Proportion and scale are closely interrelated. While scale alludes to the size of something compared to a reference standard or to the size of something else. proportion refers to the proper or harmonious relation of one part to another or to the whole. Our perception of the physical dimensions of architecture, of proportion and scale, is imprecise. It is distorted by the foreshortening of perspective and distance, and by cultural biases. The intent of all theories of proportions is to create a sense of order and harmony among the elements in a visual construction. A proportioning system establishes a consistent set of visual relationships between the parts of a building, as well as between the parts and the whole. Although these relationships may not be immediately perceived by the casual observer, the visual order they create can be sensed, accepted, or even recognized through a series of repetitive events. Proportioning systems can visually unify the multiplicity of elements in an architectural design by having all of its parts belong to the same family of proportions. They can provide a sense of order in, and heighten the continuity of, a sequence of spaces. They can establish relationships between the exterior and interior elements of a building. A number of theories of "desirable" proportions have been developed in the course of history. They include; Golden Section, Classical Orders, Renaissance Theories, Modular, Ken, Anthropometry, and Scale.
Golden Section
Mathematical systems of proportion originate from the Pythagorean concept of 'all is number' and the belief that certain numerical relationships manifest the harmonic structure of the universe. The proportion known as the Golden Section has been in use ever since the days of antiquity. The Greeks recognized the dominating role the Golden Section played in the proportions of the human body. Renaissance architects also explored the Golden Section in their work. In more recent times. Le Corbusier based his Modular system on the Golden Section. Its use in architecture endures even today.
The Golden Section can be defined as the ratio between two sections of a line, or the two dimensions of a plane figure, in which the lesser of the two is to the greater is to the sum of both. The Golden Section has some remarkable algebraic and geometric properties that account for its existence in architecture as well as in the structures of many living organisms. Any progression based on the Golden Section is at once additive and geometrical.
 |
| Villa Stein at Carches, France, 1927. Le Corbusier. |
Le Corbusier's use of the Golden Section in seen at the Villa Stein in Carches, built in 1927. The rectangular proportion in ground plan and elevation, and also the inner structure of the ground plan show the Golden Section.
The Orders
To the Greeks and Romans of classical antiquity, the Orders represented in their proportioning of elements the perfect expression of beauty and harmony. The basic unit of dimension was the diameter of the column. From this module were derived the dimensions of the shaft, the capital, as well as the pedestal below and the entablature above, down to the smallest detail. Intercolunmnination is the system of spacing between columns, was also based on the diameter of the column. Because the sizes of columns varied according to the extent of a building, the Orders were not based on a fixed unit of measurement. Rather, the intention was to ensure that all of the parts of any one building were proportionate and in harmony with one another. The different types of Orders include; Tuscan, Doric, Ionic, Corinthian, and Composite.
 |
| Image: Colman, David. "Shortlist." Elle Decor. Nov. 2010. 118. |
The Petit Trianon at Versailles was designed by Ange-Jacques Gabriel by the order of Louis XV and was constructed between 1762-1768. It was the home of Queen Marie Antoinette. Corinthian pilasters decorate the northern facade.
Renaissance Theories
The architects of the Renaissance, believing that their buildings had to belong to a higher order, returned to the Greek mathematical system of proportions. Renaissance architects believed that architecture was mathematics translated into spatial units. Applying Pythagoras' theory of means to the ratios of the intervals of the Greek musical scale, they developed an unbroken progression of ratios that formed the basis for the proportions of their architecture. These series of ratios manifested themselves not only in the dimensions of a room, but also in the interlocking proportions of a sequence of spaces or an entire plan.
Andrea Palladio (1508-80) was probably the most influential architect of the Italian Renaissance. He wrote The Four Books on Architecture, published in Venice in 1570.
"Beauty will result from the form and correspondence of the whole, with respect to the several parts, of the parts with regard to each other, and of these again to the whole.; that the structure may appear an entire and complete body, wherein each member agrees with the other, and all necessary to compose what you intend to form." Andrea Palladio, The Four Books on Architecture, Book 1, Chapter 1.
 |
| Image: Waldron, William. "A Look to the Past." Elle Decor. Nov. 2010. 207. |
The Modulor
Le Corbusier developed his proportioning system, the Modulor, to order "the dimensions of that which contains and that which is contained." He saw the measuring tools of the Greeks, Egyptians, and other high civilizations as being "infinitely rich and subtle because they formed part of the mathematics of the human body, gracious, elegant, and firm, the source of that harmony which moves us, beauty." He therefore based his measuring tool, the Modulor, on both mathematics and the proportions of the human body. Le Corbusier began his study in 1942, and published The Modulor: A Harmonious Measure to the Human Scale Universally Applicable to Architecture and Mechanics in 1948. A second volume, Modulor II, was published in 1954. The basic grid consist of three measures, 113, 70, and 43 centimeters, proportioned according to the Golden Section. Le Corbusier saw the Modulor not merely as a series of numbers with an inherent harmony, but as a system of measurements that could govern lengths, surfaces, volumes, and "maintain the human scale everywhere." It could "lend itself to an infinity of combinations; it ensures unity with diversity... the miracle of numbers." The principle work of Le Corbusier that exemplified the use of the Modulor was his Unite d'Habitation at Marseilles built 1965-68.
 |
| Sainte Marie de La Tourette, Le Corbusier, France, 1956-60. |
The "Ken"
The ken was introduced in the latter half of Japan's Middle Ages. Although it was originally used simply to designate the interval between two columns and varied in size, the ken was soon standardized for residential architecture. The ken became an absolute measurement. It was not only a measurement for the construction of buildings but evolved into an aesthetic module that ordered the structure, materials, and space of Japanese architecture.
The size of a room is designated by the number of its floor mats. The traditional floor mat was originally proportioned to accommodate two persons sitting or one person sleeping. As the ordering system of the ken grid developed, however, the floor mat lost its dependence on human dimensions and was subjected to the demands of the structural system and its column spacing. Because of their 1:2 modularity, the floor mats can be arranged in a number of ways for any given room size. And for each room size, a different ceiling height is established to the following; height of the ceiling = number of mats x 0.3. In a typical Japanese residence, the ken grid orders the structure as well as the additive, space-to-space sequence of the rooms. The relatively small size of the module allows the rectangular spaces to be freely arranged in linear, staggered, or clustered patterns.
Anthropomorphic
Anthropometry refers to the measurement of the size and proportions of the human body. Anthropometric proportioning methods are functional ones. They are predicted on the theory that forms and spaces in architecture are either containers or extensions of the human body and should therefore be determined by its dimensions. The difficulty with anthropometric proportioning is the nature of the data required for its use. Average dimensions must always be treated with caution since variations from the norm will always exist due to the difference between men and women, among various age and racial groups, even from one individual to the next.
The dimensions of the human body affect the proportion of things we handle, the height and distance of things we try to reach, and the dimensions of the furnishings we use for sitting, working, eating, and sleeping. A special field has developed from a concern with human factors is ergonomics, which is the applied science that coordinates the design of devices, systems, and environments with our psychological capacities and requirements.
In addition to the elements that we use in a building, the dimensions of the human body also affect the volume of space we require for movement, activity, and rest.
 |
| Image: Davies, Roger. "Director's Focus." Elle Decor. Sept. 2010. 144. |
Scale
Scale refers to how we perceive or judge the size of something in relation to something else. In dealing with the issue of scale, therefore, we are always comparing one thing to another. In drawing, we use scale to specify the ratio to that which it represents. For example, the scale of an architectural drawing notes the size of a depicted building in comparison to the real thing.
Visual Scale
Visual scale is of particular interest to designers. It refers not to the actual dimensions of things, but rather to how small or large something appears to be in relation to its normal size or to the size of other things in its context.
 |
| Image: Martin, J.J. "Milan." Elle Decor. Oct. 2010. 186. |
Human Scale
Human scale in architecture in based on the dimensions and proportions of the human body. We can gauge a space whose width is such that we can reach out and touch its walls. We can use elements that have human meaning and whose dimensions are related to the dimensions of our posture, pace, reach, or grasp. Such elements as a table or chair, the risers and treads of a stairway, the sill of a window, and the lintel over a doorway, not only help us judge the size of a space but also give it a human scale.
Of a room's three dimensions, its height has a greater effect on its scale than either its width or length. In addition to the vertical dimensions of a space, other factors that affect its scale are: the shape, color, and pattern of its bounding surfaces; the shape and disposition of its openings; and the nature and scale of the elements placed within it.
