Han VandevyvereKatholieke Universiteit Leuven Onderzoeksgroep CAAD en ontwerpmethodologie Kasteelpark Arenberg 1 B-3001 Heverlee BELGIUM
Bauhüttengeheimnis)
[Shelby 1977: 46ff]. One could indeed pretend that back-tracking
a hidden geometrical composition is just Hineininterpretierung
(hind-sight interpretation). This discussion often seems
to end up in a confrontation between "believers" and
"non-believers", each of them furnishing evidence of
his or her conclusions. To take into account
some justified criticism, from the very beginning the analysis
of the town hall of Louvain was approached in a very pragmatic
way: if the scheme behind it was not evident and simple,
the idea would be rejected.However, there is a double reason for setting up an investigation into the existence of a scheme. First of all, the middle ages were undeniably a time of highly symbolic language. And secondly, the evidence from other research affirmed the point of view that taking a closer look at the Flemish town halls was at least worth doing. For the development of an inquiry, it is necessary to have the disposal of a minimal basic set of rules. There should be little discussion about the existence of these rules, and if so, some rules should be given more credit than others. They should confront the results of a purely graphical/numerical analysis with a set of recognizable ordering principles. However, the symbolic connotation of the design rules or schemes is at this moment not under consideration. Only the "visible" level, the graphical evidence stemming from a plan, is examined. In this way, where Louvain is concerned, different issues were regarded, with a certain "probability rate" for each rule. We want to mention some of them, before reviewing the Louvain analysis itself. The set of basic ordering rules was considered as follows: - The preference of the master builder to use simple series of integer numbers, so as to obtain simple ratios between the dimensions.
- What is found to set up a plan should also be found in the
elevations. Plan and elevation are linked to each other, as stems
from this 15th century statement:
*...ainer stainwerchs von massen oder von ausczug ... aus dem grunde (zu) nemen*: i.e., the measures for the upgoing stone-work are taken from the ground,[1] a principle that has already been illustrated in multiple occasions. - The preferential use of geometrical constructions that can
easily be constructed with the compass and the carpenter's square,
among which we mention:
- the construction based on a square and its turned down diagonal, resulting in a rectangle of which the sides relate to each other in a 1:Ö2 ratio (1:1.41...). We shall call it the "root-2 rectangle" (Figure 1).
- the construction based on a square and the corresponding golden section rectangle, defining a ratio of 1:(1+Ö5)/2 or (1:1.618...). We shall refer to it as the "golden section rectangle" (Figure 2).
- It is in any case advisable to check a design in the measurement units that were in use at the moment and place of construction. As a matter of fact, every Flemish city used a different system of feet and rods.[2]
- Less probable, but to be checked as well, is a more complex
construction based on a circle, its inscribed square and equilateral
triangle (Figure 3).
It can be considered as a graphical method of approximatively
cutting off one seventh part of the side of a square. The graphical
representation is given in Figure 3, and shows that besides the
approximative 1:7 ratio, one can find a similar 1:3 ratio in
this scheme. In the analyses that follow, the construction will
be referred to as the "quatrain scheme".A medieval
quatrain (a type of 4-line verse) is said to state this method.
The German version of this quatrain is cited by Mathila Ghyka
in his work on the Golden Section [Ghyka 1969: 72], whereas the
French version of it has been mentioned by Johan Ballegeer in
a study on the town hall of Bruges [Ballageer 1987: 20]. It goes
as follows:
*Un point dans un cercle*[3] Et qui se place dans le carré et le triangle; Connais-tu le point? Tout est pour le mieux; Ne le connais-tu pas? Tout est en vain. J. Ballegeer has applied the corresponding scheme to the latter building. This analysis is discussed below.
As a general principle, we assume that the more simple and
straightforward a scheme is, the more probable its original intention
looks. A major issue, then, is the precision that should be requested
for such a scheme.
All measures are a multiple of +/- 5,75 m or +/- one rod. If we consider this +/-5.75 m as a module M, then we can find the average value for M by summing up all the given dimensions of the building and dividing the result among the corresponding summed number of modules M that these dimensions are supposed to represent:
M = 199.47 m / 35 = 5.699 m = 0.998 Louvain rod. We can conclude that the Louvain rod was the basic module
to set out the plans and elevations for the building. The error
of the calculated module (5.699) in comparison to the assumed
module (one rod or 5.71 m) is only 0.2%. - The building volume is based on a cubic grid, modulated following the local measurement system. The width of the main cubes is 2 Louvain rods, and the width of the secondary cubes is 1 rod.
- The projection of the front façade shows a contouring square for the composition, with dimensions of 6 by 6 rods.
- Superimposing the quatrain scheme on the front façade, we notice that the division in seventh parts gives the level lines for some major composition elements such as the top of the front door (1/7) and the top of the roof balustrade (5/7). Evidence for the intentionality of the quatrain scheme is, however, weak.
Considering different compositional
elements, it becomes clear that the building should be thought
of as constructed on a socle. This socle is formed by the ground
level. The main, representative floor with its big hall is situated
at level 1, and this fact is visually accentuated in the exterior
by the gallery that jumps out from the front façade. As
such, the building volume above the socle appears to be based
on a cube of 4 x 4 x 4 Oudenaarde rods (given a cube with 23.45
metre side, the deviation from 4 rods is 2 %). Again, the result
is best appreciated from a graphical representation (Figure
10ab and Figure
10c). Subdividing
the overall cube in smaller cubes with a side of either 1 or
2 rods, we only arrive at the conclusion that the cornices
are halfway the height of the 4 rod cube. The lateral gable is
inscribed in a 2-rod square whereby its top is situated at the
midpoint of the upper side, a scheme we have found in Louvain
too. However this square is shifted a little bit to the left
in order to accommodate the front gallery. Whether the general
diagonal coinciding with a side of the gable triangle defines
also the position of the tower top, remains a speculation. Again,
the cubic system does not at all define the divisions of the
façades. - The height of the socle is defined by the quadrant point of the circle circumscribing the 4 x 4 rod square.
- Dividing the vertical side of this square into 7th parts, we see that the top of the balustrade is at the 4/7 level line.
- The sides of the corresponding equilateral triangle coincide with the outer roof planes of the two main lucarnes, whereas its top coincides with a central pointed arch of the belfry tower.
By shifting this scheme half a radius R of the circle upwards, i.e. putting the base of the new equilateral triangle at the midpoint level of the 4 rod square (or situating the new quadrant point of the circle on the base of the equilateral triangle), we notice further that: - The top of the R/2 shifted triangle indicates the top of the tower.
Finally we should notice that the quatrain scheme is another
reference to the 1 - 3 - 4 series, the circle having 1, the triangle
3, and the square 4 sides. - The building volume is elaborated following the local measurement system, and is basically defined by a 4 x 4 x 4 rod cube put on a socle.
- The front façade composition originates from a contouring square which represents the front face of this 4 rod cube.
- Drawing the quatrain scheme from this square establishes some key points of the composition, and the same is in force to the division of the square in 7th parts.
- Shifting this scheme R/2 up gives the height of the belfry tower.
The analysis that follows is only fully elaborated for the front part of the left wing. This wing was first constructed from 1402-1420, together with the initial belfry tower. Jakob van Tienen was most probably the architect [Maesschalck and Viaene 1960]. Later, from 1444-1455 the tower was made higher by Jan van Ruysbroek, and three houses to the right were incorporated in the complex, in a manneristic style. However, close observation of the façade of this newer wing shows fundamental differences with the older one. Moreover, as a whole, the town hall composition is severely asymmetric. This asymmetry is rather historical and accidental, and not of the subtle kind such as we find in Louvain. For neither the back part of the left wing (the Gothic side wing) nor for the right wing has a sound geometrical system been found. Data was lacking to complete an adequate analysis of the tower. For the right wing, different master builders and construction periods may be responsible for the loss of a unitarian geometrical scheme. For the left side wing and the tower, a hypothesis can be brought forward, but with some reservation. The local measurement units are as follows: 1 foot = 0.27575 metre; 1 rod = 16 1/3 feet = 4.5039 m(the small rod) or 17 1/3 feet =4.7797 m (the big rod). We now proceed with the numerical analysis of some major dimensions. The axial / external measures of the first building phase (1402 - 1420) (with exception of the tower):
The axial / external measures of the second building phase (1444 - 1455):
As in Oudenaarde, it becomes clear that level 1 is to be taken
as a reference plane. The initial front house of 1402-1420 is
based on a volume of 3 x 6 x (3 + 3) small Brussels rods, put
on a socle. Also here, the socle is clearly marked by the gallery
of the front façade. The contouring square of this façade
is consequently 6 small rods large or 98 Brussels feet. The profile
of the attic is found from a triangle within the top lateral
square of 3 rods, in a similar way as for Louvain and Oudenaarde. - The height of the socle is defined by the quadrant point of the circle circumscribing the 6 x 6 rod square.
- Dividing the vertical side of this square into 7th parts, we see that the top of the balustrade is at the 4/7 level line.
We may conclude that there was a basic scheme for setting
out the plans for the first building campaign, very much as what
is found for other town halls. How the schemes should be interpreted
for the side wing and the tower section remains rather unclear.
Further analysis is needed. For the additions of the second building
campaign, the question is if any scheme was followed at all. - The front part of the building volume is based on a cubic grid, where one cube has a rib of 3 small Brussels rods.
- The front façade composition originates from a contouring square of 6 small rods wide.
- Drawing the quatrain scheme and the 7th parts division from this square, establishes some key points of the composition.
in situ control measurement for the
length of the front façade. The local measurement units
are as follows : 1 foot = 0.2743 metre; 1 rod = 14 feet (2x7
feet) = 3.8402 metre [Vandewalle 1984: footnote 4].We have hypotheses put forward by J. Ballegeer [Ballegeer 1987] concerning two elements: 1. The basic volume under the roof has 7 x 5 x 3 Bruges rod dimensions, whereas the overall height of the composition is 7 rods. 2. The quatrain scheme can be applied to the front façade, as shown in Figure 7b. These observations can be analysed, commented and eventually further elaborated. First, the precision of the volumetric modulation is examined. The in
situ measurement of the front façade gives us a length
of 26.38 m, being 6.87 Bruges rods. This means a deviation from
the theoretical 7 rods of 1.9%, which is
highly acceptable (Louvain had typical deviations of 2%
on average). Secondly, J. Ballegeer does not account for the
roof volume in Figure 7b; he only considers the turrets for analysing
the upper part of the façade composition. However, it
has become clear from the other examples that the roof also obeys
to the overall geometrical concept. So we will reconsider the
building volumes and the front elevation, based on a set of survey
plans made by L. Devliegher and J. and L. Vierin.The quatrain scheme provided by J. Ballegeer goes further in its elaboration than what we have put forward up to now for the other town halls. He has confirmed that it is a compagnonesque construction, thus pointing at an essential source of information. The "Compagnons" indeed originate from the medieval building lodge tradition.[8] In the present approach, the quatrain scheme was only used in its most basic form when analysing the other town halls. As said before, this is for reasons of evidential value. The more complex the proposed composition rule, the more evidence should be carried for it. In other words, if we should want to do further investigation on the application of the quatrain principle, we should have the disposal of more precise and parallel information in addition to what is gained from a first, purely dimensional, analysis. Because we don't have this detailed information at this moment, we look again at what is the result of the "basic" analysis, keeping in mind the findings of the other designs. It should also be noticed that the complex scheme as drawn by J. Ballegeer in Figure 7b, appears to have several inaccuracies for what concerns the representation of the façade, resulting in some inaccurate conclusions. For the present analysis, detailed survey plans are used to start over the whole process again from the beginning. The first thing we can observe reconsidering the town hall plans, is that the gable (attic) profile is based on an equilateral triangle that sits on the 3 x 5 x 7 rods volume (Figure 15ab and Figure 15cd). This is a principle different from what we found for the other town halls (equilateral triangle vs. square division triangle). Secondly, applying the quatrain scheme as proposed by J. Ballegeer, we see that the contouring square for the front façade accounts for the top of the stone pinnacles of the three turrets, but not for the roof ridge which is at a higher level. We should move the scheme 0.5 rod = (7x2)/2 = 7 feet up if we want to start reasoning from the roof ridge, as could be done for the other buildings. Considering the two shifted schemes we notice now that: - For the lower scheme, the equilateral triangle coincides with the metal node on the roof top of the mid turret and the roof planes of the two lower lucarnes;
- The division in 7th parts shows that the front door height corresponds with level 1/7, the base of the turrets with level 4/7 and the balustrade top with level 5/7;
- For the upper scheme, the equilateral triangle coincides with the top of the metal flag of the mid turret;
- The base of the contouring square coincides with a ridge in the stonework and the baseline of the windows;
- The division in 7th parts shows that level 1/7 coincides with the top of the 6 front door pinnacles and level 4/7 gives the cornice line.
Summarizing the schemes for Bruges, we can say that: - The building volume is elaborated following the local measurement system, and is basically defined by 3 x (5 or 7) x 7 Bruges rods.
- The front façade composition originates from two contouring squares of 7 rods.
- Drawing the quatrain scheme from these squares establishes some key points of the composition, and the same is in force to the division of the square in 7th parts.
- The two quatrain schemes are shifted 7 Bruges feet one to each other.
After analysing these four buildings in a more or less extensive way, three other examples of Gothic town hall architecture of the low countries were examined, this time outside the actual Belgian territory. Depending on the amount of material that could be collected, the analysis is limited to a merely graphical inquiry of the front façade, or of the building-plans. The results are a checkpoint for what has been put forward before.
- The building is inscribed in a cubic grid, which is starting from the 0.00 floor level (note that in Bruges the 0.00 floor is exactly at street level). The central interior wall and the second floor are also located along the grid. In the front façade we find a countouring square as a result;
- The turrets have their base at half the height of this square, coinciding with the cubic grid;
- The attic profile is based on an equilateral triangle, as in Bruges, and has its top coinciding with the cubic grid;
- Drawing the 7th part division, we notice that level 1/7 gives the door height, coinciding with a window division, level 4/7 gives the cornice and level 5/7 gives the top of the stonework of the turrets. The quatrain scheme itself does not provide more specific points.
- A partial square grid can be discovered, but we cannot speak of a cubic grid.
- The contouring square can be drawn, but does not account for the roof ridge.
- Applying the quatrain scheme upon this square, we find some key lines for the composition.
- The division in 7th parts doesn't work starting from the quatrain scheme, but starting from the roof ridge height.
- The front façade fits in a square. The design is probably based on a cubic grid, resulting in a subdivision of the contouring square in 9 subsquares;
- Two quatrain schemes, one shifted R/2 to the other, can be drawn. The triangle of the shifted scheme coincides with the outer ridges of the 3 equilateral gables;
- The division in 7th parts for the first scheme gives us the foot of the 7 arches at level 1/7, the top of the arches at level 2/7 and the top of the (formal) balustrade at level 5/7.
An initial set of probable design rules has been tested, leading to the conclusion that the following principles may very well have been in use when the master builders set out their projects: - The cubic grid: the main lines of the building respect a volumetry ordered by a juxtaposition of cubes. If not, we still find an expression of the main dimensions in simple series of local measurement units (the rod of the particular city where the building was constructed).
- The front square: the front elevation, including the projection of the roof, is dictated by a contouring square. This square may be put on a socle.
- The quatrain scheme: other key points of the main façade are ordered by this scheme, which represents a square, a circle and an equilateral triangle with the same centre point. Out of it derives a division of the square side in 7th parts, which on its turn defines other elements of the composition.
These three principles reflect aspects of the basic organization
of the building. The cubic grid can be considered as the "sketch
design rule", but does not systematically refer to elements
such as centre lines or exterior edges. In general, the precision
of the schemes is at the highest in the front façades,
and less pronounced in ground plans or building sections. Subdivisions
of the façade or the positioning of interior walls and
floors often show no direct concurrence with the schemes, and
have for the present been analysed more
systematically. However, in some cases such as Veere,
there seems to be an obvious application of the principles for
the interior subdivisions.
Only a first reflection on the role of the city will be made here. The Flemish (and Brabant) cities obtained, through the 13th-15th century, an advanced political independence. They became major trade centres for the known western world, and accumulated an unestimable amount of wealth. Bruges can, in a way, be considered as the New York of the 14th century. For example, the first stock exchange activities took place on a square in this town, giving origin to the term beurs (bourse, bolsa, borze,...). The cities were so powerful
that they could threaten the king of France, impose their conditions
on the Flemish counts, and so on. The mutual rivalry between
the towns themselves resulted in numerous little wars - as far
as they were not making coalitions against a common enemy. The
city hall and the belfry tower were not only the most important
institutional buildings of these communities, they were the very
symbol of the civic pride and power and of a new consciousness.Different elements indicate that, from a more metaphysic point of view, the city could be thought of as a microcosm. This microcosm forms part of the macrocosm, and obeys to a parallel, similar set of rules. On the pragmatic level, for example, each town not only had its own jurisdiction and privileges, but also its own units of measurement. Apparently, this fact was more important than the chaos that must have resulted from endlessly recalculating quantities or adapting rules while going from one city to another. Consequently, the emblematic city hall was always set out in local measures -- and this was only the beginning of a more complex symbolic story. The front façade, which is the "face" of the town hall and of the city, can in its turn be regarded as a symbolic representation of this microcosm. The square and the circle add up to a mandala,[10] an archetypical form representing the relation between the earth (the square, the finite) and the universe (the circle, the infinite). The façade of the town halls in our analysis is a square, and thus the absolute expression of earthly strength and stability. But in its relation to the circle, it refers as well to the metaphysical. This combination of both elements is very essential, for in the middle ages, one never put forward anything without considering its proper place in the cosmic order.
[2] With regard to these measurement systems, it has
been proved that they stayed in use nearly unchanged until the
French Revolution. At the moment of the introduction of the metric
system, commissions were set up by the French in every new "Département",
to establish very precisely the relations between the old and
the new measurement units. The reports of these commissions compose
a capital source of knowledge about the medieval measurement
systems. A detailed description is to be found in [Vandewalle
1984]. [3] "A point in a circle - And that can be situated
in the square and the triangle - Do you know the point? All is
for the better - Don't you know it? All is in vain." [4] This point of view will be put in perspective below
when considering the town hall as a microcosm within the macrocosm,
the first obeying to and representing the same principles as
the latter. [5] See Origins of Surveys
Plans and Models Used below for more details on sources.
[6] One should always be suspicious about the originality
of these balustrades, because they were sometimes added, mostly
in the 19th century, to obtain a more "high" Gothic
look. An example is the St.-Pieter's church in front of the Louvain
town hall. Another example, where this happened with the town
hall is Middelburg (the Netherlands). [7] For an additional hypothesis on the construction
of the first building plan, [Vandevyvere 2000: 185-188]. [8] For an introduction on the Compagnons, see [Bayard
1977]. The organization still exists today and forms highly skilled
craftsmen who are trained in particular for restoration work.
[9] This can however not be said with absolute certainty.
In the future, some archive files residing in Paris could bring
more clarity about the details of the reconstruction process.
We do know for example, that the arches of the front façade
were recuperated for the reconstruction. [10] C.G. Jung points out that the Mandala scheme can
often be found in medieval representations. See [Jung 1993] and
[Jung 1963].
Note: All plans are 20th century surveys, made for documentation, maintenance and restoration purposes.
Bayard, J.-P. 1977. Ghyka, M. 1969. Jung, C.G. 1963. Jung, C.G. 1993. Maesschalck, A. and J. Viaene. 1960. Shelby, L.R. 1977. Vandevyvere, Han. 2000. Het stadhuis van Leuven: een geometrische
analyse. Vandewalle, P. 1984.
Han Vandevyvere
graduated from Katholieke Universiteit Leuven in 1989. Since
then he has combined working at the Computer
Aided Architectural Design research group of the Architecture
Department, Katholieke Universiteit, Louvain under Prof.
H. Neuckermans with practicing as an architect. He is presently
at Modulo Architects, Brussels. Work at CAAD research group has
included digital reconstruction of the building history of the
Leuven town hall. Work in construction practice has included
historic-archaeological research on Gothic houses, for restauration
purposes. More about Han Vandevyvere can be learned from his
homepage.
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