Chapter 6

Proportion and Scale

The Golden section is a scale relationship between two dimensions of a plane or line , in which the equation of the lesser to the greater is the same as the greater to the whole: a quotient of 0.618 to 1.000.  This mathmatical eqaution began with the Pythagorean idea that numerical relationships bring unity to the universe.  Greeks believed that the Golden Section was visible in the human body, therefore, buildings that housed the body should have the same proportionate balance. 

The Golden Section may be written as an algebraic equation 

 a  =  b                                                                                                           

 b    a+b

The Golden section is similar to the Fibonacci series where each tern is reached by the sum of the preceding two numbers:  1, 1, 2, 3, 5, 8, 13.....

A Golden rectangle may be formed using the theory of the Golden section and may be carried out indefinently with each section remaining in a similar relationship to all other parts as well as the figure as a whole.

The Orders of classical Roman and Greek architicture represented forms the contained both consistancy and elegance.  Measurments were based on the circumference of the column.  Everything down to the smallest details of the building were determined by the columns and their spacing.  The order are:  Tuscan, Doric, Ionic, Corinthian and Composite.                          The order of Temples by intercolumniation, diameter, height and spacing of columns :  Pycnostyle,  Systyle,  Eustyle,  Diastyle and  Araeostyle.

The architects of the Renaissance Theories believed that their designs were part of a greater plan.  They also used the Greek classification of scale.  The renaissance gave birth to an infinite advancement of numerical scales that was the foundation of their building.  Renaissance architect Andrea Palladio suggested that there are seven "beautiful and proportionable" scales for rooms:  circle, square, 1: 2,  3:4,  2:3,  3:5 and 1:2.  Palladio also developed equations to determine the appropriate ceiling size.  Flat ceilings were equal to the rooms width.  Vaulted ceilings in square rooms were one-third greater than their width.  For other rooms the Pythagoras' theory was used to regulate the ceiling heights.  This was a theory that used math, geometry and harmony.

The Modulor is a system of proportions determined by LeCorbusier.  He based this modulor system of order on both the Golden Section and the Fibonacci Series, as well as the dimensions of the human form.  His scale contained three measurements based on the human body: 113 cm, 70 cm and 43 cm.

The Ken is a method of measurment developed during Japan's Middle-Ages. The ken is used to determine the construction, materials, space and order of a building.  In Japan, the diameter of a room is calculated based on size of the floor mats (3 x 6 shaku or 0.5 x 1 ken).  Floor mats have become a standard measurement for floor systems and column width.

Anthropometry is a scale of measurement based on the size and scale of the human body.  This theory states that architecture is an continuation of humanity and should be compatable to the body's shape and form.  Anthropometry must factor in changes in the body due to differences in sex, race and age.  Ergonomics is the science that deals with the design of gadgets and surroundings and how they work with the human body. 

Proportions are also determined by visual and human scales.  Visual scale is the reference of how large or small a structure is comapared to the standard size of the object ( small or large). Visually, it is how design elements are seen and how they related to one another individuallyand as a whole. The human scale is determined by the measurements and scale of a human body.  Scale in relation to our body can determine how we feel in that space.  The height of the ceiling in a room has the strongest effect on a rooms scale.  Other factors that alter the scale of a room include: color, pattern and shape of the facade,                                                                        placement, size and order of openings,                                                                                                     the proportion and essence of items placed in the room.