An architect's approach to medieval geometry
Many architectural historians have difficulties in dealing with a built object when their schooling is in documents and photographs. I have chosen to illustrate this from Stephen Murray's, Notre-Dame, cathedral of Amiens. The power of change in Gothic , Cambridge, 1996, because I read his geometric analysis very carefully before reviewing it for the Australian medieval magazine, Parergon.
I would like to think that what I am going to say may be of some benefit to nearly all architectural historians. It is not a commentary on Stephen, for he wrote a fine book with the courage to bare his heart and his love of this great work. But the root issue is that too few architectural historians have any training in building processes, in measuring and in drawing, in translating a drawing into a building, and in the day to day exigencies of construction. I had attempted to provide some training in the 1970s that would rectify this in two workshops I organized for art historians at Chartres, but when I later attempted to have similar exercises included as part of art-historical studies I. received little support.
Twenty-five years ago I developed the analytic techniques for above-ground archaeology that I call Toichology, and they are used by many scholars, including Stephen. Yet he makes no reference to my Contractors of Chartres in which these techniques were first developed - an omission I mention because in a comment on the construction sequence at Chartres he cites in evidence only a short work by van der Meulan. Could this be because he, like many others, finds that the detail, the geometric studies and the constructional understanding in my work lies too far outside the current teaching paradigm for easy comprehension?
I wonder if this is why the only historian to have asked the present maître d'oeuvre for the keys of the cathedral to check out my work did so earlier this year. Is this why relatively few articles are published nowadays on medieval architecture, and does it contribute to the 80 percent slump in conference sessions dedicated to this topic over the past fifteen years? Avoiding having to understand how a building is constructed may be one cause to the deep malaise in the profession. I feel it needs to be addressed if Gothic architectural studies are going to develop further.
The core of the problem can be seen in Stephen's least skill - construction geometry. Yet geometry is the essence of the master's methodology and communication, and therefore of his creative process, for it is only through geometry that he can control the job and maintain consistent instructions to his men - which he does through the templates. Geometry is so important that it is the sole technique found in the late medieval instruction books. It pervades every decision. [See Shelby's articles in Speculum and the JSAH in 1972, and mine in the Architectural Association Quarterly in 1973, 1979 and 1982].
If we are to fully understand the master's process we need to study his geometric methods in every part of the building. After all, it is often far easier to work our geometric processes in small elements like doors, piers and windows than by tackling the whole. These micro studies will give clues to the master's methods, and in my experience will nearly always indicate the precise length of his foot measure. It is particularly important to know the geometric sequence in the piers, as these (both by logic and experience) will be linked to and probably derived from the overall geometry of the plan. This was definitely the case at Chartres, Durham and the chapel in the Tower of London.
Typical of most academic studies on medieval geometry, Stephen has limited his search for the initial layout to the lowest visible stones, and only to those on the interior. Was it raining? Or does the outer stonework have nothing to do with holding up the inner?
He found that the pier axes form a double square of 50x25 feet, using the classic Roman foot of 295 mm. He extended this foot into the aisles and located the glass at 30 feet. At this point I became very puzzled. He had stated that "the building was designed and built from the ground up". Yet, in the same breath, he could argue that the lowest courses were set out from the glass line, a plane of construction that would not have been placed for many years.
The acid test for any geometric system is whether it can be used successfully on a vacant site. The setting out of the lowest stones has to be made as easy as possible, being in the midst of the mud and dust of a site open to the weather.
To discover the geometry of a building we need to think of the process of construction in the same way as the master would have. He is firstly, before any aesthetic considerations, concerned with structural stability. Three elements are concerned with support: the piers, the walls and the buttresses. As logic would suggest, at Chartres the three key intersecting points flay through the centres of these three elements that support the vast weights overhead. In setting out to discover any design we have to empathetically mirror the processes used by the mason, and include these three centres. Stephen has totally ignored two of these three: the wall and the buttress. Choosing the glass presumes that this is what held up the building.
The centre of the piers is usually easy to determine. The walls and buttresses may offer alternatives. In the earlier buildings the geometry would often be taken to the face of the wall and the outer face of the buttress. The concept of the axis lying within the wall and buttress seems more to do with the twelfth century than the eleventh. Both methods are illustrated in two of Villard's plans and in the two apsidal towers at clerestory level at Chartres. I would think that each method should be checked out before deciding which was used.
However, for this discussion, I will stick to the Chartrain system. The wall axes run through the point where the diagonal axes through the aisle ribs meet within the wall, S in Fig. 1, and the epicentre of the buttresses E where the diagonals from the outer corners meet the main axis. (See "epicenter" in the index of The Contractors of Chartres for more details.) The building logic behind this is that as the buttress is reduced in size as the height of the building increases the position of the epicentre remains constant.
I applied this to Amiens using the measurements Stephen gives in the appendix. This showed that S and E are in the ratio of v2:v3 to the main axis. That is, the wall centres were ad quadratum to the axis of the church, and the buttresses ad triangulum, which reminds one of a later attempt to choose one or other for the cathedral of Milan. One is the diagonal of a square and the other of a triangle. Both these dimensions are based on a length 1½ times the bay width of 25 feet.
In the other direction the ratio of the span between the piers P to the distance from P to the epicentre of the buttress E is v3:2v2, Fig. 2. This links the high vaults which are supported on the piers to the buttresses which were built to stabilize them.
Using the diagonals and simple rectangles that form these ratios I have set out the whole plan of a dozen cathedrals on university grounds, full size, twice in mud, with students and wine flagons to mark the major intersections. When done in situ one has to realize how simple the methodology is, and how easily grasped. Again and again we have in less than a morning set out the most difficult part of a church, the choir with its apse and chapels, to the same ±20 mm accuracy found at Chartres.
Working to a hypothetical glass line this could not be done.
Stephen suggests that the overall dimensions of the cathedral were added bay by bay around a predetermined crossing, using a series of squares and arcs so that "peripheral spaces will be unfolded from the central square". This is odd, for God is not the sum of His parts, but each aspect of His Creation is a reflection of the Whole. This was (and is) a basic tenet of Christian theology, and we would hope to find it reflected in the geometry of its most important expression. I would hope that any great sacred building would be designed within a large primary figure. At Chartres I called this first step in the geometry the Creation Figure.
This figure was bounded by the distance between the high altar and the labyrinth one way, and the walls of the transepts in the other, Fig. 3 (see chapter VIII in The Contractors of Chartres). This initial form of one large diamond bounded by two smaller ones was not an accidental shape, but filled with meaning. Where trinitarian designs have been noted with three equal triangles, this church was dedicated to the Virgin, who was usually represented flanked by two angels. This may be why a modified tripartite scheme was used to set out her home.
Once the figure is determined the next step is to anchor it in reality by ascribing distances to each part. It would seem to me most important in a society that lived the spiritual life to ensure that there was a logical step-by-step evolution from the first geometry to the axes and from them to the elements. Only in this way could the first statement be integrated into the rest of the architecture, just as God's hand was to be seen in even the smallest aspect of His creation. So a major test of whatever system the art historian finally comes up with should be the steps that could be taken from the Creation Figure to the simple foot lengths used in the pier-wall-and-buttress axes.
If this is there, then there is a further question: was there any meaning in sizes chosen for the first figure? At Chartres these could have been 'calculated' from the dedication of the building using what is called gematria, an ancient system in which each letter is numbered from A as one, B as two, etc. to Z. At Chartres the first master used the Roman Foot (determined from the axes) 352 of which measured the length of the largest diamond, being the distance between the labyrinth and the altar. In gematria this actually could have been obtained from the consecration of the building as "Beata Virgo Maria Assumpta".
So I essayed this system at Amiens (using whatever measurements I could garner from Stephen's book). A cross with four equal arms seems to sit between the labyrinth and the centre for the eastern end in the east-west direction, and between the walls of the transepts in the other. Each arm of this cross measures 208 Roman Feet. The cathedral was dedicated to the Virgin as "Beata Virgo Maria Mater Dei". In gematria this phrase adds up to the same 208 used in the central cross. Maybe the geometries and the dedications in other buildings should be checked out.
I have given these alternative geometries to suggest that there may be many interesting ideas that could present themselves by approaching the construction process in the manner of a builder, not an historian. From my training I do not know Latin and am not the best examiner of documentary sources. Others do this work much better than I. But I do know construction and have, besides designing as an architect, built some 150 buildings as the on-site contractor. I say to you all, great buildings are built, and that documents and photographs and occasional measurements are no substitute for the heavy, tiring and passionate job of being that builder.
I am, and have always been most willing to share this knowledge. It is my dearest wish that those in my colleagues would learn to use the Toichological skills I have developed. Stephen is a friend and a dedicated scholar. As I said before, I am not having a shot at him, but using his book as the text for a morality play. This is an appeal to broaden the training of architectural historians so the work they do on buildings will be more real in the world of construction.
John James bibliography