The Origins of Le Corbusier’s Modulor

Miguel A. Martín
Architecture, Senior
ARLH 208: Modern Architecture 2
Professor Rossell
Winter 2010
MW11
February 26, 2010

The Origins of Le Corbusier’s Modulor:
Adaptive Reuse of Historical Precedence

The twentieth century gave rise to grate masters of architecture and design. During the middle of the century on the onset and outbreak of world conflict many architects including Le Corbusier switched from the construction of design to a more theoretical exploration of design. Le Corbusier developed and patented an interesting methodology of scaling the proportions of his architecture to the human body. However his Modulor system was far from original, it was developed upon long standing systems of proportions which were historically developed in pursuit of discovering and establishing a universal proportional law.

When studying modern architecture of the twentieth century, it is hard not to bring up the works of Le Corbusier. Charles Edouard Jeanneret, (Le Corbusier’s birth name) was born in a Swiss watch making town close to the French boarder named La Chaux-de-Fonds.(1) As a child, Le Corbusier studied as an industrial designer and engraver at the local school.(2) Le Corbusier never formally studied as an architect and began to branch into the field when he was eighteen. His first series of buildings where developed in the tail end of the arts and crafts movement in his home town.(3) It was not until the pre-war era when his Purist Villas began to explore proportional systems.(4)

Within Le Corbusier’s collection of works, his Purist Villas of the pre-war era demonstrate the earliest examples of his use of proportional systems to regulate and justify his designs. Le Corbusier’s tools of choice were the Traces Regulaleurs or Regulating Lines. Le Corbusier described these lines as a “necessity for order … a guarantee against willfulness … a means to an end…”(5) The use of regulating lines to define the measurements for building elements such as “doors, windows, panels etc.” can be exemplified with Le Corbusier’s 1916 Villa (Fig. 1)(6). The use of Regulating Lines for design and layout was not unique to Le Corbusier; he admits in his own writings that his observations of renaissance masters such as Michelangelo and his design of the Capitol in Rome led Le Corbusier to develop his similar principles (Fig.2)(7).

Another fine example of Le Corbusier’s use of Regulating Lines can be seen in his design for the Villa at Graches in 1927. Here Le Corbusier uses the Regulating Lines to measure a pattern of structural bays of 2-1-2-1-2 (Fig.3)(8). At this point in Le Corbusier’s Carrier, he has moved past the use of Regulating Lines as a design system; “Rather Le Corbusier used regulating lines to make certain modifications and corrections in his plan or verify and confirm them.”(9) It was not until after the construction of the Villa at Graches that Le Corbusier produced drawings that featured the facades of the villa with a note of .618 in references to the “Golden Section”(10). None of Le Corbusier’s pervious drawings featured this note and appeared to be used as a means of justification and verification of his proportions(11).

Jeffery Hildner a Professor at the University of Virginia discusses in his paper, “Remembering the Mathematics of the Ideal Villa” the specifics of the use of the golden section with respect to the Graches Villa structural system and its proportions. The Villa demonstrates a numerical sequence that relates to the structural bays and to the ratios of their formations(12). Even though Le Corbusier was never formally educated in the sciences, he flexed his mathematical knowledge when incorporated the use of an elegant ratio of a square to a double square(13).

The mathematical ratio of the “Golden Section” can be traced to many cultures, such as the Babylonians (Fig. 4), Egyptians (Fig.5), Greeks, and eastern Buddhist (Fig. 6) cultures(14). Perhaps the most influential on Le Corbusier were the Greeks and their construction of the Parthenon (Fig. 7)(15). The “Golden Section” can be represented in the ratio of((1+ √5)/2:1), which can be approximated to 1.618:1 which again relates back to Le Corbusier’s added notation to his drawings of the Villa at Graches(16). The ratio between the Graches structural bays has been referred to as a 2-1-2-1-2 ratio but can also be represented as A-B-A-B-A. This interchange of representation of the ratio yields another historical inspiration that of the “rhythm of Palladio’s Italian villa.”(17)

The series of ratios that were expressed in these historic examples can be related to musical harmonies. When comparing the proportions at the Villa at Graches there is a variation between the North-South facades and the East-West facades. This variation is the doubling of proportions from the smaller façade to the larger and “the grid is now seen to be ordered by four significant numbers: 1, 2, 3, and 4.”(18) If the interrelationships of the structural grid were to be broken down into independent ratios such as 1:2, 1:4, 1:3, and 3:4 the villa’s harmonic schema can be seen (Fig. 8)(19). Graches can be considered a “finely tuned Pythagorean instrument… [that acts] as [a] regulator of visual and organizational phenomena…” (20)

The “Golden Section” was examined by Leonardo Da Pisa, also known as Fibonacci who discovered a mathematical relationship (a + b) : a = a : b which produces a sequence of numbers that rapidly approaches the Golden Section(21). Extraordinarily the relationship between Fibonacci sequences and the “Golden Section” has become a center of Western mathematical thought(22). Several men including Zeising and Hambridge produced treatises before Le Corbusier even began to develop his work at Graches(23). Zeisings asserted that the “Golden Section” was an underlying proportion system that could be applied universally to everything; while Hambidge assumed that the logarithmic spiral of botanical growth could be applied to structure(24). These systems would have a short lived presence due to their quest of universal application which was universally questioned.

In the years leading up to the Second World War, France, like most of the world had fallen into an economic depression. Compounded by the political turmoil in Europe during the years of conflict, Le Corbusier and other architects from the same era found themselves increasingly restricted in the number of commissions gained from their respective homelands(25). Some of the commissions Le Corbusier received during the thirties “often included new ideas that others exploited even before he was able to do so himself in executed work.”(26) In these situations Le Corbusier was commissioned as a consultant only, like his work on the Ministry of Public Health in Rio de Janeiro which was later developed by a number of architects including Lucio Costa and Oscar Niemeyer (Fig. 9)(27). Le Corbusier began to refine his ideas in his Modulor project which he would later execute after the war.

The post-war years left much of Europe in a mode of reconstruction. Le Corbusier had already been working on his Modulor project in hopes it would fall into a “role as a framework within which to design ‘standards’, types or models, so as to ensure a high level of refinement in the product to be mass produced.”(28) The notion of mass produced housing was not new to Le Corbusier, who had previously designed prototypes like the Maison Citrohan and the Freehold Maisonettes (Fig. 10 and 11). There was a genuine necessity for standardization for the production of an estimated one million homes in order to “prevent the key problems expected as a result of the industrialization of the construction industry.”(29) In the years leading up to the end of the war and just after, several groups meet within Europe to discuss these needs.

One major organization developed in efforts to standardize the process of construction was the Association Française de Normalisation (the French Association for Standardization) or the AFNOR. This organization, founded in 1940 was composed of politically appointed architects, engineers and other experts(30). Initially this organization would only grant Le Corbusier the right to practice architecture (even though he lacked a formal degree) and deny him admittance to the committee in charge of developing the standards. Le Corbusier appealed for appointment “detailing his continuous professional concern with these [standardization] issues.”(31) Eventually the AFNOR would grant him an appointment, however Le Corbusier soon realized his ideas that would eventually develop in to the Modulor would fall upon deaf ears. In 1941 Le Corbusier split from the AFNOR to form his own group, ASCORAL or the Association des Constructeurs pour la Rénovation Architecturale (32). The aim of this group was to seek out laws of universal harmony in a “series of standards implicitly superior to those being developed by AFNOR.” (33)

Le Corbusier’s answer to the standardization of the construction industry was his modular. It was developed on the principles of proportions set forth by the “Golden Section” and Fibonacci sequences. However unlike his predecessors, Le Corbusier regulated his proportional schema to the realm of relative rather than absolute standards (34). “Taking man in his environment, instead of [utilizing] universals” Le Corbusier was able to quell some skeptics due to its lack of “metaphysical connotations”(35) Le Corbusier stated in his own manifesto that “man looks at the creation of architecture with his eyes, which are 5 feet 6 inches from the ground (Fig. 13).(36)” Relating the human body to Modulor enabled a “co-ordination at every level from town planning to furniture.”(37) The Modulor which consisted of “two divergent series of irrational numbers derived from the Golden Section” had its roots in the early proportional explorations by Le Corbusier in his work on the purist Villas like that of Graches (Fig. 12)(38).

Figures

Le Corbusier, 1916 Villa

Le Corbusier, 1916 Villa

Michelangelo’s Capitol of Rome

Michelangelo’s Capitol of Rome

Le Corbusier: Villa at Garches North elevation

Le Corbusier: Villa at Garches North elevation

Ziggurat at Ur

Ziggurat at Ur

Great Pyramid of Cheops

Great Pyramid of Cheops

Tibetan Canon for Buddha Figures

Tibetan Canon for Buddha Figures

Parthenon

Parthenon

Villa at Graches Harmonic Ratios

Villa at Graches Harmonic Ratios

The Ministry of Public Health, Rio de Janeiro

The Ministry of Public Health, Rio de Janeiro

Maison Citrohan

Maison Citrohan

Freehold Maisonettes

Freehold Maisonettes

The Modulor Series

The Modulor Series

Modular Series related to Human Stature

Modular Series related to Human Stature

Table of Figures

Figure 1 Le Corbusier, 1916 Villa
Le Corbusier, Towards a New Architecture, Reprint ed. 1931 (Mineola, NY: Dover, 1986), 80

Figure 2 Michelangelo’s Capitol of Rome
Le Corbusier, Towards a New Architecture, Reprint ed. 1931 (Mineola, NY: Dover, 1986), 78

Figure 3 Le Corbusier: Villa at Garches North elevation
Roger Herz-Fischler, “Le Corbusier’s ‘Regulating Lines’ for the Villa at Garches (1927) and Other Early Works,” Journal for the Society of Architectural Historians 43, no.1 (March, 1984):54.

Figure 4 Ziggurat at Ur
Gyorgy Doczi, The Power of Limits: Proportional Harmonies in Nature, Art & Architecture. (Boston: Shhambhala, 2005): 47.

Figure 5 Great Pyramid of Cheops
Gyorgy Doczi, The Power of Limits: Proportional Harmonies in Nature, Art & Architecture. (Boston: Shhambhala, 2005): 41.

Figure 6 Tibetan canon for Buddha figures
Gyorgy Doczi, The Power of Limits: Proportional Harmonies in Nature, Art & Architecture. (Boston: Shhambhala, 2005): 113.

Figure 7 Parthenon
Gyorgy Doczi, The Power of Limits: Proportional Harmonies in Nature, Art & Architecture. (Boston: Shhambhala, 2005): 108.

Figure 8 Villa at Graches Harmonic Ratios
Jeffery Hildner, “Remembering the Mathematics of the Ideal Villa,” Journal of Architectural Education 52, no.3 (February, 1999): 146.

Figure 9 The Ministry of Public Health, Rio de Janeiro
Henry-Russell Hitchcock, Architecture: Nineteenth and Twentieth Centuries, 4th ed. (New Haven: Yale University Press, 1977), 520

Figure 10 Maison Citrohan
William J.R. Curtis , Modern Architecture Since 1900s, 3rd ed. (New York: Phaidon Press, 1996), 170

Figure 11 Freehold Maisonettes
Le Corbusier, Towards a New Architecture, Reprint ed. 1931 (Mineola, NY: Dover, 1986), 246

Figure 12 The Modulor Series
Le Corbusier, The Modulor, Reprint ed. 2004 (New York: Faber and Faber, 1954), 51

Figure 13 Modular Series related to Human Stature
Le Corbusier, The Modulor, Reprint ed. 2004 (New York: Faber and Faber, 1954), 67


Notes

1 Kenneth Frampton, Modern Architecture: A Critical History, 3rd ed. (London: Thames & Hudson, 1992), 149
2 Ibid.
3 Ibid.
4 Judi Loach, “Le Corbusier and the Creative Use of Mathematics,” The British Journal for the History of Science 31, no.2 (June, 1998):185-215.
5 Le Corbusier, “Towards a New Architecture: Guiding Principles,” in Programs and Manifestos on 20th-century Architecture, ed. Ulrich Conrards, trans. Michael Bullock (Cambridge, Mass.: The MIT Press, 1971), 60.
6 Le Corbusier, Towards a New Architecture, Reprint ed. 1931 (Mineola, NY: Dover, 1986), 80
7 Ibid. 78
8 Roger Herz-Fischler, “Le Corbusier’s ‘Regulating Lines’ for the Villa at Garches (1927) and Other Early Works,” Journal for the Society of Architectural Historians 43, no.1 (March, 1984):53-59.
9 Ibid. 57
10 Ibid. 53-56
11 Ibid.55
12 Jeffery Hildner, “Remembering the Mathematics of the Ideal Villa,” Journal of Architectural Education 52, no.3 (February, 1999):143.
13 Ibid. 145
14 Gyorgy Doczi, The Power of Limits: Proportional Harmonies in Nature, Art & Architecture. (Boston: Shhambhala, 2005).
15 Jeffery Hildner, “Remembering the Mathematics of the Ideal Villa,” Journal of Architectural Education 52, no.3 (February, 1999): 147
16 Rudolf Wittkower, “The Changing Concept of Proportion,” Daedalus 89, no.1 (Winter, 1960):202.
17 Hildner, “Remembering the Mathematics of the Ideal Villa”: 147
18 Jeffery Hildner, “Remembering the Mathematics of the Ideal Villa,” Journal of Architectural Education 52, no.3 (February, 1999):145.
19 Ibid. 146
20 Ibid. 147
21 Rudolf Wittkower, “The Changing Concept of Proportion,” Daedalus 89, no.1 (Winter, 1960):204-205.
22 Ibid.
23 Ibid.
24 Ibid 205-206.
25 Henry-Russell Hitchcock, Architecture: Nineteenth and Twentieth Centuries, 4th ed. (New Haven: Yale University Press, 1977), 519
26 Ibid.
27 Ibid 519-520.
28 Judi Loach, “Le Corbusier and the Creative Use of Mathematics,” The British Journal for the History of Science 31, no.2 (June, 1998):202.
29 Ibid.
30 Le Corbusier, The Modulor, Reprint (New York: Faber and Faber, 1954), 33.
31 Judi Loach, “Le Corbusier and the Creative Use of Mathematics,” The British Journal for the History of Science 31, no.2 (June, 1998): 203
32 Ibid.
33 Ibid.
34 Rudolf Wittkower, “The Changing Concept of Proportion,” Daedalus 89, no.1 (Winter, 1960):212.
35 Ibid.
36 Le Corbusier, “Towards a New Architecture: Guiding Principles,” in Programs and Manifestos on 20th-century Architecture, ed. Ulrich Conrards, trans. Michael Bullock (Cambridge, Mass.: The MIT Press, 1971), 61.
37 Judi Loach, “Le Corbusier and the Creative Use of Mathematics,” The British Journal for the History of Science 31, no.2 (June, 1998): 204
38 Wittkower, “The Changing Concept of Proportion”: 212

Bibliography

Primary Sources
Le Corbusier. The Modulor. New York: Faber and Faber, 1954.
Le Corbusier. Towards a New Architecture. 1986 Reprint. Mineola, NY: Dover, 1931.
Le Corbusier. "Towards a New Architecture: Guiding Principles." In Programs and Manifestos on 20th-century Architecture, by Ulrich Conrads, translated by Michael Bullock, 59-62. Cambridge, Mass.: The MIT Press, 1971.
Secondary Sources
Curtis, William J.R. Modern Architecture Since 1900. 3rd. New York: Phaidon Press, 1996.
Doczi, Gyorgy. The Power of Limits: Proportional Harmonies in Nature, Art & Architecture. Boston: Shambhala Publications, 2005.
Frampton, Kenneth. "Modern Architecture: A Critical History." 149-160. London: Thames & Hudson, 1992.
Herz-Fischler, Roger. "Le Corbusier's "Regulating Lines" for the Villa Garches (1927) and Other Early Works." Journal of the Society of Architectural Historians 43, no. 1 (March 1984): 53-59.
Hildner, Jeffrey. "Remembering the Mathematics of the ideal Villa." Journal of Architectural Education 52, no. 3 (February 1999): 143.162.
Hitchcock, Henry-Russell. Architecture: Nineteenth and Twentieth Centuries. 4th. New Haven: Yale University Press, 1977.
Loach, Judi. "Le Corbusier and the Creative Use of Mathmatics." The British Journal for the History of Science 31, no. 2 (June 1998): 185-215.
Wittkower, Rudolf. "The Changing Concept of Proportion." Daedalus 89, no. 1 (Winter 1960): 199-215.

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