**MODULATION and PROPORTIONS**

It has been seen that certain Compositional Values or Patterns persist
even through the scaling such as the reductions or enlargements.
These compositional values, whatever scales or measures they may
relate, are of pure numbers.

Compositions of pure numbers have a degree of order, called the
System of Proportions. When the order occurs as a pervasive system,
whole to the parts or parts to the whole, a

**System of Modulation**occurs.
A System of Modulation inherently will have some kind of System of
Proportion, but a System of Proportion may not have any apparent
System of Modulation. A System of Modulation is an

*intellectual contribution to the composition*, whereas most of the Proportion Systems defy such definition, and so seem intuitive.
According to the arithmetical definition, a Proportion is the equality
of Ratios. A Proportionate Ratio manifests with numbers that have
some contextual relationship, such as

*adjacent numbers in sequence, in a matrix or in multi lateral composition*(between length, width and height). A proportion is an ideal relationship between two numbers, defined as the division of one number by the other.The
Golden Section in Architectural Theory |

Golden Section and other Systems of Proportions: Historically many
Systems of Proportions and Systems of Modulation have been
attempted.

Golden Section, is an order of a Geometric Proportion based on a
specific ratio in which the Whole relates to the Larger Part, just as the
Larger Part relates to the Smaller Part. For example a line AC (whole)
is divided into two unequal parts, AB (larger part) and BC (smaller
part). The ratio of AC / AB (whole / larger part) is same as the ratio of
AB / BC (lager part / smaller part). Mathematical this reads as AC/AB
= AB/BC or inversely as AB/AC = BC/AB.

This ratio is known as the Divine Proportion. The Golden Rectangle,
whose length and width are the segments of a line divided according
to the Golden Section, occupies an important position in paintings,
sculpture, and architecture, because its proportions have long been
considered the most attractive to the eye.

Another Proportioning System is the Ratio of √2 : 1 = 1.4142 : 1 The
simplicity of this derivation (a square root of 2 is the diagonal, in a
square of side length 1) is paralleled by the ease of maintaining the
proportion through division or multiplication of the proportioned
rectangles.

Many complex Numeric Orders have been devised and tried, but none
has yet proved to be a universal system. The most common are the
various Arithmetic Orders, in which through a specific formula
(equation) the numbers are sequenced to form a Logical Series. The
Fibonacci Series is an arithmetic order (1,2,3,5,8,13,21,34,55...) That has
been shown to have an Order of Proportion between adjoining two
numbers (3/5, 5/8, 8/13, 13/21, 21/34...).

There is an on going search for an Order or Modulation System that
coordinates various limb sizes (anthropometric measures), of not only
an average or a perfect human being, but people of different races
(different stature).

Corbusier's Modulor System (https://www.flickr.com/photos/eager/5031911411) |

The 'Modulor System' was essentially a linear system. Human
perception of solid - 3D forms are conditioned by the perspective or
converging view. The perspective view depends on the distance and
angle of vision of the object. From every point in space one gets a
different perspective, and so our perceptions of objects' measures
are ever changing.

No definite system that truly works for such a dynamic situation has yet
been devised. A Modular Measure System based on the Ergonomics
(usage through human limbs), may not work, for the visual and other
sensorial (aesthetic) needs.

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