The theories of proportion discussed below will help to explain the what proportion is and how it can create good design.
The Golden Section is based on observations in nature and mathematical formulas. It can be best understood with the help of this diagram:
photo from Francis D.K. Ching's Architecture: Form, Space, and Order, page 303
This illustrates the Golden Section as the whole is able to be subdivided into proportional parts...the largest square has the same dimensional ratio as the second largest, third largest, and so on. This means that the algebraic equation in the diagram above holds true.
The Golden Section has been used since the days of antiquity and once again became of great interest in the Renaissance and continues to be with modern designers. As for interior designers, the concepts of the Golden Section can be used in many ways including how its is used below.
The shapes of the door frame (b) and window pane (a) are in proportion to each other. This creates a harmonious and aesthetically pleasing relationship between a part and its whole.
The diagram below simplifies the proportioning system of the Golden Section:
"The Orders" refers to the classical order of columns. Romans and Greeks used the diameter of a column to be the basis of a proportioning system which created beauty and harmony in architecture as a whole...again, showing how proportion relates the parts to its whole. The diameter of the column determined the dimensions of the shaft, capital, the pedestal, the spacing between the columns, and so on. There are five common forms of orders: Tuscan, Doric, Ionic, Corinthian, and Composite (listed from stockiest and simplest in decoration to more slender and ornamental). Since each has a distinct look, each shows different proportions in relation to the whole column. For example, if there were a Tuscan column and a Corinthian column of the same height next to each other, the shaft of a Tuscan column would not share the same dimensions as the Corinthian.
The picture below of a new construction house illustrates how columns and proportion relate.
Although the architecture of the house is not built with the columns as the basis for proportion, it shows a contemporary use of columns as an integral part of proportion. Imagine if the columns were wider or slimmer... the house would seem off. As it is, the columns are in proper proportion to the house a whole helping to create a harmonious design.
The diagram below shows how the parts are determining the rest of the design:
This concept refers to the ideal room dimensions Renaissance architects developed to bring their architecture to a higher level. These architects derived spatial units from Pythagoras' ratios and the Greek musical scale. Seven ideal plan shapes for room were decided upon by one of the most influential architects of the Italian Renaissance, Andrea Palladio: circle, square, 1:√2, 3:4, 2:3, 3:5, and 1:2.
For interior designers, the shape of a room plays a major part in the overall design. It may present problems or opportunities as in the space pictured below:
Suppose this room is square, one of the ideal room shapes. This gives the designer the opportunity to create a symmetrical, centralized space which would add to the formal-ness and strength of the space which is often a goal for dining rooms. Putting a circular table in the middle of the room with a strong light fixture above does just that.
This diagram relates to how this floor plan might look:
This system of proportioning was developed in the 1940s by Le Cobusier and is based on mathematics and the proportions of the human body. He came up with a system of numbers that could determine lengths, volumes, and surfaces while maintaining the human scale in his architecture.
Le Corbusier used the Modular system to bring human scale to the Unite d'Habitation at Marseilles shown below:
He used a variety of panel sizes and surfaces to show the diversity of the Modular system. The diagram below shows an example of the some of the facades using his proportional system:
This is a Japanese proportional system that uses the dimensions of floor mats to determine the size of a room, column spacing, and room height. Floor mats typically have a 1:2 ratio and therefore can be arranged in a variety of ways.
The room below is an example of how the Ken is used. Notice how the floor mats fit perfectly in the spaces creating a unified whole:
Photo found at http://pixdaus.com/pics/12608310717JuXmnt.jpg
This diagram illustrates an example of a 6 mat room layout:
This refers to basing measurements and proportions on how the human body interacts with space and the items in it.
For interior designers, these proportions are especially important as they affect our ability to function in a space. Take this simple living room furniture set up:
Photo found at http://www.traditionalhome.com/design_decorating/howwelive/atlanta-colonial-remodel_ss4.html
This arrangement shows the concept of anthropometry and how our spaces have to work with the proportion and measurements of our bodies. The seat height relates to the height of the coffee table height in a way that make sense when they are being used together. The furniture is used in a proper proportion to the size of the room so that there is adequate space for circulation.
The diagram suggests the human movement needed to be accommodated while sitting in a chair:
As stated at the very beginning of this post, scale refers to the relationship of size between one object and another. Often, we are given cues to how to relate the size of objects to each other. For example, in architecture, doors are typically a good indicator of the scale of a structure.
The diagram below shows how scale relates the size of two objects: