Modulor

The Modulor is an anthropometric scale of proportions devised by the Swiss-born French architect Le Corbusier (1887–1965).

The Modulor is a system of measurements on a human scale created by Le Corbusier from the golden ratio. “The Modulor is a measurement tool derived from human stature and mathematics.A man-arm-raised provides at the determining points of the occupation of space, the foot, the solar plexus, the head, the the end of the fingers, the arm being lifted, three intervals which generate a section of gold, called Fibonacci On the other hand, mathematics offers the simplest variation as the strongest of a value: the simple, the double, the two sections of gold. ” The Modulor makes it possible to define a single, universal scale that does not refer to the metric system or the feet and inches system. It is designed to create a functional and optimized space for the man making the house a “living machine” without reducing his desire to create space, light and vegetation. A dwelling created with the dimensions Modulor aims to provide the inhabitant with a feeling of well-being and comfort. The Modulor applies to the dimensions of the house, but also to the dimensions of the furniture.

It was developed as a visual bridge between two incompatible scales, the imperial and the metric system. It is based on the height of a man with his arm raised.

It was used as a system to set out a number of Le Corbusier’s buildings and was later codified into two books.

History
Le Corbusier developed the Modulor in the long tradition of Vitruvius, Leonardo da Vinci’s Vitruvian Man, the work of Leon Battista Alberti, and other attempts to discover mathematical proportions in the human body and then to use that knowledge to improve both the appearance and function of architecture. The system is based on human measurements, the double unit, the Fibonacci numbers, and the golden ratio. Le Corbusier described it as a “range of harmonious measurements to suit the human scale, universally applicable to architecture and to mechanical things”.

With the Modulor, Le Corbusier sought to introduce a scale of visual measures that would unite two virtually incompatible systems: the Anglo Saxon foot and inch and the French metric system. Whilst he was intrigued by ancient civilisations who used measuring systems linked to the human body: elbow (cubit), finger (digit), thumb (inch) etc., he was troubled by the metre as a measure that was a forty-millionth part of the meridian of the earth.

In 1943, in response to the French National Organisation for Standardisation’s (AFNOR) requirement for standardising all the objects involved in the construction process, Le Corbusier asked an apprentice to consider a scale based upon a man with his arm raised to 2.20 m in height. The result, in August 1943 was the first graphical representation of the derivation of the scale. This was refined after a visit to the Dean of the Faculty of Sciences in Sorbonne on 7 February 1945 which resulted in the inclusion of a golden section into the representation.

Whilst initially the Modulor Man’s height was based on a French man’s height of 1.75 metres (5 ft 9 in) it was changed to 1.83 m in 1946 because “in English detective novels, the good-looking men, such as policemen, are always six feet tall!” The dimensions were refined to give round numbers and the overall height of the raised arm was set at 2.262 m.

Of the works leading to the creation of the Modulor, Robin Evans notes that the female body “was only belatedly considered and rejected as a source of proportional harmony”.

The regulator layout
Before designing the Modulor, Le Corbusier used the principle of the regulator layout to determine the proportions of his buildings. The method of the regulator plot is based on the use of triangles rectangles to determine the proportions of a building, indeed they allow to find a height and a width whose beauty is visible with the naked eye, contrary to certain arbitrarily chosen proportions: “a module measures and unifies, a regulator plot constructed and satisfied”; “The regulating layout is a spiritual satisfaction that leads to the search for ingenious relationships and harmonious relationships, and gives the work eurythmy.” Among the works built with the help of the regulator route, we find the Capitol in Rome or the Petit Trianon in Versailles. Le Corbusier, meanwhile, used this tool to draw the Villa Schwob, the house of Amédée Ozenfant as well as the houses La Roche-Jeanneret. In addition, Le Corbusier not only used the regulator layout for architecture, but also for painting. Thus, “The Bottle of Orange Wine” and “Guitar Stack of Plates and Lantern” were composed according to this principle.

Observation of natural structures
During his first training as a designer of watch cases and during the construction of the first houses, Le Corbusier was influenced by the Art Nouveau, who advocated the return to natural forms. In his work as a draftsman, he became aware of the geometric structures found in nature and of a way of combining natural forms and geometrical rigor.

The painting
After a period of “purist” painting where only objects are painted, Le Corbusier introduces more and more the human body in his works. He thus creates a synthesis between human and abstract elements. This synthesis work in his painting precedes the development of Modulor.

The music
Early on, Le Corbusier, from a musical background, is interested in the relationship between music and architecture. He is interested in the work of architects integrating the notion of rhythm in architecture. His brother Albert teaches rhythm in Germany in a school built by architect Tessenow, trying to adapt architecture to this activity. Le Corbusier wants to imagine an “architectural” range similar to the musical range. Le Corbusier also associates music with mathematics and science in general: “It is not music that is a part of mathematics, but rather science, which is a part of music, because it is based on music. proportions and resonance of the sound body engenders all proportions.

Le Corbusier hypothesizes that the harmony of buildings such as the Parthenon or certain traditional habitats comes from the use of precise measures constituting a coherent system. These precise measurements were human: bends, fingers, thumbs, feet, span. The use of the metric system has lost these references that had a human dimension.

Literature
Among the books that belonged to Le Corbusier, we find: The golden ratio: Rhythms, The golden ratio: Rites as well as Aesthetics and proportions in nature and in the arts4 in which a face is linked to the Golden ratio. These books show Le Corbusier’s interest in mathematics and his desire to give proportions to the human body. This is how the Modulor is born.

The creation of Modulor
Modulor is not the first measurement system on a human scale used in architecture. Ernst Neufert is a German architect born on March 15, 1900 in Freyburg, Germany and died in 1986 in Bugnaux-sur-Rolle, in the canton of Vaud. Ernst Neufert is one of the first Bauhaus students and assistant to Walter Gropius. In 1936, he created a measurement system 12 at the scale of a man of 1.75 m. This measurement system is based on the proportions of the golden ratio, as well as the Oktameter, a series of measures also created by Neufert. In addition, the system is compatible with the Achsmaß / Tafelmaß system of the Luftwaffe, used to design aircraft hangars. The Bauentwurfslehre, name given to the Neufert system, is suitable for all types of construction and also provides for interior design, ie all types of furniture, the height of the stairs and so on … No source shows a link between Le Corbusier and Ernst Neufert.

The idea of the Modulor begins to germinate in the spirit of Le Corbusier in the early 1940s. He writes in the Charter of Athens published in 1941: “The dimensioning of all things in the urban system can only be governed by the “The human scale” and “Architecture, after the defeat of the last hundred years must, once again, be put at the service of man. She must leave the sterile pumps, lean over the individual and create for the happiness of the latter, the amenities that will surround, making them easier, all the gestures of life “6. These are the first fruits of Modulor, born from the desire to connect man to architecture, to unite nature and mathematics.

Indeed, if Le Corbusier chose the golden ratio to create the Modulor, it is because it comes from the geometric suite of Fibonacci, present in nature: “I noticed that a relationship between the golden section and the geometric sequence act decisively on the proportioning of the forms of nature. To my surprise, comparing my findings with your Modulor, I saw that the results of both systems are similar. “Influenced by the various books written on the subject, such as that of Adolf Zeising and probably influenced by his friend Andreas Speiser, specialist in group theory, Le Corbusier chooses this system of proportions that has strongly affected before the Parthenon in Athens.

The word Modulor is composed of the words “module” and “gold”. “Gold” implies the golden ratio. Module, means that it is a basic unit, applicable in series. The Modulor was originally intended to be applicable to architecture, but also to any other areas, such as the sizing of a car for example. We find this idea of mass application in BAUHAUS and their desire to industrialize their products. The Modulor is linked to Le Corbusier’s modular architecture, its desire to create a housing unit and to build it in series, as it was able to do in the Cité Radieuse of Marseille.

The development of the Modulor was launched in 1942, after Le Corbusier recorded in different harmonious architectures, such as the Parthenon, a height of about 2.20 m between the floor and the ceiling, approximately the size of a man with his arm raised. Thus, he entrusts his instructions to Hanning, a young collaborator: “Take the man-arm-up, 2.20 m high; install it in two superimposed squares of 1.10 m; play on the two squares, a third square that must provide you with a solution. The place of the right angle should be able to help you locate this third square. With this grid of site and settled on the man installed on the man inside, I am persuaded that you will reach a series of measurements granting the human stature (the arm raised) and the mathematics. “. In August 1943, a first proposal came from Hanning. In December of the same year, Elisa Maillard, a member of ASCORAL who is also working on the Modulor project, proposes a corrective sketch of Hanning’s drawing. The resulting system is a compound of rectangles skillfully drawn from a section of gold and a regulator plot.

The grid is now employable, but Le Corbusier is not satisfied, that is why he puts it to study by other collaborators in 1945. That’s when Le Corbusier and his colleagues choose a height of 1.75 m tall man That’s when the patent is taken.

The construction of the Modulor
Here is the prototype of Hanning, this one is made of a square (1) of which we added a section of gold of one side (2) and of which one traced diagonal folded8 of the other (3). We thus obtain a set of four rectangles and an angle passing in the middle of the initial square (4). The angle obtained is a right angle, and therefore here a regulator plot.

This is the second prototype, proposed by Maillard. It consists of a square (1) to which is applied the golden section of one side (2) and the installation of a right angle on the half of the initial square (3). Then, the large rectangle obtained is divided into two equal parts (4). We thus obtain two squares equal to each other and to the initial square. A final step is to draw a symmetry of the smallest rectangle belonging to the system and drawing a median along the length (5).

The final Modulor is made up of three main measures: the height of the man who is 1.83 m, the height of the man with the raised arm which is 2.26 m and the height of the navel which is the half that is 1,13 m. These three lengths have a ratio equal to the number of gold one with the next. The Modulor is also composed of two series, the blue series and the red series, called Fibonacci, because the addition of the two previous terms gives the following term. The initial measure of the red series is the distance between the man’s belly button and the top of his head which is 70 cm. From this measure, the red series decreases to zero and increases to infinity with a ratio equal to the golden ratio between each term. The blue series is based on the same principle, but the initial length is the distance between the raised hand of the man and his solar plexus located at 1.40 m from the ground. These different values of these two series are used by Le Corbusier in some of his constructions. In this image, the values are accurate, but Le Corbusier sometimes uses rounded values to facilitate measurements.

Promotion
On the 10 January 1946, Le Corbusier on a visit to New York met with Henry J. Kaiser, an American industrialist whose Kaiser Shipyard had built Liberty Ships during World War II. Kaiser’s project was to build ten thousand new houses a day, but he had changed his mind and decided to build cars instead. During the interview, Le Corbusier sympathised with Kaiser’s problems of coordinating the adoption of equipment between the American and British armies because of the differences in units of length and promoted his own harmonious scale.

On the same trip he met with David E. Lilienthal of the Tennessee Valley Authority to promote the use of his harmonious scale on further civil engineering projects.

He also applied the principle of the Modulor to the efficient design of distribution crates in post war France.

Graphic representation
The graphic representation of the Modulor, a stylised human figure with one arm raised, stands next to two vertical measurements, a red series based on the figure’s navel height (1.08 m in the original version, 1.13 m in the revised version) then segmented according to Phi, and a blue series based on the figure’s entire height, double the navel height (2.16 m in the original version, 2.26 m in the revised), segmented similarly. A spiral, graphically developed between the red and blue segments, seems to mimic the volume of the human figure.

The Modulor 2 was drawn by André Maissonier and Justino Serralta.

Practical application
Le Corbusier used his Modulor scale in the design of many buildings, including:

Unité d’Habitation à Marseille
In his first book on the subject The Modulor, Le Corbusier has a chapter on the use of the modular in the Unité d’Habitation. The modular governs: the plan, section and elevations; the brise-soleil; the roof; the supporting columns and the plan and section of the apartments. It was also used for the dimensions of the commemorative stone laid on 14 October 1947. A version of the Modulor Man was cast in concrete near the entrance.

Church of Sainte Marie de La Tourette
In the Church of Sainte Marie de La Tourette Le Corbusier floors the majority of the church in pale concrete panels set to Modulor dimensions. Also, the engineer Iannis Xenakis applied the Modulor system to the design of the exterior vertical ventilators or “ondulatoires”.

Carpenter Center for the Visual Arts
In the Carpenter Center the Modulor system was used for the brise-soleil distances, the floor to floor heights, the bay distances and the column thicknesses. Le Corbusier conceived that the dimensioning of the entrance ramp would be “visible essay on the mathematics of the human body”.

Publication
Le Corbusier published Le Modulor in 1948, followed by Modulor 2 in 1955. These works were first published in English as The Modulor in 1954 and Modulor 2 (Let the User Speak Next) in 1958.

The 2004 reprinted box set including both books was printed in a square format using the Modulor with the series twenty seven to one hundred and forty reduced in size to one tenth.

Commemorative Usage
A picture of the Modulor appears on the eighth banknote series on the 10 CHF Swiss banknote dedicated to Le Corbusier.

Modulor Applications
Once the Modulor is finished, Le Corbusier applies his new measurement system in almost all his constructions. It is with this tool that the Claude and Duval factory, the Cité radieuse, the Tourette convent, the Jaoul houses, the Chandigarh institutions or the Cap-Martin shed are drawn. This shows that the Modulor is suitable for all kinds of buildings. These are not the only buildings built with Modulor, the chapel of Ronchamp, for example, is also designed according to these proportions.

The Claude and Duval factory
Building whose studies were started in 1947 and the construction completed in 1951; the factory was put into production at the beginning of 1952. The work thus constitutes historically the first concrete application of Modulor. This hosiery factory was the only industrial building made by Le Corbusier. It remains as the prototype of the unfinished reconstruction of the city of Saint-Die des Vosges according to the plans designed by Le Corbusier at the end of the war. A statue of The Man with the raised arm symbolizing the Modulor is built in the center of the city of Vosges to recall this episode.

The Radiant City of Marseille is a building designed by Le Corbusier, built between 1947 and 1952, to accommodate social housing. Le Corbusier applies the principle of modular architecture, that is to say, it aligns and superimposes a single dwelling unit. This building is a city-building, indeed, it also includes shops and services. The Radiant City of Marseille is a very complete building with regard to the application of the Modulor, all the measures are from the Modulor and the whole was created for the well-being of the man and the functionality of the house. The Modulor allowed Le Corbusier to use only 15 different measures for the entire construction. The ceilings, for example, peak at 2.26m in height, but they are only part of the fully modulated housing unit on a human scale. The balcony railings, the kitchen and the furniture are all given by the red and blue series of Modulor. The dimensions of the apartment are also derived from these series, the width of 4.19 m is given by the addition of two terms of the blue series: 53 and 366 centimeters. The Modulor leaves nothing to chance, it sizes everything up to the thickness of the floor given by the blue series.

The convent of Tourette
In 1959, Le Corbusier completed the Convent Sainte-Marie de la Tourette9. Despite his atheism, Le Corbusier was asked by Father Marie-Alain Couturier to draw this building. The latter combines the Modulor with purism, light and music. Purism translates into the use of simple geometric figures that make up the building. Le Corbusier gives a particular dimension to the light in this building, in fact, different stained glass windows are cut in different ways and placed in places studied so that the light gives a particular sensation. The music is in the spacing of the poles between the windows in some common rooms and corridors. These spaces translate a rhythm, a music that Le Corbusier asked to create to a collaborator, Xenakis. The Modulor is found among other things in the cells of the Dominican friars, the height, the length, the width, the loggias (balconies) and the windows are given by the blue and red series of Modulor.

Jaul houses
The Jaoul houses are two villas located in Neuilly-sur-Seine, built in 1953 by Le Corbusier. These houses are made after the war with materials like brick or flat tile, cheaper than concrete. These villas are a concrete application of the Modulor, that is to say that all dimensions are from the Modulor: the patterns of the walls and windows, the doors and the heights of the ceilings.