Modulor
Encyclopedia
The Modulor is an anthropometric scale
of proportion
s devised by the Swiss-born French architect
Le Corbusier
(1887–1965).
It was developed as a visual bridge between two incompatible scales, the Imperial system and the Metric system
. It is based on the height of an English 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.
, Leonardo da Vinci's
Vitruvian Man
, the work of Leone 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 2.20m 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 1.75m it was changed to six feet 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 2.26m.
, an American industrialist whose Kaiser Shipyard had built Liberty Ships
during World War Two. 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 English 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.
, and a blue series based on the figure's entire height, double the navel height (2.16m in the original version, 2.26m 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 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.
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".
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".
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.
Scale (ratio)
The scale ratio of some sort of model which represents an original proportionally is the ratio of a linear dimension of the model to the same dimension of the original. Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. In such...
of proportion
Proportion (architecture)
Proportion is the relation between elements and a whole.-Architectural proportions:In architecture the whole is not just a building but the set and setting of the site. The things that make a building and its site "well shaped" include the orientation of the site and the buildings on it to the...
s devised by the Swiss-born French architect
Architect
An architect is a person trained in the planning, design and oversight of the construction of buildings. To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the...
Le Corbusier
Le Corbusier
Charles-Édouard Jeanneret, better known as Le Corbusier , was a Swiss-born French architect, designer, urbanist, writer and painter, famous for being one of the pioneers of what now is called modern architecture. He was born in Switzerland and became a French citizen in 1930...
(1887–1965).
It was developed as a visual bridge between two incompatible scales, the Imperial system and the Metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...
. It is based on the height of an English 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 VitruviusVitruvius
Marcus Vitruvius Pollio was a Roman writer, architect and engineer, active in the 1st century BC. He is best known as the author of the multi-volume work De Architectura ....
, Leonardo da Vinci's
Leonardo da Vinci
Leonardo di ser Piero da Vinci was an Italian Renaissance polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer whose genius, perhaps more than that of any other figure, epitomized the Renaissance...
Vitruvian Man
Vitruvian Man
The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci circa 1487. It is accompanied by notes based on the work of the famed architect, Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and...
, the work of Leone Battista Alberti
Leone Battista Alberti
Leon Battista Alberti was an Italian author, artist, architect, poet, priest, linguist, philosopher, cryptographer and general Renaissance humanist polymath...
, 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
Architecture
Architecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...
. The system is based on human measurements
Anthropometry
Anthropometry refers to the measurement of the human individual...
, the double unit, the Fibonacci numbers, and the golden ratio
Golden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...
. 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
Anglo-Saxons
Anglo-Saxon is a term used by historians to designate the Germanic tribes who invaded and settled the south and east of Great Britain beginning in the early 5th century AD, and the period from their creation of the English nation to the Norman conquest. The Anglo-Saxon Era denotes the period of...
foot and inch
Inch
An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot...
and the French Metric system. Whilst he was intrigued by ancient civilisations who used measuring systems linked to the human body: elbow (cubit
Cubit
The cubit is a traditional unit of length, based on the length of the forearm. Cubits of various lengths were employed in many parts of the world in Antiquity, in the Middle Ages and into Early Modern Times....
), finger (digit), thumb (inch) etc., he was troubled by the metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
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
AFNOR
Association française de Normalisation is the French national organization for standardization and its International Organization for Standardization member body....
) 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 2.20m 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 1.75m it was changed to six feet 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 2.26m.
Promotion
On the 10 January 1946, Le Corbusier on a visit to New York met with Henry J. KaiserHenry J. Kaiser
Henry John Kaiser was an American industrialist who became known as the father of modern American shipbuilding. He established the Kaiser Shipyard which built Liberty ships during World War II, after which he formed Kaiser Aluminum and Kaiser Steel. Kaiser organized Kaiser Permanente health care...
, an American industrialist whose Kaiser Shipyard had built Liberty Ships
Liberty ship
Liberty ships were cargo ships built in the United States during World War II. Though British in conception, they were adapted by the U.S. as they were cheap and quick to build, and came to symbolize U.S. wartime industrial output. Based on vessels ordered by Britain to replace ships torpedoed by...
during World War Two. 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 English 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
Tennessee Valley Authority
The Tennessee Valley Authority is a federally owned corporation in the United States created by congressional charter in May 1933 to provide navigation, flood control, electricity generation, fertilizer manufacturing, and economic development in the Tennessee Valley, a region particularly affected...
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 (1.08m in the original version, 1.13m in the revised version) then segmented according to PhiPhi
Phi may refer to:In language:*Phi, the Greek letter Φ,φ, the symbol for voiceless bilabial fricativeIn mathematics:*The Golden ratio*Euler's totient function*A statistical measure of association reported with the chi-squared test...
, and a blue series based on the figure's entire height, double the navel height (2.16m in the original version, 2.26m in the revised), segmented similarly. A spiral
Spiral
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.-Spiral or helix:...
, graphically developed between the red and blue segments, seems to mimic the volume of the human figure.
Practical application
Le Corbusier used his Modulor scale in the design of many buildings, including:Unité d'Habitation in Marseilles
In his first book The Modulor, Le Corbusier has a chapter on the use of the modular in the Unité d'HabitationUnité d'Habitation
The Unité d'Habitation is the name of a modernist residential housing design principle developed by Le Corbusier, with the collaboration of painter-architect Nadir Afonso...
. The modular governs: the plan, section and elevations; the brise-soleil
Brise soleil
Brise soleil, sometimes brise-soleil , from French, "sun breaker"), in architecture refers to a variety of permanent sun-shading techniques, ranging from the simple patterned concrete walls popularized by Le Corbusier to the elaborate wing-like mechanism devised by Santiago Calatrava for the...
; 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
Casting
In metalworking, casting involves pouring liquid metal into a mold, which contains a hollow cavity of the desired shape, and then allowing it to cool and solidify. The solidified part is also known as a casting, which is ejected or broken out of the mold to complete the process...
in concrete
Concrete
Concrete is a composite construction material, composed of cement and other cementitious materials such as fly ash and slag cement, aggregate , water and chemical admixtures.The word concrete comes from the Latin word...
near the entrance.
Church of Sainte Marie de La Tourette
In the Church of Sainte Marie de La TouretteSainte Marie de La Tourette
Sainte Marie de La Tourette is a Dominican Order priory in a valley near Lyon, France designed by architects Le Corbusier and Iannis Xenakis and constructed between 1956 and 1960. Le Corbusier's design of the building began in May, 1953 with sketches drawn at Arbresle, France outlining the basic...
Le Corbusier floors the majority of the church in pale concrete panels set to Modulor dimensions. Also, the engineer Iannis Xenakis
Iannis Xenakis
Iannis Xenakis was a Romanian-born Greek ethnic, naturalized French composer, music theorist, and architect-engineer. He is commonly recognized as one of the most important post-war avant-garde composers...
applied the Modulor system to the design of the exterior vertical ventilators or "ondulatoires".
Carpenter Center for the Visual Arts
In the Carpenter CenterCarpenter Center for the Visual Arts
The Carpenter Center for the Visual Arts at Harvard University, in Cambridge, Massachusetts is the only building actually built by Le Corbusier in the United States, and one of only two in the Americas...
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.
Criticism
Critics of the Modulor have raised concerns with the system. In the words of Robin Evans, the female body "was only belatedly considered and rejected as a source of proportional harmony".Commemorative Usage
- A picture of the Modulor appears on the eighth banknote series on the 10 CHF Swiss banknoteBanknotes of the Swiss francThe first banknotes in Switzerland were issued in 1825 by the Caisse de Dépôt of the city of Bern.During the 19th century the Cantons had the right of printing notes. Following the law of 8 March 1881 the Swiss National Bank had the exclusive right to issue banknotes in Switzerland. First notes...
dedicated to Le Corbusier.
See also
- Body proportionsBody proportionsWhile there is significant variation in anatomical proportions between people, there are many references to body proportions that are intended to be canonical, either in art, measurement, or medicine....
- Rudolf WittkowerRudolf WittkowerRudolf Wittkower was a German art historian.-Biography:He was born in Berlin and moved to London in 1934. He taught at the Warburg Institute, University of London from 1934 to 1956 and then at Columbia University from 1956 to 1969 where he was chairman of the Department of Art History and...
- Vitruvian ManVitruvian ManThe Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci circa 1487. It is accompanied by notes based on the work of the famed architect, Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and...
- AnthropometryAnthropometryAnthropometry refers to the measurement of the human individual...
- ErgonomicsErgonomicsErgonomics is the study of designing equipment and devices that fit the human body, its movements, and its cognitive abilities.The International Ergonomics Association defines ergonomics as follows:...
- Rule of thumbRule of thumbA rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation. It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination...
- List of strange units of measurement
- Preferred numberPreferred numberIn industrial design, preferred numbers are standard guidelines for choosing exact product dimensions within a given set of constraints....
, especially the section about Renard series, which covers a mathematical approach on evenly distributed numbers using geometric sequences, for use in constructing houses or devices.
Sources
- Curtis, William, and Eduard F. Sekler. 1978. Le Corbusier at Work: The Genesis of the Carpenter Center for Visual Arts. Cambridge, MA: Harvard University Press.
- Evans, Robin. 1995. The Projective Cast: Architecture and Its Three Geometries. Cambridge, MA: MIT Press. ISBN 0-262-05049-8 Second impression of the 2000 facsimile reprint of the first English edition, in 2 volumes, 1954 and 1958. ISBN 3-7643-6188-3 (Basel); ISBN 0-8176-6188-3 (Boston)
- Ostwald, Michael. 2001. "The Modulor and Modulor 2 by Le Corbusier (Charles Edouard Jeanneret), 2 volumes. Basel: Birkhäuser, 2000" [book review]. Nexus Network Journal 3, no. 1:145–48.