Proportion and scale are closely interrelated. 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.
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.
A number of theories of "desirable" proportions have been developed in the course of history. They include; Golden Section(ratio), Classical Orders, Renaissance Theories, Modular, Ken, Anthropometry, and Scale.

The Golden Ratio

Two quantities are in the golden ratio (golden section)if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.

Le Corbusier based his Modular system on the Golden Section.

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.

The Golden Section

Parthenon, Acropolis, Athens.This ancient temple fits almost precisely into a golden rectangle.

The Golden Spiral

Assume that rectangle ABCD is a Golden Rectangle.Hence, AD/AB =AE/ED. But, FE = AE, FE/ED= Phi.
Hence, rectangle FCDE is a Golden Rectangle.
We have two similar rectangles and so since
Phi = AD/EF then BD/CE = Phi.
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 Golden Ratio In Human Body

The first example of the golden ratio in the average human body is that when the distance between the navel
and the foot is taken as 1 unit, the height of a human being is equivalent to 1.618.
Some other golden proportions in the average human body are:
The distance between the finger tip and the elbow / distance between the wrist and the elbow,
The distance between the shoulder line and the top of the head / head length,
The distance between the navel and the top of the head / the distance between the shoulder line and the top of the head,
The distance between the navel and knee / distance between the knee and the end of the foot.

Principle Of Architecture

Axis:
A Line established by two point in space about which form and spaces can be arranged in symmetrical and balanced manner

Symmetry :The balanced distribution and arrangement of equivalent forms and spaces on opposite sides of dividing plane or about a center axis.

Hierarchy:
The articulation of importance and significance of form or space by its size shape and placement relative to other forms and spaces of organization.

Principle Of Architecture

Rhythm:
Unifying movement characterized by patterned repetition or alteration of formal elements or motifs in same or modified forms.

Datum:
A line plane or volume that , by its continuity and regularity , serves together , measure and organize a pattern of form and spaces.

Transformation The principle that an architectural concept or organization can be retained, strengthened and built
upon through a series of discrete manipulation and transformations.

AXIS

Induce Movement :
The axis is a linear condition , it has qualities of length and direction and induce movement and views along its path

Termination At Both Ends

Renforced By Defining Edges

Established By Symmertical Arrangement

Axis

Darwin D. Martin House & Estate : buffalo New York , 1904. Frank Lloyd Wright

Axis

Darwin D. Martin House & Estate : buffalo New York , 1904. Frank Lloyd Wright

Axis

Villa Madama , Rome 1517 , Raphael Sanzio.

Symmetry

Types of symmetry :
Bilateral Symmetry : Balanced arrangement of equivalent elements about a common axis.

Radial Symmetry : Equivalent elements balanced about Two or more axes that intersect at center point.

Symmetry

Unity Church : oak park Illinois, 1906. Frank Lloyd Wright

Symmetry

Great Stupa at Sanchi , india c.100B.C.

Symmetry

Baths ( thermae) of Caracalla , Rome 211-17 AD

Hierarchy

Hierarchy is achieved by
Size :Dominate architectural composition by being significantly different in size.

Shape: Can be made visually dominate by clearly differentiating their shape from other

Placement : Strategically placed to call attention to themselves as being the important elements in composition .

Hierarchy

Villa Trissino in Meledo : Andrea Palladio

Datum

A line plane or volume that , by its continuity and regularity , serves together , measure and organize a pattern of form and spaces.

DUBAR SQUARE, Patan , Nepal , Renovated 17th century

Datum

Salvation Army Hostel , Paris , 1928-33 Le corbusier

Datum

Marin County Civic Center , San Rafael , California 1957 , Frank Lloyd Wright

Repetition

Katsura imperial Villa , Kyoto , Japan , 17th century

Repetition

We tend to group elements in random composition according to
Their closeness or proximity to one another.

The visual characteristics they share in common.

Repetition

Jama Masjid , Gulbarga , India 1367

Rhythm

Rhythm refers to any movement by a patterned recurrence of elements or motifs at regular or irregular intervals .
The movement may be of our eyes as we follow recurring elements in a composition.

Victorian Facades , San Francisco street

Rhythm

Multiple Rhythm can be laid over one another in the façade of building.

Studies of internal Façade of a Basilica by Francesco Borromini