We speak of an architectural system as long as one ideal of confi guration is valid. Beyond this basic and, perhaps, somewhat nebulous idea there is nothing permanent, there is only change. The relationship of the whole and the parts, and of the parts to each other, are dictated by the ruling idea of the system, but the variations are infi nite. The artist searches for ever new solutions. This is the essence of artistic development.1 In this view of history, Emil Kaufmann privileges what he terms systems over historical demarcation through stylistic features. When considering architecture up to the twentieth century, he proposes there have been three systems, each dif- ferentiated by the reciprocity between component parts and the composition as a whole. The fi rst is the ‘ancient system’ of the Graeco-Roman period as epitomized by the theories of Vitruvius. Kaufmann proposes that while there are proportional relationships between parts and in relation to the whole, there is no differentiation or hierarchy between parts in ancient Graeco-Roman architecture.2 The second distinc- tive system is located from the fourteenth-century Italian Renaissance through to the architecture of eighteenth-century France. Kaufmann refers to this entire period as the ‘Baroque system’. His proposition is that the Baroque maintained the ideals of harmony and proportion from the Graeco-Roman system, but introduced a new compositional principle.
The parts now should be presented not only in aesthetically satisfying relationships of size and in mathematical reciprocity, but they should be differentiated as superior and inferior components.3
The phrase ‘mathematical reciprocity’ is a reference to the key theoretical text under- pinning the Renaissance, Leon Alberti’s Ten Books of Architecture. The principle of part-to-whole harmony is captured by the term concinnitas, which appears multiple times in Alberti’s treatise. According to Wittkower, this relates to the aspiration for a uniform system of proportion throughout all parts of the building, based on the ‘Pythagorean system of musical harmony’.4 Fellow historian George Hersey clarifi es the principles by which concinnitas can be achieved.
According to Alberti’s doctrine concinnitas is the primary principle of nature. It is based on number in the Pythagorean sense. When concin- nitas is present in a building the observer is challenged to work out the values involved in its siting, planes, or elevations (collocatio), and in the volumes (fi nitio). When the totals and their components equal particular values (certum numerum), the building’s concinnitas or beauty has been revealed.5
While there seems to be consensus between Wittkower and Hersey that com- position is reliant on the application of Pythagorean number, there are few direct references within Alberti as to the optimal proportions. Wittkower cites a discus- sion of musical harmony, located prior to one reference for types of plan sizes, as evidence that, ‘for Alberti, harmonic ratios inherent in nature are revealed in music’.6 Alberti’s recommendations for plan types are the square (1:1), one to one and a half (2:3) and one to one and a third (3:4), which, as Wittkower points out, relate to simple musical consonance. He concludes that the key to understanding Renaissance proportion, as interpreted through Alberti’s writing, is the principle of number generation using compound ratios. For example, the series 4:6:9 is gener- ated by sequentially applying the ratio of 1:1.5. The use of number series to create proportional relationships was developed alongside the overriding principle of bilat- eral mirror symmetry.7 The outcome being harmonic proportional relationships in the respective parts, replicated across the central viewing axis to produce an ideal confi guration.
For Kaufmann, what stylistically is referred to as the high Baroque, is the extreme manifestation of hierarchy between parts. The attempt to produce bal- anced symmetrical harmony based on proportional relationships is increasingly at odds with the Baroque articulation of a competing hierarchy of features. The goal of
concinnitas becomes increasingly harder to maintain when the second requirement
for differentiation between parts is accentuated.
Sixteenth century architects began to realize there was no solution: that it was impossible to bring the individual parts into a perfect union and at the same time to endow some of them with power. One can strive for the reconciliation of graduation and concatenation, but one can never reach it. Gradation in particular is the natural foe of integration.8
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exaggerated scale of vertical and horizontal components; the exaggeration of volutes and introduction of spiral towers in an attempt to resolve the vertical and horizontal; exaggeration of details; the treating of stone as soft and fl exible matter (as a consequence of the attempt to express binding forces between parts); and the anthropomorphic or animistic transformation of components.
In Italy, the tension between unifi cation and hierarchy led to extreme manifestations, such as the fl uid facades of Borromini and Guarini. Perhaps the most inventive outcome in relation to the Borromini facades was the introduction of concave and convex planes, which bind vertical and horizontal surface behind highly articulated columns and cornice. An original solution to the Baroque dilemma of the competing demands for unifi cation and articulation, the curved planes and other swirling details produce sensual facades that literally ripple with tension.
Kaufmann, after some discussion of the drawings of Boullée and the architecture of Ledoux, lists the formal characteristics of what he considers to be the third system of composition. The ancient system was based on harmonic, non-hierarchical relations between parts, while the Baroque introduced to this the competing idea of hierarchical differentiation. In the third system parts are not related, but are what Kaufmann terms independent or individual. He proposes two general categories by which independence is achieved – repetition and antithesis. While there was repetition in the ancient and Baroque systems, the difference Kaufmann identifi es is that in the third system, parts are repeated as individual units. These are not proportionally related using harmonic number series, nor are they part of a hierarchical system of competing features. Identical components are duplicated side by side, arrayed without any alteration in size, or the same component is scaled to produce what he terms ‘reverberation’. These tactics of simple repetition and scaling provide relatively neutral facade compositions, prefi guring to some degree the arrival of twentieth-century modernism.