Gothic Town Halls in and around Flanders,
A Geometrical Analysis
Katholieke Universiteit Leuven
CAAD en ontwerpmethodologie
B-3001 Heverlee BELGIUM
This present article is the result of an
investigation into some geometrical schemes that can be supposed
to underlie the building-plans of a number of Flemish Gothic
town halls. Among the most famous of them, we can mention Brussels,
Louvain, Oudenaarde and Bruges, all of them built from the late
14th till the early 16th century.
for this investigation was a detailed analysis of the town hall
of Louvain [Vandevyvere 2000], and the conclusions resulting
from it. All this shows that the building has been set up by
using a module based on the local, medieval measurement units.
The most important parts of the analysis will be reconsidered
in this article. It was so fascinating that, from this analysis,
the research has been carrying on to other Gothic town halls
in Flanders and the neighbouring regions. The results give evidence
of the fact that similar schemes have been applied to these buildings,
although with local variations. Consequently, the hypothesis
of a set of geometrically designed principles that seem to define
a whole range of civic buildings, is put forward. This can be
compared to what has already been pointed out for the church-architecture
of the middle ages.
In order to render an account
of every step in the reconstruction of the geometrical system,
the article will follow the methodological démarche of
BACK-TRACKING GOTHIC DESIGN TECHNIQUES:
WHAT TO LOOK FOR?
A major problem in reconstructing
scenarios used to design medieval buildings is the lack of hard
evidence about them. One of the consequences has been a continuous
polemic about whether the medieval master builder used some more
or less secret schemes or not (the 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, 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
- 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.
- 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
Un point dans un cercle
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.
Close observation of the town
halls in the study seems to indicate that the medieval builder
had another concept of precision than we have. For example, he did not feel obstructed by particular
conditions of the program or building site that would prevent
him from realizing a scheme to the centimetre. A striking example
of this flexibility and freedom is the sophisticated use of 'near-symmetry' in a design. Symmetry as we understand
it nowadays is a concept derived from rationalistic thinking
- we may call it mathematical or 'dead' symmetry. The middle
agers however made much use of 'natural' symmetry, such as we
find, for example, in the composition of the human face. In this
case, there is a balance between two opposite aspects: as a consequence,
something looks symmetrical, but it is in fact assymetrical.
A lot of evidence for this way of working was found in the Louvain
town hall [Vandevyvere 2000: 173-177]. It is significant that
in the 18th century, in Louvain as well as in Bruges, the façade
of the town hall was altered to make it look more strictly symmetrical
- following the new fashions, a proof of the 'distance of spirits'
that was emerging with the "Enlightenment".
similar to those for symmetry apply as well to measuring. The
often noticed, unaccounted deviation from a strict scheme, apparently
without any valid reason, stands in contrast with the
simultanuous rigorousness of that scheme. It would appear that
the medieval builder appreciated the contradiction as a mode
of expression, a language corresponding with his world-view.
This puts us in a difficult situation,
apparently taking away the ground we are standing on to prove
the very existence of the scheme. It will turn out that only
by considering every case individually, we can evaluate the grounds.
In other words, the argument of precision is not handled in a
theoretical way, but in a practical and case by case approach.
The master builder had a unity in thinking and handling -- let
us call his attitude a particularistic approach within a general
frame -- and by consequence we should try to re-enter this spirit
rather than to look through our own conceptual glasses, since
these are defined by our own time and culture.
illustration of the need for this switch in attitude could be
the quatrain scheme: it gives indeed about one seventh of the
side of the square, but with an error of about 2.5%. It is not
the mathematical construction of 1:7. Or, to use still another
example: if nature, and so reality, always approaches the golden
section but never exactly achieves it, why should one
try to represent it exactly in a design? 
A totally different
aspect of the precision issue is the availability and reliability
of the surveys used. These are mostly
plans made in the 20th century for restoration purposes. For
Louvain, the existing plans of the building were controlled by
re-measuring important points of the building on the site, in
a combined digital and traditional
way, that is, using a combination of "computerized"
tools such as a "full station" and "traditional"
tools, without electronics or integrated data processing. From
these measurements, the plans were re-calibrated so
as to obtain a precision from 5
to 10 centimeters. The reference is the size of the building,
+/- 30 meters wide (by 10 meters deep and 50 meters high), so
as an average we speak about a 0.25% relative error on measurements:
7.5 cm / 3000 cm = 0.0025%. The deviation of the original plans
mostly proved to be minimal and of no influence to the conclusions
of the analysis. For the other buildings analysed here, only
in situ re-measuring will give absolute certainty about
the precision of the survey drawings. It should be said, however,
that the schemes and principles put forward in this study absorb
without problems small deviations such as those resulting from
'average accurate' building surveys.
seven buildings will be examined, less or more in detail. A major
group of four are located in the actual Flanders (the former
Flanders and Brabant): Louvain, Oudenaarde, Brussels and Bruges.
A minor group of three is located just over the borders: Arras
and Saint-Quentin in North France, and Veere in the Southern
Netherlands (Figure 4). All of the latter are situated on
a location that was once part of Flanders, or under a strong
influence of it.
LOUVAIN, STARTING POINT FOR THE ANALYSIS
As mentioned before, the town hall
of Louvain, near Brussels, was investigated first. The material
resulting from this analysis was important for carrying on the
research to other buildings.
The Louvain town hall, or more precisely the Voirste Huys
(front house) of it, was built between 1448 and 1469. Louvain
intended to build a prestigious project (Figure
intended to surpass in splendor the recently finished town hall
of Brussels. The design as it stands now was provided
by Mattheus De Layens.
To trace series of numbers
in the dimensioning of the building, we should think in Louvain
feet and rods. One foot in Louvain stood for 0.2855 m, and 20
feet composed one rod (5.71 m).
We consider now the axial dimensions of the building:
Length of the building, between the centre lines of the
33.42 m or 5.85 rods
Depth of the building, between the centre lines of the
11.91 m or 2.09 rods
Height from the average ground level up to the cornice
of the roof:
22.86 m or 4.00 rods
Height up to the ridge of the roof:
34.98 m or 6.13 rods
Height up to the top of the corner spires (enveloping cone):
46.12 m or 8.08 rods
Height up to the top of the mid spires:
50.18 m or 8.79 rods
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
Sum of the dimensions:
199.47 m or 34.93 rods
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%.
of any individual dimension from the assumed modular dimension
is never more than 4.3%, and the average deviation for all the
dimensions is 2%. All of this is calculated in the supposition
that we were always counting from the right reference line.
It is far more interesting to look for what this
gives in a graphical way (Figure
6). The building can thus be considered
as inscribed in a juxtaposition of cubes, all of them having
a side of two Louvain rods (= 2M). Only for the top of the mid
turrets, the cubic mesh should be subdivided into cubes of a
side half so long (= M). The plan is 1 (major) cube deep and
3 cubes wide. Up to the roof cornice, we have a height of 2 cubes,
up to the roof ridge, 3 cubes, and up to the top of the corner
turrets, 4 cubes, together all of them are defining the basic
volumetry by a simple series of the numbers 1 - 2 - 3 - 4. For
the four corner turrets, the second node of the metal flag coincides
with the top of the enveloping cone of the spire and indicates
the cubic gridpoint; for the two mid-turrets the top flag itself
indicates the modular gridpoint. The cubic grid only defines
the dimensions of the shrine-like volume of the building, and
clearly not the division of the façades. No corresponding
positioning of interior floors and walls (omitted in the ground
plan scheme) was noticed either.
Whether the grid
lines should be considered as centre lines or exterior edges,
is hard to define. It looks rather as if the architect made a
modular "sketch design" volume, and later detailed
the building in a more free way. Within the 2M cubic grid, the
roof profile is obtained by constructing a triangle from the
base of one of the major squares to the midpoint of its top side.
This explains why we have indeed a measured roof slope of 63.4
degrees, this angle being exactly the arctangent of a 2:1 ratio.
Another conclusion which can be derived from the
graphical representation is that the projection of the front
façade is, with the exception of the turrets, inscribed
in a square (Figure 7a). At this point it becomes interesting
to compare the front façade with a scheme provided by
J. Ballegeer for the Bruges town hall (this scheme will be further
elaborated and commented on below). A square appears to define
the basic contour of the front façade in this case too.
Carrying on the analogy, we can verify the results
of the superposition of the "quatrain scheme" on both
façades. We first look at some aspects of the Bruges front
façade. Here, the contouring square measures 7 Bruges
rods. We notice that the front doors are 1 Bruges rod high, and
that the top of the balustrade battlements  is at 5 rods from the ground level
(i.e. 5/7 of the square side).
If we draw the same scheme on top of the Louvain front façade
and indicate the seventh parts of the square side, we notice
that the top of the front door equally corresponds with level
1/7 of the square side, and the top of the balustrade with 5/7.
The 1/7-line for the door seems to explain why it has a strange
cut-off from the window rhythm, letting two minuscule openings
between the top of the door arch and the horizontal cross arms
corresponding with the overall window division line at that level.
Moreover, the lines 2/7 and 3/7 coincide with horizontal ridges
in the stonework. However, the whole thing is put into question
if we look at the line 4/7, which has no echo in the façade.
Therefore we accept the scheme for what it is and make no further
Summarizing the analysis for Louvain, we can
- 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,
OUDENAARDE, EARLY RENAISSANCE PERFECTION
The second building
to be analysed is the town hall of Oudenaarde (Figure
9a). The construction was started
in 1526 by Hendrik Van Pede, and in 1530 the building was about
finished. Looking at the ground plan, one immediately sees that
a square defines its set up (Figure
9b). However, the elevations do
not show a likely evident scheme. We start again with a numerical
analysis of the major dimensions of the building. Therefore we
should measure it in Oudenaarde feet (1 foot = 0.2851 metre)
and rods (1 rod = 21 feet [i.e., 3x7 feet] = 5.9871 metre) [Vandewalle
1984: footnote 4]. The axial / external measures of the building:
length on the turret axes:
24.0 m = 4.01 rods
24.2 m = 4.04 rods
length on the axes:
23.4 m = 3.91 rods
24.2 m = 4.04 rods
Height level 0 to ridge of the main roof:
28.2 m = 4.71 rods
Height level +1 to ridge of the main roof:
23.1 m = 3.86 rods
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
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
We now consider another numerical
system emerging from the 7 bays division. The average width of
a bay of the front façade is, expressed as a fraction
of the total width, 4/7 rods or (4 x 3 x 7)/7 = 12 Oudenaarde
feet. In reality, the centre bay with the tower and the two outer
bays are a bit wider, and the others are a bit narrower. The
main hall of the ground floor, on the other hand, is composed
of a 3/7 square with respect to the basic 4-rod square, or 3
x 12 feet. The front gallery has a depth of 7 feet. Further along
the 4/7 position of the balustrade top in elevation will be discussed
(i.e.: 4 x 12 feet from the base of the main square). It is interesting
to notice a preferential occurence of the numbers 1 - 3 - 4 -
7 - 12, where 7 = 3+4 and 12 = 3x4 so that the basic trio is
1 - 3 - 4. The rod itself, by being 3x7 feet, causes part of
the "number system" and is as much of a symbolic character.
The next step in the analysis
consists in superimposing the quatrain scheme on the front
façade. We can now establish the following observations:
- 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
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.
Comparing with Oudenaarde
to Louvain, we find a lot of common points. However, where Louvain
seems to have a more arithmetic character (numerical juxtaposition),
Oudenaarde relies more heavily on the quatrain scheme and is
essentially geometric. Oudenaarde shows
a Renaissance influence in its careful and precise elaboration.
This is in contrast with numerous earlier buildings where
one did not worry about a wall or more standing "out of
line" (see further with Brussels, Bruges and Veere).
Summarizing the schemes for Oudenaarde, we can say
- 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
BRUSSELS, A BIT OF CHAOS
Analysing the town hall of Brussels, one
of the most famous examples, is anything but comfortable (Figure 11).
It has a scattered building history and there exist two different
local measurement systems [Vandewalle 1984: footnote 4], one
in which a rod is composed of 16 1/3 feet and another one in
which a rod is 17 1/3 feet. In contrast with the systems of Oudenaarde
(1 rod = 21 = 7 x 3 feet) or Bruges (1 rod = 14 = 7 x 2 feet),
working with these numbers is cumbersome.
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):
Front façade, length on the axes:
= 6.08 small rods
=5.73 big rods
East façade (front house), length on axes:
= 2.94 small rods
=2.77 big rods
East façade (remainder side house):
= 4.22 small rods
=3.98 big rods
Height level 0 up to the ridge of the main roof:
= 7.44 small rods
= 7.01 big rods
Height level 1 up to the ridge of the roof:
= 6.11 small rods
= 5.75 big rods
The axial / external measures of the second building phase
(1444 - 1455):
Front façade, length on the axes:
= 4.62 small rods
=4.35 big rods.
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 depth of the side wing seems, at first sight, rather to obey
to a Ö2 proportion: 3 rods x
Ö2 = 4.24 rods. Or did the master
builder play a joke by building the side
wing 4 large rods deep? (In the same way, we can wonder if the
7 big rods total height of the building is a coincidence.) Since
this wing is not completely perpendicular to the front side,
it is better to judge things from a graphical point of view.
A hypothesis is put forward in Figure
it remains largely uncertain. It looks as if the tower section
can be incorporated in the Ö2 system, and it belongs indeed to the same
building phase. But a number of strange constructive arrangements
in the tower should be further investigated before any conclusion
is made. The second building phase seems to lack any of
the logic of the first. A less clear concept stems also from
the façade composition: cut off windows, leaping bays. We didn't take the analysis any further.
The front façade of the left wing is
most promising for further investigation, since it presents the
original design, and has the contouring 6 rod square. Again,
the cubic grid does not account for façade divisions such
as window framing. However, superimposing the quatrain scheme
on this façade, we find some striking coincidences with
the scheme of 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.
We may say that Brussels is not only very renowned, but enigmatic
as well and even chaotic. And so it is not surprising that several
historians have troubled their heads about its fuzzy logics by trying, for example, to explain the eccentric
position of the tower gate. Where ratio fails, legend
finds a solution: it says that the architect saw his "mistakes"
only after completion of the building (!), and committed suicide...
Summarizing the schemes for the first phase of Brussels
and Figure 13c),
we can say that:
- 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.
BRUGES, THE FOUNDING FATHER
The town hall of Bruges was
built from 1376 to 1420 and is one of the initial examples at
the base of a whole tradition (Figure
14). In its construction intervened
three people who might be the architect: J. van Rijsel, M. Saghen
and J. Roegiers. The analysis for Bruges was performed mostly
graphically, with an 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].
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.
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.
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.
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
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.
The link between the two 7 rod schemes is a 7 feet displacement.
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
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.
VEERE, SMALL COUSIN OF BRUGES
The Gothic town hall
of Veere, a small city situated in the province of Zeeland (the
Netherlands) has been influenced by the Bruges design in a direct
16). It was built between 1474 and 1517, probably by Evert
Spoorwater. The tower is from a later date, about the end of
the 16th century, and is not further given consideration to here. The schemes shown in Figure 17ab
and Figure 17cd are self-explanatory. We summarize:
- 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
ARRAS, THE FREESTYLER?
The town hall of Arras was built
from 1501 to 1506. The adjacent belfry tower was started earlier,
around 1460, and finished later, in 1554. The complex has been
destroyed during the First World War and consequently been reconstructed,
in 1922. At this occasion, the only element that is noticed to
have changed in the front façade is the balcony (compare
the photograph from 1914, Figure
18, with the reconstruction drawing,
Such intentional changes appear to have aimed at restoring the
medieval situation. Following the same philosophy, "anomalies"
such as the eccentric position of the middle arch of the gallery
have been meticulously respected. Most probably, all the redimensioning
matches exactly the initial design.
On the ground plan,
Figure 18, we notice that the corpus behind the gallery has a
footprint of 3 aligned squares. We will call the length of this
figure 3M, where M corresponds with the side of a composing square.
The overall ground plan however, does not fit in a juxtaposition
of squares or its derived rectangles. The front façade
has then a contouring square of 3M if we consider its height
up to the top of the gable finishings (they reach about 2 metre
above the roof ridge). This is not as usually found for the other
town halls. However, if we analyse the design from the roof ridge
downwards, we find the cornice on a distance M under this ridge
and the main window ridge 2M under it, resulting in a partial
series of 6 "groundplan squares" in the front façade,
the series being displaced with respect to a regular 9 square
If we come back to the contouring square
and draw the quatrain scheme on it, we see that the base of the
equilateral triangle coincides with an outer buttress ridge,
and that the lateral sides coincide with the tangents of the
outer windows and oculi. This is a strong indication for the
original intentionality of the contouring square as it is presented
here. Strange however, is that a division in 7th parts of this
contouring square does not reveal anything. We should instead
consider the height from the ground level up to the roof ridge.
Dividing this distance in seven equal parts, we find the following:
level 1/7 at the gusset of the arches, level 2/7 at the main
window ridge, level 3/7 at the secondary window ridge (not very
visible on the scheme), level 4/7 through the centre points of
the oculi, level 5/7 at the top of the balustrade and level 6/7
defining the height of the gable pinnacles. An additional interesting
feature of the roof ridge is that the top of the belfry tower
is exactly three times higher (75 m against 25 m for the roof
height). Summarizing, we can mention the following:
- 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.
If we assume that the reconstruction of the building after World
War I was done carefully, we come to the conclusion that a very
free and fragmentary interpretation of the design canons seems
to have occurred in Arras.
SAINT-QUENTIN, A DIFFERENT CONCEPT FITTING
IN WITH THE CLASSICAL RULES
The town hall of Saint-Quentin in Aisne
(France) was finished in 1509. Colard Noël and Oudart de
Marle can be put forward as possible designers of the building.
It shows Renaissance influence (as Oudenaarde); the gallery has
probably been copied from Arras.
the analysis, we only have an old photograph to our disposal
at this moment. It has been selected because of its very central,
frontal camera-position, which guarantees a minimal lens deformation
of the façade geometry. Given this, it was decided to
risk the performance of an analysis directly on the photograph
(Figure 20). Of course, a survey analysis would be desirable
in the future. The tower was not considered since it is of a
later and less interesting construction.We conclude:
- 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.
THE GEOMETRICAL LEVEL
From a mainly graphical analysis
performed on 7 cases, some hypotheses on the historical design
schemes used for 14th to 16th century Gothic town halls in (or
near) Flanders and Brabant can be formulated.
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.
For other proportion
rules, such as the use of the Golden Section, no evidence was
yet found. Indeed, the Golden Section seems to be more important
in Renaissance architecture.
It is obvious that
fairly ideal examples are presented. There are interesting town
halls out of the same period that present a more "chaotic"
geometry, for example, because they were built in several phases
and over a long period, or because the design was altered during
the construction. More research should be carried on after this
first exploration of the field. On the one hand, the geometrical
investigation should go into more detail (surveys, in situ
measurements). On the other hand, literature should be consulted
further (inquiry of known design methods, in particular the teachings
of the Compagnonnage).
THE SYMBOLIC LEVEL
If a particular geometry was intended, it should be put against
the framework of a certain time and space. Most probably, an
interpretation of the geometry of the city hall designs within
the paradigm of medieval symbolic thinking will be possible.
Indications about this are currently being examined.
Only a first reflection on the role of the city will be made
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.
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,
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.
would like to thank architects and collaborators of archives
and technical services for providing me with building-plans and
data. Mr. Van Rompaey for the Louvain survey, Mrs. Van De Cappelle
for reviewing the text from linguistic point of view, and Prof.
H. Neuckermans for giving me time, tools and confidence.
 Citation from "Die
Satzungen des Regensburger Steinmetzentages nach dem Tiroler
Huttenbuche von 1460", in Zeitschrift fur Bauwesen
46 (1896), quoted in [Shelby 1977: 168]. return
 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]. return to text
 "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." return to text
 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. return to text
 See Origins of Surveys
Plans and Models Used below for more details on sources.
return to text
 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). return
 For an additional hypothesis on the construction
of the first building plan, [Vandevyvere 2000: 185-188]. return to text
 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.
return to text
 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. return
 C.G. Jung points out that the Mandala scheme can
often be found in medieval representations. See [Jung 1993] and
[Jung 1963]. return to text
ORIGIN OF SURVEY
PLANS AND MODELS USED
Survey plans from the Technische Dienst Stad Leuven (Louvain
technical services) and in situ control measurements of
major points of the building served for the construction of the
presented computer drawings.
Survey plans of the Technische Dienst were presumably made in
1953 by architect A. Moerkerke.
Topographical control measurements were done by Anton Van Rompaey
and Han Vandevyvere in 1999.
Survey plans obtained from the Technische Dienst Stad Oudenaarde.
Mixed set of plans made around 1938, 1966 and 1993.
Survey plans from the Technische Dienst Stad Brussels
Survey plans made by architects J. and L. Vierin in 1939, except
ground plan after L. Devliegher.
Survey plans obtained through the "Zeeuws Archief"
(archives of the Dutch Province of Zeeland, Middelburg), coming
from the "Centrale Dienst Gemeentewerken", Serooskerke,
Reconstruction plans obtained from "Archives départementales
Pas-de-Calais", plans made in 1924 by architect P. Paquet.
Saint-Quentin: Photograph reproduced from M. Battard and J. Lestocquoy, "Beffrois, halles,
hôtels de ville dans le Nord de la France et la Belgique",
Commission départementale des monuments historiques
du Pas-de-Calais. Etudes historiques 2 (Arras: Brunet, 1948).
Note: All plans are 20th century surveys,
made for documentation, maintenance and restoration purposes.
J. 1987. Stadhuis Brugge, De Gulden Engel. Wommelgem.
Bayard, J.-P. 1977. Le Compagnonnage en France. Paris:
Ghyka, M. 1969. Le nombre d'or: rites et rythmes pythagoriciens
dans le développement de la civilisation occidentale.
Jung, C.G. 1963. Herinneringen, dromen, gedachten.
Arnheim: Van Loghum Slaterus.
Jung, C.G. 1993. Symboliek van de Mandala. Rotterdam:
Maesschalck, A. and J. Viaene. 1960. Het stadhuis van Brussel
(Mensen en bouwkunst in Boergondisch Brabant). Louvain.
Shelby, L.R. 1977. Gothic design techniques. The fifteenth-century
design booklets of Mathes Roriczer and Hanns Schuttermayer.
Carbondale and Edwardsville (IL): Southern Illinois University
Vandevyvere, Han. 2000. Het stadhuis van Leuven: een geometrische
analyse. Jaarboek van de geschied- en oudheidkundige kring
voor Leuven en omgeving 39: 171-192.
Vandewalle, P. 1984. Oude maten, gewichten en muntstelsels
in Vlaanderen, Brabant en Limburg (Belgisch centrum voor
landelijke geschiedenis 82). Ghent.
ABOUT THE AUTHOR
Engineer-architect 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
The correct citation for
this article is:
Vandevyvere, "Gothic Town Halls in and around Flanders,
1350-1550: A Geometric Analysis", Nexus Network Journal,
vol. 3, no. 3 (Summer 2001), http://www.nexusjournal.com/Vandevyvere.html
Copyright ©2001 Kim Williams
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