time scale, shows clearly the quickness of the ordered glissandi, the moment of reawakening from the stochastic hypertrophics. Xenakis, Metastaseis score, Bars 317333
T. Friebel Metastaseis Derivatives T. Friebel Derivatives from ELEVATIONS: 5 Models juxtaposed
The further diagrams which result from these studies, those which could be considered as toying with an illusion of understanding')0#'40'10+$1+15.'647'+"'.89%"&.'+-.'49.8.*'":'+-.';4&*'<(=><<<? T. Friebel Derivatives from PLANS: 5 Models juxtaposed
T. Friebel Derivatives Proportions juxtaposed
“The more constraints one imposes, the more one frees oneself of the chains that shackle the spirit.” Igor Stravinski