L < Co,Bu•I« Dovdopod Tho Modulo, ')"T<M of Proportion Botwoon

The MIT Press Cambridge, Massachusetts London, England The Projective Cast Architecture and Its Three Geometries Robin Evans Chapter Seven Comic Lines By pulling his guideropes harder, he was L< Co,bu•i« dovdopod tho Modulo, ')"t<m ofproportion botwoon 1943 and 1955, designed and built the chapel at Ronchamp between able to bend the skiffappreciably; this was 1950 and 1955, said the Modulorwas in the chapel, and then challenged possible because his tiller did not simply con- anyone to find it there. In his book on Ronchamp he wrote that his building was "informed by all embracing mathematics," and declared: trot a flat rudder aft, but bent the long keel, "The Modulor everywhere. I defY the visitor to give, off hand, the di 2 from the fore-end, to right to left, upward mensions of the different parts of the building." In his book on the Modulor he wrote of Ronchamp: "It was a pleasure, here, to allow free and downward, according to his directional play to the resources of the Modulor, keeping a corner of one's eye on the game to avoid blunders. For blunders lie in wait for you, beckon you requirements. on, tug at your sleeve, drag you down into the abyss." 3 Le Corbusier was very fond of quoting Albert Einstein's generous epigram that the Modu Alfred ]arry, Exploits and Opinions of lor was a way of proportioning things that "makes the bad difficult and Dr. F austroll, Pataphysicist1 the good easy," 4 yet he himself seems to have been in at least two minds about it. Only ten days or so after distributing Modulor tape measures to his assistants, he forbade their use. 5 But the Modulor was given free play at Ronchamp. The word "free" oc curs often in this building's history. Canon Ledeur tempted Le Corbu sier to accept the chapel commission with an assurance of total creative freedom. Le Corbusier described what he did there as "totally free archi tecture,"6 and discussed it in a chapter entitled "Free Art" in Modulor II Of all his work, Ronchamp is the building that seems to have escaped 1 +-.JS architecture's limited inventory of forms most completely. The appar 1:-2-, ently successful escape from the restraint of drawing board geometry is so the dimensions had to be approximations. The Fibonacci series, an an important ingredient of its perceived freedom. It is also the reason additive series in which the ratios between successive terms converge to why Modulor proportions are hard to find, for the Modulor belongs to ward the golden section, made the calculations much easier. (Start with a long line of theories on the subject of architectural proportion that pre any two numbers, add them together to get a third number, then add the suppose comparisons between flat rectangular shapes, and, since these second and third to get a fourth, and so on-for example, 1, 1, 2, 3, 5, are few and far between at Ronchamp, we are led to believe that the 8, 13, etc.). Because inconveniently large gaps were left on the ladder of Modulor must have some deeper, hidden presence in the architecture. dimensions, a second sequence from 1.13 meters was intertwined with the first. The two syncopated sequences, one twice the other, were called the red and the blue series. 7 147 Notre-Dame du Haut, Ronchamp, The most notable features of the Modulor were the attempt to make Le Corbusier, 195G-1955, view.from practical, anthropometric dimensions ("measures ... related to the stat ure of man") identical with aesthetic proportions. and the doubling up of south. the series-a simple but elegant way of producing further proportional resonances while reducing the distance between consecutive Modulor measures. All this can be gleaned from the two rambling volumes of the Modulor, published in 1950 and 1955. They give the impression of being hastily edited, personal notes that sometimes read like confessions where one would expect the impersonal language of the log book. In one respect, though, these journals, although full of self-congratulation, are generous, even selfless, since they expose to public view thoughts that are normally kept out of sight. Candid exposure of the ego can turn heroes into clowns. Le Corbusier, acknowledged for decades to be a great architect, was dabbling in mathematics, about which he understood little. He tells us so. He makes mistakes. He records them when others point them out, but persists, and ends up convincing himself that the original mistakes were somehow more true than the corrections. 8 What makes study of the Modulorworthwhile, despite its amateur math The Modulor began as an ambitious but prosaic attempt to solve the ematics and strident proclamations, are the insights it offers into the di problem of coordinated dimensioning throughout industry and ended up lemmas of architectural design, especially the difficulty of being both as an equivocal statement of faith in an order that lies beyond cognition. certain and free. Any rule carries with it the eventual prospect of reduced Meanwhile Le Corbusier, helped by many others, developed a system of liberty, but new rules can be surprisingly unruly, clearing away customs proportioning, less elastic than most because it was tied to a specific set and habits that have stood in the way for ages. Thus, for a time, perhaps of measurements. A string of dimensions in a constant ratio was extrapo quite a long time, new rules can offer a way round the obvious. In the lated from 2.26 meters, finally agreed upon as the height of a man with first place, the Modulor would "change everything, opening the doors of arm upraised. The ratio was the golden section, vaunted since the mid the mind to the free flow of the imagination." 9 Then, perhaps, in the nineteenth century as the mathematical fount of physical beauty. The longer run, it would provide an instrument on which to play inexhaust 148 Le Corbusier, The Modulor, red golden section is irrational, ible themes. Both possibilities were contemplated by Le Corbusier. The and blue series. instrument that he had in mind was not such as a violin, which has no THE P R 0 J E C T IV E CAST 274 C 0 M I C L I N E S 275 inbuilt restriction of pitch, but a keyboard, which is constructed in accor through our use of language: the opposite of a man is a woman. Lan dance with the rigid intervals of the musical scale. For him this was the guage enables us to deny this, but makes affirmation easier. important thing: the tempered scale had expanded the horizons of music by defining the intervals between notes more exactly. So when Le Cor Just look at the way in which our understanding ofLe Corbusier's career busier's assistants produced miserable results with the aid of the Modular is facilitated by pitting opposites against one another: functionalism ver (which they did), he would say that he had given them a tuned instru sus symbolism, the international versus the regional, the autocrat versus ment that they were incapable of playing properly. At first he liked to the populist, the technocrat versus the poet, rationality versus irrational think that the Modular might sweep away the imperial and metric scales ity, progress versus origin, science versus myth, the machine versus the of linear measurement, just as equal temperament had swept aside less hand, calculation versus intuition, surface versus mass, the straight line adaptable musical scales. versus the curved, geometric versus free form. It is a useful list, the more easily applied because most of these distinctions can be found in Le Cor These relatively sophisticated, though extravagant, arguments show that busier's writings. Le Corbusier can be presented as two consecutive sides the issue of freedom-the artist's freedom-was made prominent by Le of an argument, passing from one proposition to another in a phase Corbusier in the Modular as well as at Ronchamp, although we are still change that extended from 1928 to 1950. He was thus twice able to cre no nearer to understanding how the rectilinear system of proportion was ate architecture anew, as Jencks put it, 13 first in accordance with the left applied to the curving chapel. hand terms, then with the right-hand terms of these antonyms. Many judicious commentators point out that this picture of the two Corbusiers The world according to Le Corbusier was divided. As it got more so, is oversimplified, but even those who reject it as a general explanation of intimations ofjoining the broken halves became more frequent. Le Cor his work often resort to it in explanation of Ronchamp, which is rightly busier had always held out prospects of resolution, and there was always regarded as an extreme case. "Ronchamp expresses a liberation of Corbu a strong hint that he, personally, was to be the agent of reconciliation. sier from Corbusier," proclaimed the Princeton professor Jean Labatut Latterly his identity shifted from the administrator who makes the world in 1955.14 work properly to the artificer who puts the image of the world back to gether. The recent critical attention devoted to Le Corbusier's powers of In this same picture the Modular registers as a last, faltering attempt to synthesis in his later work is quite justified, yet we might contemplate discover a rational basis for architecture, an attempt that was superseded the possibility that Le Corbusier exaggerated divisions so that his por before it was complete. Le Corbusier's decade of investigations into pro trayal of himself as potential unifier should hold good.

Load more