A proportional response.

We often underestimate just how much of an influence the Greeks had on the world, Western society and maths more than anything else. The idea of democracy contributed to the establishment of the United States government, for example. Science and mathematics contributed the most to our sense of fundamentals, however. Pythagoras's theorem is a fundamental of trigonometry and geometry. These in turn are the foundation of proportion and scale, which are also necessary elements of interior design just as they are for architecture.

There are many kinds of proportion used for architecture and interior design: material proportions, structural proportions, manufactured proportions, all used to define where and how certain elements can be placed to create a functional and safe building or space. We take this one step further, however, and shuffle these elements to also create something aesthetically pleasing. To do that, we take a closer look at scale and proportioning systems or theories.

The Golden Section comes from Pythagoras himself, and was used to build most of the ancient Greek monuments and temples. It's a mathematical concept, a progressive geometric expression, that starts with a rectangle. If cut into a square on its shorter size, the smaller rectangle left over will have the same shape as the original, but scaled smaller. When this is continued (whether cut into smaller and smaller squares, or added to in a reverse process), the lines created when beginning from the corner of the smallest shape will spiral out like a nautilus shell.

This basic idea can be carried through into interior design in very simple ways, like the windows above that carry over into the cabinetry. It creates a sense of connection or context with the rest of the space. In fact, that is a key concept to keep in mind regarding proportion and scale: their properties rely on a relationship with other elements. One gets a sense of scale or proportion only when compared with surroundings.

Similarly, the Classical Orders are another proportioning system the Greeks and Romans gave us, architecturally. They are based upon the dimensions of a column's diameter; since the five different types of columns each tended to have its own dimensions, each gave its name to an order. Therefore we have the Tuscan (Roman), Doric (Greek), Ionic (Greek, Corinthian (Greek), and Composite (Roman) columns and capitals that lend their dimensions to the buildings in which they are integrated (hence intercolumniation).

Image credit: Clarke, Gerald. "Temples of Light." Architectural Digest. October 2006. 144. (Overlay mine.)

The skylight seen above has a Greek temple front on its exterior, and so its interior follows its lines nearly exactly. The lines don't follow directly below it, but the space below is still proportional to it.

Then during the Renaissance, Andrea Palladio applied Greek concepts to determine optimal ratios for architecture (Renaissance Theories). This gave rise to the seven ideal plan shapes for rooms: circle, square, 1: (square root) 2, 3:4, 2:3, and 1:2. 

Image credit: Rowlands, Penelope. "Charles Allem." Architectural Digest. September 2006. 229. (Overlay mine.)

The proportions seen in Charles Allem's apartment here follow the 2:3 ratio or proportional system.

Then Modernists caught revolutionary fever from many of the artists and politics of their time, and wanted to promote forward-thinking and not be tied to the past. The results were not always successful; Le Corbusier developed his own proportioning system that could not entirely divorce itself from the Golden Section. He did, however, reconcile it (for the most part) with human scale: his Modular is based upon a six-foot tall man, with base units coming from how he sits, bends or stands such that it follows the Golden Section. Three main measurements are used and repeated (in centimeters): 113, 183 and 226.

Image credit: Giovannini, Joseph. "Taking on the SKY and SEA." Architectural Digest. October 2006. 237. (Overlay mine.)

While its aims were to be applied universally (much like the International Style Le Corbusier attempted to design), it did not see as much popularity as the more classic proportioning systems. The above pictures are another way to reconcile the same concepts (human scale and the Golden Section); they appear similar to, but are likely different from, the Modular.

Western proportioning systems are not the only ones out there, however. In Japan, there is a system revolving basically around the proportions of the tatami mat, which was intended to either seat two people or let one person sleep on it. This system is called the Ken, and tends to look very grid-like when laid out (though occasionally linear or staggered, depending on the orientation of the mat units). Each room is built according to how many mats it can or will accommodate: 3-mat, 4-mat, 6-mat, and so on.

Image credit: "Editors Select Properties Around the World." Architectural Digest. February 2005. 146.

Frank Lloyd Wright, who was inspired by the Ho-o-den of the first Chicago World's Exposition, is likely to have known about the Ken. The windows above come from one of the houses he designed in Chicago.

As design progresses, we become more and more concerned about it being as accessible as possible. Interior design is particularly concerned with human needs, so it follows that human scale and proportion governs how we design spaces for our clients. This means we must be educated in the study of anthropometrics, which are human measurements. We generally design for the human average, but sometimes need to deviate due to different measurements thanks to age, ethnicity/race, or other genetic factors. By extension we must also be mindful of divisions of public, social, and personal space (proxemics) in our interiors, or we inadvertently create spaces too large or small for our clients' comfort.

Image credit: O'Keeffe, Linda. "Northern Exposure." Metropolitan Home. June 2008. 162. (Overlay mine.)

Here we see the designer (who is also the client) in relation to the sofa in her living room.

Most fundamentally, we must be concerned with scale, which helps determine our proportions. Scale refers to size, and tends to be fixed. Francis Ching defines it as "a fixed proportion used in determining measurements and dimensions" (Architecture: Form, Space and Order, p 301). We can get a visual sense of how large or small something is when it is in relation to another object, such as a figure standing next to a building. We can also manipulate that sense of scale by increasing or decreasing elements such as patterns within an object or space: a busy pattern on the walls of a room could make the room seem smaller than it is.

Image credit: Gorlin, Alexander. "Louis Kahn Remembered." Architectural Digest. February 2005. 134. (Overlay mine.)

Louis Kahn was very conscientious regarding proportion and scale and knew how to manipulate them to great effect. In the above picture, if we had no piano or other item to give us an idea of its scale, we might be tempted to believe that the central building is smaller than it really is due to the towering structures surrounding it.