Proportion & Scale

Golden Section

The golden section is a mathematical system of proportion that is defined by the concept that certain numerical relationships show the harmonic structure of the universe. It has been used in architecture since its antiquity and is still used today.

More specifically, it is defined as the ratio between two dimensions of a line or plane where the lesser of the two into the greater is the greater into the sum of both. See below a diagrammatic example of golden section.

Below is an example of the golden section being used in architecture. 

Photo: Eiffel Tower

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The Orders

The Orders comes from the early beliefs of the Greeks and Romans. They represent in their proportions the elements of perfect unity and harmony. The basic unit of measurement is the diameter of the column, which is how other dimensions came to be, such as the shaft, capital, and pedestal.

Because the Orders vary in their sizes depending on the building, there is no fixed unit of measurement for them. The different orders include Tuscan, Doric, Ionic, Corinthian, and Composite. See below a diagrammatic example of the different parts of a column.

Below is an example of the Orders being used in architecture.

Photo: New York Court of Appeals

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Renaissance Theories

The Renaissance theories came from the belief that the Greek mathematical system of proportions expressed perfect harmony and unity. The architects of the Renaissance believed that their work needed to belong to a higher order so they started using the Greek mathematical system of proportions. They believed that architecture was mathematics translated into spatial units and buildings.

With the concept of the Greek mathematical system of proportions in mind, they developed their own progression of ratios that became the basis of proportions for their architecture. This series not only worked on just rooms, but sequences of spaces, and entire plans. See below a diagrammatic example of renaissance theories.

Below is an example of the renaissance theories being applied to real world architecture.

Photo: Saint Pierre Raphael 

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The Modulor

The Modulor is a proportioning system developed by Le Corbusier that is designed to order “the dimensions of that which contains and that which is contained.” It is based on both mathematics and the proportions of the human body. It is a series of numbers that are proportioned according to the Golden Section. The basic grid consists of the three measures, 113, 70, and 43 centimeters. He saw this series of harmonic numbers as being able to maintain the human scale everywhere. See below a diagrammatic example of the Modulor.

Below is an example of the Modulor being used in architecture.

Photo: Carpenter Center for the Visual Arts by Le Corbusier

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The "Ken"

The ken is a unit of measure developed by the Japanese. It was originally used to designate the interval between two columns and varied in size, however it later was standardized for residential architecture and became an absolute measurement. Along with being a measurement for the construction of buildings, it was what ordered the structure and space of Japanese architecture.

The two methods of using the ken measurement are the Inaka-ma method and the Kyo-ma method. The Inaka-ma method uses a ken grid of 6 shaku (1 ken) and it is used to determine center-to-center spaces between columns. This measurement is used to determine the standard tatami floor mat, which are 1 ken (6 shaku) by 0.5 ken (3 shaku). The Kyo-ma method is when the floor mat dimensions remain constant and column spacing (ken module) varies according to the size of the room. See below a diagrammatic example of a ken module.

Below is an example of a traditional Japanese interior designed using the ken module.

Photo: CG Architect

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Anthropomorphic

Anthropometry is the measurement of sizes and proportions in relation to the human body. The proportioning of anthropometry seeks functional solutions. It is based on the idea that forms and spaces in architecture are either containers or extensions of the human body.

Ergonomics is the special field that deals with the concerns with human factors. It is a unique science that combines the design of our environments with our physiological and psychological requirements. See below a diagrammatic example of anthropomorphism.

See below an example of anthropometry being used in the real world.

Photo: Pix Good

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Scale

Scale is defined by how we perceive the size of something in comparison to something else. When dealing with scale, we are always comparing one thing to another thing. In drawing, scale is used to specify the size ratio between an illustration and that which it represents. For example, the scale figure used in architectural drawings notes the size of the building in relation to the real thing. See below a diagrammatic example of scale.

In the photo below, you can tell that the couch is small since the baby fits on it like a normal size person would on a regular size couch.

Photo: Honside

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