TOPIC QUESTION: IN WHAT WAYS CAN ‘THE MODULOR’ AND THE IDEAS IT
CONTAINES BE USED TO INTERPRET UNITE D’HABITATION, ITS ARCHITECTS
INTENTIONS AND THE CULTURAL CONTEXT IN WHICH THE BUILDING WAS
PRODUCED?
Le Corbusier created the ‘Modulor’ with the intentions of reviving the connections
between the proportions of man and architecture. The technological developments of the
20th century enabled Le Corbusier to bring his vision to reality. To understand the
mathematical concepts and derivations behind the ‘Modulor’ and how they are applied to
building designs, it is important to consider the individuals who influenced and contributed
to the study of human proportions. These include famous architects and mathematicians
such as Vitruvius, Pacioli, Neufert and Zeising. Alongside these individuals, mathematical
concepts such as the the Golden Ratio, the Golden Section and the Fibonacci series are
also significant in the development of Le Corbusier’s ‘Modulor’ In this essay, I will analyze
the historical and cultural context in which contributed to the development of the ‘Modulor’,
and how it plays a significant role in interpreting the structural dimensions of the Unite
D’Habitation in Marseilles. Moreover, the proportioning system the ‘Modulor’ operates on,
reflects Le Corbusier’s design philosophy of integrating human proportions into
architecture.
To understand Le Corbusier’s ideas towards the human proportions which he
explains in the ‘Modulor’, we must discuss the very early ideas that arguably started the
whole system of proportional design. Vitruvius was known to be one of the earliest
architects to examine the human body and apply it to architectural theories, creating an
early stage of a proportioning and design system. His works of ‘De architectura’ shows his
detailed drawing of his canon, which includes a man placed inside a circle and a square.
He uses it as an example of nature’s modulor development and as a model for the
proportional rules that must be followed. “What Vitruvius is regarding is an immobile man,
without volume or inner vitality; he is a simple ideogram characterized merely by the
potential of his measurements to form geometric and proportional relationships”. (Mario
Curti, 2014, p1) His technique of the navel as the centre of a circle circumscribing the
outstretched hands and feet shows very similar ideas to the six-foot man with his arm
raised. Le Corbusier took this to his own understanding and created the Golden Section in
a way that was psychological rather than practical. His interests, like Le Corbusier, trails
back to Greek architecture where he claimed that “no Temple can have a rational
composition without symmetry and proportion, that is, if it has not an exact calculation of
members like a well-shaped man”. Le Corbusier believed that he had discovered a
“measurement unit that harmonized with the human scale, universally applicable both to
architecture and mechanics” in the Modulor, which he created using the golden section. It
can be argued that while finding the proportion of the Modulor man, he was indulged with
the mathematical derivations from the Hellenistic period, inspiration which Vitruvius also
took but he was unable to fully understand the meaning of the conflict between idea and
nature. Only until he continued Vitruvius works to creating the Golden Section, the Modulor
became much clearer.
In the early renaissance, the Golden Section was an important mathematical
theory that was heavily used for architecture. Architect Luca Pacioli became determined to
revive the proportional involvement into architecture during the renaissance period and this
heavily influenced Le Corbusier as well. Firstly, Pacioli was known to be a great admirer of
the Golden Section, as evidenced by the name of his treatise, Divina proportione, which
comprises 3 independent work. The difference between Vitrivus and Pacioli could be
argued that Pacioli was more of an admirer of the Golden Section whereas Vitruvius barely
mentioned or used it during his de architectura drawings. His experience from Greek
broadens his knowledge and he creates his own understanding of art and proportions.
Therefore, he is the first to acknowledge the so called homo vitruvianus with spread legs,
so that it must be expanded violently to fit the square, whilst involving his interest in the
Golden Ratio. One of Pacioli main contributions to creating a proportional and design
system was adding a third geometrical from, continuing from Vitruvius’ “homo vitruvianus”.
Unlike Vitruvius where he focuses on the entire human form, Pacioli draws an equilateral
triangle and positions it on a head profile (with irregular grid) since, in his opinion, the
human head is the noble part of the body and therefore the center of the measurement
system. Consequently, Pacioli begins his treatise with the basic forms of circle, square,
and triangle. From this theory, he recommends simple rations of integral numbers while
irrational numbers should be used separately. If Le Corbusier followed this advice, his
proportional principles in the Modulor might have turned out quite different with much better
accuracy but also Pacioli’s work was very significant with the use of the Golden Ratio that
led to Corbusier’s approach to the works of the Golden Section.
The Fibonacci Series became significant from the beginning of the proportional
system and without it, the Modulor would have never existed. To understand why that is,
we must examine its original studies by Adolf Zeising. He also took interest in human
proportions and the universal law, which was the golden section. As a result, he divides
the total height of a man’s body into four principal zones: top of head to shoulder, shoulder
to navel, navel to knee, and knee to base of foot. “He deals in a loose manner with
numbers, only using the lower numbers of the Fibonacci series as approximations,
replacing the 89 by 90.” (Marcus Frings, 2002, p18) He concludes that the proportion of
the first two zones to the second two is 1: Golden Ratio. Zeising can be argued to be one
of the first architects to introduce the Golden section into the literature on art and used in
for practice in architecture and he shows this in his creation of his own human proportion
drawings. It could be then argued that it influenced Le Corbusier to take interest into the
Fibonacci series as well. It can be seen in the Red and Blue sequences, the smaller values
mimic Fibonacci numbers and Le Corbusier prefers to calculate through this method
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instead of the golden ratio. “The Modulor system was inspired by classical foundation such
as the Vitruvian man but also by medieval number progressions taken from the Fibonacci
series, which Le Corbusier applied to a module of 2.26cm (which he then diminished to its
half: 1.13cm) and integrated with the golden section.” (Francesco Benelli, 2015, p7) As a
result, the approximate numbers of the Modulor scale inherit the Fibonacci property up to
errors caused by approximations. This would then lead to the final proportions that would
help Le Corbusier to easily apply it to his project but also concurrently exposes certain
deviations which probably had a negative impact on the idea of the Modulor, this will be
later discussed in this essay.
The 20th century showed a burst of interest in proportions and human interaction
with architecture. This age gave a rebirth to the Golden Section and applying it to
architecture. Architects such as Johannes Ludovicus Mathieu Lauweriks and Peter
Behrens experimented and attempted to develop their own system for human proportions.
Most notably Neufert and Le Corbusier. In the spirit of Antique, Gothic, and Renaissance
architecture, Neufert propagates the Golden Ratio as an architectural theory of proportion
that, when combined with his own normed steps, lead to a “spiritual permeation” and a
rebirth of architectural creation through “an inner law”. “In fact, Neufert and Le Corbusier
seem to use the Golden Section as a way to embellish their own subjective artistic creation
by theory and ratio.” (Frings, 2002, p26) Le Corbusier was inspired by Neufert and his
proportional system as the final Modulor drawing can be seen to take inspiration from his
drawing in Bauordnungslehre from 1943.
Before Le Corbusier approached the Modulor, he was strictly using the principle
of ‘traces regulateurs’ (or measure-rules) to his earlier projects. This was his initial stage
of ‘proportional’ design theory and applying it to his architecture, specifically his façade
designs. An example of his initial use of this proportion system is the Villa Stein at Garches,
built in 1927. He considers this design to be ‘the place of the right angle’ where he uses
regulating lines and the golden section. “The two main facades of the house are
approximate golden rectangles; in fact the basic diagram of the façade is identical with one
of the classic methods of constructing a golden section. The only difference is that here a
reciprocal golden rectangle (…) is inscribed at both ends.” (Richard Padocan, 1999, p324)
Here Le Corbusier uses a strict method of consistent repetition of similar proportions and
this was what mainly lead him to the Modulor where it gave him a complete system of
measures that automatically generated golden section and related ratios in whatever he
designed.
From the traces regulateurs, Le Corbusier created the Modulor and it was
essentially a final stage of his own proportional and design system, diagrams and
equations leading to the 6-foot man with an arm raised up. Firstly, I will try to describe the
mathematical point of view in simple terms, as many equations were derived leading to the
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final dimensions. He basically discovered a solution for harmonious mass production
standardization based on mathematical foundations and human scale. The Milliard
Diagram was designed to solve the problem of the ‘Three Squares’ construction where
trying to place a man-with-arm-upraised inside 2 squares to find the third square. “The
discovery or invention of the Modulor more effectively placed the architectural mind under
the ruling sign of the set-square.” (Alain Pottage, 1996, p66) Furthermore, the diagram
begins with a simple grey square of sides 1.10m and combining it with a golden rectangle.
By placing a midline in the grey square, we can find a point C so that ABC is a right angle.
Although, it is proven this approach it geometrically wrong but both this diagram and the
red and blue sequences use the Golden Ratio. The motives of this diagram made sense,
as it is apparent it descended from his passions, but the use of irrational numbers lead to
the impracticality of the Modulor for future use.
These flaws must be explained as it might have consequently be one of the main
reasons why the Modulor was shortly never used in practice after the building of the Unite
d’Habitation and any other of Corbusier’s later projects after this. The problem was the
irrational numbers that were used to find the dimensions of the 6-foot-modulor man. In the
Modulor, Le Corbusier discusses his Blue and Red sequences. This was a way to further
prove the proportions of the Modulor man after placing the figure onto the Milliard diagram.
The scale has four main features: it is focused on human proportions, it corrects a
mismatch between the Anglo-Saxon and French metric systems, it offers instructions for
building aesthetically from prefabricated materials, and it is calculated using the ‘right angle
law’ and the Golden ratio rule. “According to Le Corbusier’s theory, the presence of the
Golden ratio connects the scale with the rules of harmonic design. Hence by definition the
terms of the Modulor should form a geometric progression”. (Natasha Rozhkovskaya,
2019, p5) The outcomes of the Red and Blue sequences gave the final measurements of
red beginning with 1.83m, but then this did not satisfy Corbusier’s goal so he added the
blue row where the measurement reaches to height of the raised hand, reaching up to
2.26m instead of 1.83. This theory would then be applied to almost the entirety of Unite
d’Habitation’s architecture. The use of irrational numbers during the studies of the Red and
Blue sequences are impractical for design or construction. This is important as many of
the architects that came before Le Corbusier believed to stay away from using irrational
numbers, whereas Le Corbusier continued to do so in the Modulor. “Even a very high level
approximation comes at a cost: by switching to approximate values of the sequence, one
cannot satisfy both properties … for all elements of the sequence.” (Natasha
Rozhkovskaya, 2019, p5) These sequences were carefully derived from the golden ratio
and therefore forming a geometric progression, which created the red and blue sequences.
As he famously applied this theory onto Unite in Marsailles, this allows us to use Unite to
question whether it worked and will it still be practical enough for future use. For example,
the dimension of the interior spaces for the children’s rooms are proven to be quite
restricting and claustrophobic with little privacy that the children were forced to go outdoors
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in order to do some activities. Another good example can be seen inside Unite’s floor to
ceiling level that was raised past the Modulor’s height to 260cm. This design flaw also can
lead to an assumption that 230cm floor (based on Modulor dimensions) is just too low for
today’s standards.
In terms of cultural context, the production of Unite d’Habitation was due to the
main reason of the war. Post World War 2, housing demand increased after many of them
were destroyed. Corbusier already began his intentions of revolutionizing housing from the
First World War. Engineers only discovered new ways of combining different materials
together after the Second World War. This Premodernism era gave a clear pathway of
rebuilding many of these broken structures, but also using the Modulor as main
architectural theory when rebuilding these housings. This includes “Organic” architecture,
the influence of civil and military engineers, Functionalism and Rationalism. The availability
of these new engineered materials, such as the innovative reinforced conceret, gave the
recurrent silhouette with a narrow waist and wide shoulders a basic and yet great goal for
Le Corbusier, which was to literally give postwar architecture a bit of humanity and
objective order. “Geometry is the language of man” (Le Corbusier, 1923). It could be
argued that the Modulor and the hardships of the war gave Le Corbusier an opportunity to
begin a new style of architecture, which is known until this day as Modernism. The
combination of reinforced concrete and large glass windows gave birth to many of Le
Corbusier’s ideas and also notably future architects ideas, and this began with the
intentions of the Modulor.
Another way to view Le Corbusier’s approach to Unité d'Habitation is by combining
his theories of the Modulor with his 5 Points of Architecture. The first point explains “Pilotis”
– by replacing supporting walls by a grid of reinforced concrete columns. He became the
first architecture to make a studied use of rough-cast concrete. The invention and
availability of this new and adaptable material gave Corbusier the decision of entirely
designing the building to be made of reinforced concrete beams and pillars, with section
steel combined with short beams of folded sheet aluminum, balustrades of vibrated and
perforated concrete. Secondly, using a free design for the ground plan where there are no
supporting walls. This leaves the internal use very spacious. This point was not too
apparent as Corbusier’s design was strictly keeping the living spaces as spacious as
possible with no supporting walls or columns inside, including the corridors. Third point
states freeing the design of the facade by separating the exterior from its structural
functions and constraints, which ties with the fourth point where horizontal windows cuts
the façade along its entire length, therefore natural light hits the interior rooms equally. The
units are designed to extend from each side of the building and have a double height living
room, reducing the number of necessary corridors to one per three floors. He uses an
interlocking design strategy to support his third point, he does this by having 2 floors on
each room but only connected with one main corridor. By doing this, it allows the
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opportunity of placing more of these units interlocking each other. As a result, most of the
social activities are located on the roof of the building with only a few shops found inside
the Unité. Although a lot of Corbusier’s Modulor is not apparent inside, where instead of
230cm, the ceiling height reaches up to 260cm. This goes over the limit for the Modulor
but the reasoning of this is because 230cm is not suitable or even comfortable for human
standards today. Returning to the fourth point, Corbusier strategically places his building
responding to the climate and sun path. The windows are carefully designed by using
brises-soleil. In his book Le Poeme de l'Angle Droit, he constructed a drawing of a tall
building with his sun analysis of the both summer and winter directions during the day, this
building referring to Unité d'Habitation. The east and west facing brises-soleil are enshrined
as an intention. The brise-soleil protects a balcony at either end of the unit, allowing for
cross ventilation to flow through the narrow bedrooms into the double height space,
emphasizing an open volume rather than an open plan. The last point refers to roof
gardens, to provide essential protection to the concrete roof. His approach supports the
concept of creating an open public space on roof for anyone to experience. By placing a
garden, running track, kindergarten and gym on the roof, Unité supports this mechanistic
influence of the modernistic style.
Adding to certain flaws that can be found throughout Unite, it can be found that the
building does not actually fully follow the proportions of the Modulor. The stated
measurements from Le Corbusier were: 140x56x24m but in reality, the actual dimensions
were 139.01x53.10x25.07m. This must be noted carefully as Unite d’Habitation at
Marsailles is considered by Le Corbusier himself his most famous work that fully follows
the principles of the Modulor. “Le Corbusier does not mention this. Perhaps he recognized
the problem that Arnheim points out and concluded that relation between measures so
remote from each other… could not be appreciated and were not worth taking into
consideration” (Richard Padovan, 1999, p338) Although, he did imply in the book that the
system is only used on to the “dimensions of the individual apartments, of the separate
elements of the facades and of the various small superstructures on the roof”. And
therefore, the overall dimension of Unite d’Habitation were not intended to follow the
Modulor. Whether if this is believed to be true or not, it is fair to say that the dimensions on
which he did intend to apply the Modulor, such as the facades of Unite, it does show
dimensions that are very close. Again, this problem can also be a reason to why the
Modulor was never really used in practice shortly afterwards.
It can be said that without the influences of these many important architects stated
in this essay, the Modulor and the its ideas would have seen a different outcome that might
have altered the appearance of the iconic Unite d’Habitation we see today, or even possibly
the Modernism movement that took over the world of architecture in society today.
Although the idea was studied for many years and the Modulor was very promising, it just
turned to be quite a difficult method to follow and used in practice today, due to the irrational
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derived mathematics used by Le Corbusier and the final dimensions are just too small for
today’s standards. We can even conclude that the motives of the Modulor was mainly from
his own personal desires rather than mathematics.
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