The Geometry of Creation

Architectural Drawing and the Dynamics of Gothic Design

Robert Bork

• Publisher: Routledge
• Year: 2016
• ISBN:
  9781351888974
• Edition: 1
• Topic: Historia
• Subtopic: Historia del mundo

The flowering of Gothic architecture depended to a striking extent on the use of drawing as a tool of design. By drawing precise "blueprints" with simple tools such as the compass and straightedge, Gothic draftsmen were able to develop a linearized architecture of unprecedented complexity and sophistication. Examination of their surviving drawings can provide valuable and remarkably intimate information about the Gothic design process. Gothic drawings include compass pricks, uninked construction lines, and other telltale traces of the draftsman's geometrically based working method. The proportions of the drawings, moreover, are those actually intended by the designer, uncompromised by errors introduced in the construction process. All of these features make these drawings ideal subjects for the study of Gothic design practice, but their geometry has to date received little systematic attention. This book offers a new perspective on Gothic architectural creativity. It shows, in a series of rigorous geometrical case studies, how Gothic design evolved over time, in two senses: in the hours of the draftsman's labor, and across the centuries of the late Middle Ages. In each case study, a series of computer graphics show in unprecedented detail how a medieval designer could have developed his architectural concept step by step, using only basic geometrical operations. Taken together, these analyses demonstrate both remarkable methodological continuity across the Gothic era, and the progressive development of new and sophisticated permutations on venerable design themes. This rich tradition ultimately gave way in the Renaissance not because of any inherent problem with Gothic architecture, but because the visual language of Classicism appealed more directly to the pretensions of Humanist princes than the more abstract geometrical order of Gothic design, as the book's final chapter demonstrates.

CHAPTER ONE

The Origins of Gothic Architectural Drawing

The flowering of Gothic architecture in the decades around 1200 coincided with a dramatic increase in the importance of architectural drawings. Gothic builders certainly were not the first to use drawings in the planning process; a statue of the ancient Mesopotamian ruler Gudea of Lagash, made in the late third millennium before Christ, has an architectural plan inscribed on its lap. There is good reason to believe that drawings of one kind or another were also used by the Egyptians, the Greeks, the Romans, and some builders in the early Middle Ages.¹ None of these societies left behind a large number of original design drawings as the Gothic draftsmen would, however. Such Gothic drawings thus deserve recognition as the world’s oldest extant “blueprints.” It was only in the Gothic period, moreover, that the linearity of drawing began to directly influence the character of the architecture itself, as builders strove to reproduce in stone the virtuoso detailing conceived by the master designers at their drafting tables. The intimate relationship between geometry, drawing, and architectural practice achieved in the Gothic era went far beyond anything that had come before, and it has rarely been rivaled since. The spectacular effusion of architectural drawing in the Gothic era emerges with particular clarity when seen against the striking paucity of earlier documentation in this field.

One of the only surviving early medieval architectural drawings is the so-called Plan of Saint Gall, an idealized Carolingian monastery plan sent by Abbot Haito of Reichenau to his colleague Abbot Gozbert of Saint Gall shortly before the year 820. In a series of publications culminating in a massive and celebrated 1979 study of the drawing, Walter Horn argued that the dimensions in the drawing were based on a grid system representing 40-foot squares.² Konrad Hecht independently arrived at similar conclusions, insisting once again on the centrality of modularity in medieval design.³ More recently, Eric Fernie has argued that the proportions of the Saint Gall Plan were based on a series of geometrical unfoldings similar to, but simpler than, those later seen in Gothic design. Fernie proposes, in particular, that the length of the church was created by unfolding the diagonal of the square cloister, creating a √2 ratio. This suggestion is plausible, since it situates Carolingian design in an intermediate position between the Roman and Gothic traditions. The Roman architect Vitruvius had already mentioned rooms with proportions of 1 to √2 as one harmonious format, although his other recommendations were all for rooms of rational modular proportions. Fernie himself, moreover, claims to have found 1 to √2 relations not only in the Saint Gall plan, but also in the groundplans of several major Romanesque churches in England.⁴ This may well be correct, but precision in these matters is harder to achieve than in the study of Gothic workshop drawings.⁵ And, it is difficult to connect the Saint Gall plan directly to the later Gothic design tradition, for two basic reasons: first, because it has often been seen as an ideal theoretical exercise rather than a practical proposal for a real building project; and second, because the few surviving Romanesque drawings of specific buildings are even further removed from the workshop culture of the Gothic world. The so-called Waterworks drawing of Canterbury Cathedral, for example, is essentially an elaborate sketch with subtly inconsistent points of view, rather than a geometrically precise plan, elevation, or detail study like those common in the Gothic era.⁶

Drawings may have been used in the design process in the early Middle Ages, at least for the most ambitious building projects, but solid documentary evidence for this practice begins to emerge only at the dawn of the thirteenth century. There are, therefore, no surviving drawings related to construction of Saint-Denis Abbey, Sens Cathedral, or the other earliest specimens of Gothic architecture. The oldest surviving Gothic drawings, or at least the oldest closely related to design practice, are detail studies scratched into the stone surfaces of several French and English buildings in the 1190s. Rosette patterns, for example, appear at Soissons Cathedral, Byland Abbey, and the church of Notre-Dame-en-Vaux at Chalons-sur-Marne, while pier profiles can be found at Jervaulx Abbey in Yorkshire.⁷ Because most of these are drawn at full scale, they appear to be close cousins of the templates that would have been used to cut stones for construction. For this reason, Robert Branner argued in a fundamental 1963 article that Gothic drawing practice originally arose in the context of stone working, as detail forms grew too complicated to cut without templates being carefully drawn up ahead of time. Branner suggests that drawing then migrated, in the decades around 1200, from the worksite into the drafting studio, from stone onto parchment, and from full to reduced scale.⁸ This development, in turn, made it practical to draw whole buildings in plan and elevation, rather than just their small component pieces. Drawing thus became a powerful new tool of architectural planning. The rise of drawing, in fact, would turn out to be one of the most significant methodological innovations in the history of medieval architecture.

VILLARD DE HONNECOURT

Valuable early evidence for the emergence of drawing-based design practices comes from the portfolio of sketches produced by Villard de Honnecourt in the years around 1230. As noted previously, however, Villard probably was not a designer himself.⁹ Even the purely architectural drawings in his portfolio do not belong to a single coherent tradition of representation. Instead, they seem to depend on a mixture of influences. Some, like his drawings of the window moldings and pier templates for Reims Cathedral, suggest close familiarity with full-scale stoneyard drawings like those just discussed (folios 15v and 32r). Others attest to his awareness of more comprehensive drawings. One interesting example gives a highly schematized plan of a Cistercian church, rendered essentially as a grid of line segments, with small circles at their intersections and small rectangles at their ends describing piers and buttresses, respectively (folio 14v, Figure 1.1). This emphasis on linear armatures, and on the conceptual priority of pier axes in particular, would characterize the Gothic drawing tradition well into the sixteenth century. Villard’s more detailed plan of Cambrai Cathedral’s east end, drawn on the same sheet, likely copies a drawing he had seen in the Cambrai workshop, and his decision to produce elevations and buttress sections of Reims Cathedral may reflect his exposure to analogous prototypes (folio 31v and 32v).¹⁰ In other cases, Villard introduced perspectival cues that owe more to traditions of manuscript illumination than they do to the strictly orthogonal plan and elevation formats typical of genuine workshop drawings throughout the Gothic period. A few, such as a sketch of a clock tower, attempt to capture the full three-dimensional presence of the structure in question, although with far less sophistication than pictorial representations made in the later Middle Ages and Renaissance (folio 6v). By comparison with the later design drawings discussed in this book, moreover, Villard’s sketches were quite small. The pages of his portfolio measure only about 24 by 15 centimeters. The earliest thirteenth-century drawings from the Strasbourg workshop, by contrast, measure nearly a meter square, and some late Gothic tower drawings could reach heights in excess of 4 meters.

Even the drawings in Villard’s portfolio that appear most closely modeled on genuine workshop drawings are less than precise in their execution. The plan of the Cambrai choir, for example, was constructed with the aid of a compass, but two basic problems compromise its geometrical rigor (Figure 1.2). First, Villard’s freehand drawing of the building outlines is wobbly and imprecise, with a looser overall feel than the ruler-drawn lines seen in later workshop drawings. Second, and more interestingly, Villard’s attempted subdivision of the hemicycle into five equal slices succeeds only approximately. The construction starts fairly accurately at right, but the chapels are slightly bigger than they should be, pushing the left margin of the hemicycle below its center. A precisely analogous error occurs in the hemicycle plan that Villard developed with Pierre Corbie, which was supposed to be subdivided into seven equal slices (folio 15r).

Figure 1.1 Villard de Honnecourt, detail view showing the schematic groundplan of a Cistercian church, and a more detailed groundplan of the Cambrai Cathedral choir, from the Portfolio. Parchment, ca. 24 x 15 cm. Paris, Bibliothèque nationale de France, MS Fr 19093, folio 14v.

Such inaccuracies are hardly surprising, since medieval builders knew no simple geometrical construction to produce perfect pentagons and heptagons. Even Roriczer’s Geometria Deutsch, from 1486, includes only approximate constructions for these polygons. Medieval builders could, of course, achieve highly precise subdivisions of arcs when it truly mattered to them, as it would when laying out the hemicycle of a great church at full scale.¹¹ The east ends of Reims Cathedral and the collegiate church of Saint-Quentin, for example, incorporate highly accurate pentagonal symmetries. By the late thirteenth century, moreover, pentagonal tracery motifs had become relatively common. There is a world of difference, though, between being able to achieve pentagonal symmetry when necessary, which medieval designers could do, and being able to achieve it easily and quickly, which they could not. For this reason, pentagonal and heptagonal figures seem to occur in Gothic drawings only in those fairly rare cases where the depicted structure itself was meant to have that symmetry for some particular programmatic or symbolic reason.¹² By contrast, easily drawn figures based on the equilateral triangle, the square, and their immediate derivatives such as the octagon governed the proportions of many Gothic drawings, as the following chapters will demonstrate, even when the structure in question has no obvious triangular, square, or octagonal form.

Figure 1.2 Villard de Honnecourt, Cambrai Cathedral apse plan with geometrical overlay.

Because Villard’s drawings are fairly imprecise in their execution, interpretation of their geometrical structure must involve some subjective judgment about what is logical or natural in a given design situation, above and beyond objective quantitative analysis. In the case of Villard’s Laon tower plan, for example, it makes sense to imagine that octagons might play a role in governing the drawing’s proportional structure, since the tower core itself should have octagonal symmetry. Taking this argument a step further, it is reasonable to look for rotated square geometries in this plan, since these relate so closely to the explicitly drawn octagon of the tower core. Rotated squares deserve investigation in this context, also, because they figure so prominently in the late Gothic treatises on the design of towerlike pinnacles.¹³ Such thinking led both Ueberwasser and Velte to propose quadrature-based schemes for Villard’s drawing (see Figure 0.6).¹⁴ Their proposals differ from each other significantly, however. Ueberwasser took the span between the tower buttress faces as his point of departure, using a single set of rotated squares within this basic figure to determine the width of the tower core and the buttresses framing it. Velte, on the other hand, constructed a longer sequence of rotated squares reaching out from the central keystone to a square framing the colonnette clusters near the edge of the drawing. The incompatibility of these two published schemes admittedly casts some doubt on the reliability of geometrical research on Villard, but Hecht was wrong to suggest that this conflict automatically discredits both. Such disagreement requires, instead, that only one of the alternatives be incorrect. Of the two, Velte’s appears more vulnerable to criticism, for several reasons. First, it involves many lines that are not visible in the original drawing, including the outer framing square, and the square one-half its size that fits just inside the central octagonal space of the tower. Second, it fails to explain key features of Villard’s drawing, such as the width, span, and salience of the principal tower buttresses. Third, and conversely, it deals mainly with details, such as the keystone size, that would probably have depended upon the larger conception of the design. Ueberwasser’s scheme, on the other hand, cannot be easily dismissed.¹⁵ It plausibly connects the major lines actually present in Villard’s drawing, most notably the buttress faces, the outer walls of the tower substructure, and the inner walls of the spire octagon, using only a simple quadrature relationship. This general scheme appears credible not only because of its own internal logic, but also because it has much in common with geometrical schemes evident in many later and more carefully drawn tower plans, where compass pricks and construction lines make it clear that thinking of this general sort guided the design process. Villard’s plan lacks these telltale signs, and its crookedness and irregularity complicate geometrical analysis of its proportions.

Despite these limitations, the likely steps in the generation of the Laon tower plan prove fairly easy to discern (Figure 1.3). The original designer of the tower, whose drawing Villard may have copied, probably would have begun by establishing a large square with side lengths corresponding to the total width of the tower, measured to its outer buttress faces. This dimension would have been a crucial constraint on his design process, since it would have been determined by the size of the buttresses that had already been constructed in the lower stories of the tower. Within that outer square, he could then have inscribed a rotated square, an octagon, another rotated square, and another octagon, each smaller than the first by a fac...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• List of Figures
• Acknowledgements
• Introduction: Geometry and the Gothic Design Process
• 1 The Origins of Gothic Architectural Drawing
• 2 The Flowering of Rayonnant Drawing in the Rhineland
• 3 Italian Drawings up to 1350
• 4 Germanic Tower Drawings and the Elaboration of Tradition
• 5 Wider Horizons
• 6 The Italian Challenge to the Gothic Design System
• Conclusion: Gothic Drawings as Traces of the Creative Process
• Bibliography
• Index