The idea of Visual Weight is primordial in pictorial and architectural composition as well as being an aspect of the visual impression of objects. The proposal here is that thisVisual Weight has dimension and can therefore be measured.
The proposal will be expressed for objects rectangular in form and situated on vertical and horizontal planes as would be expected in architecture.
According to the said planes, the Visual Weight of a figure is the result of two vectorial components, one ascendant and the other descendant, the values of which will obey the following expression:
|Fp|= b* (1 + log a2/b2), |Fc|= a/(1 + log a2/b2)
Being |Fp| the modulus of the ascendant component and |Fc| that of the descendant.
This expression will give a variety of results in concord with the proportions of a rectangular figure:
Figure 1
A square presents a balance of forces. The greatest contrast in forces is seen in figures where the proportions are such that one side is double the length of the other. For greatly elongated figures, as in a particularly slender pillar, the result is an apparent bending.
The result becomes, however, particularly significant at proportions of around 8:1, represented by a classical Ionic column: equilibrium is established between two forces of the magnitude, which is a third that of the shaft.
For Doric proportions, that is of the order of 7:1, the resulting impression is one of rising, of almost over-dimensioned load-bearing capacity, whereas at 9:1, the impression is of a certain lowering, a weakening at the crown, of Corinthian elegance.
The same formulae may be deployed to express the dynamics of other proportions of interest.
For example, between 1:1.5/1.7 there is an area of interest flooded with historical examples of proportion 5:3, the “Golden Number“, 1.618. The formulae presented here identify a point of visual transition, or a “mean” in mathematical terms.
This particular set of values is not merely the result of adjusting the formulae to a series of pre-established circumstances, but on the contrary, the direct result of mathematical expression.
The formulae adduce a well-defined relationship between proportion and the physical size of the figure (a2/b2) which, with the use of logarithms, allows us to obtain non-exponential values, which are clearly more melodious, and which coincide with our own psychophysical experience.
The above analysis, for rectangular figures, may be followed for other forms. The validity of such formulae becomes evident for classical compositions as in, for example, the portico of a temple.
From an illustration by Vitruvi de Rusconi (1590):
