Proportions and Significance of proportions

‘Beauty’ has been a quality which all the makers of buildings have strived to achieve. The parameter with which ‘beauty’ is judged varies from person to person and era to era. The search to find a clue has driven man to observe nature, study it and even imitate it. In his search, man discovered certain underlying laws which governed the making of everything that exists in nature. These laws were based on the interrelationship between parts at both micro and macro level. When translated into a word it is ‘proportions’; as we call it today. Proportions are relation of one part to another or to the whole with respect to magnitude, quantity or degree.

Each civilization attached their own significance to ‘proportions’ and every branch of science and philosophy had their own meaning of it. Astronomers found proportions in relationship of Universe and the stars; the distance between them and so on, whereas musician discovered it in harmony of musical consonances, botanist related parts of plant to its whole and mathematicians found it in numbers. Sometimes it was all about numbers and at times had symbolic value and mystical significance. Plato found proportions in making of Universe and its cosmic harmony whereas Alberti found it dictating ‘Concinnitas’. The source of proportioning system has also been different, be it from geometry (Euclidian Theory), from music (Palladian Theory) or from anatomy of human body (Virtuvian Theory). However, ‘proportions’ had been central in creation of beauty. One finds mention of proportions by Vitruvius while defining ‘symmetry’, by Alberti while defining ‘Concinnitas’ and by Palladio in his concept of ‘beauty’.

In regards to music, Pythagoras is credited with developing our understanding of the harmonic series, the overtone series. It seems that Pythagoras was perhaps the first person to define the ‘consonant’, acoustic relationships between strings of proportional lengths. Specifically, strings of equal tension of proportional lengths create tones (or notes) of proportional frequencies when plucked. For example, a string that is two feet long will vibrate x times per second (Hertz). While a string that is one foot long (x/2) will vibrate twice as fast, 2x and furthermore, those two frequencies create a perfect octave.

If string vibrates at fundamental pitch x Hertz, then
x = Unison, ‘C’ Note (The Fundamental Frequency)
x/2 = First Octave, ‘C1’ Note (2/1 the Fundamental Frequency)
x/3 = A Perfect Fifth, ‘G’ Note (3/1 the Fundamental Frequency)
x/4 = Second Octave, ‘C2’ Note (equals two octaves, 4/1 the Fundamental Frequency) x/5 = A Major Third, ‘E’ Note (5/1 the Fundamental Frequency).

Figure 1 is to show that there is increase in frequency in each successive harmonics with corresponding decrease in wave length and amplitude for same length of string.

In dividing the length in this manner, Pythagoras exposed the first four overtones that have become the primary building blocks of musical harmony, an octave, a Perfect 5th, a Perfect 4th and a Major 3rd. Pythagoras also acknowledged these intervals, not only as they relate to the fundamental frequency, but to each other and found these ratios:
1:1 = Unison
2:1 = Octave
3:2 = Fifth
4:3 = Fourth
5:4 = Major Third

Figure 2 is proportional representation of Pythagorean harmonics.

Proportions are a simple tool and a precise aid to the dimensioning of objects to bring harmony into the work. Theory of proportions may not help us to produce, but it eliminates automatically the false notes in design composition. One adopts proportions to establish order and clarity on the level of geometrical equilibrium, not as a creative tool but as a tool to establish visual balance. We need not reject, we must absorb and digest, reinvent and not repeat theories of proportions in totality. We got to find our own idiom. Today when we make judgments on beauty, we do not follow mere fancy, but the working of reasoning faculty that is inborn in the mind or a faculty that is already established. Proportional relationships cause a visual delight whose triumph is beyond just being a tool of design; we need to infer scholarship of proportions as a planning grammar.

1) Shah Bhavesh, A Study In Palladian Palette Of Proportions, University of California, Los Angles, 1997.
2) Shah Bhavesh, Study Of Proportions In Villa Plans Of I Quattro Libri Dell’ Architecttura, Indian Institute of Technology, Roorkee, 2012.

Dr. Bhavesh Shah, Professor, School of Interior Design, Unitedworld Institute of Design (UID)

Disclaimer: The opinions / views expressed in this article are solely of the author in his / her individual capacity. They do not purport to reflect the opinions and/or views of the College and/or University or its members.

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