University of Virginia Library

I.14.3

SCALE USED IN DESIGNING THE
PLAN

A WORD OF CAUTION

In turning, at this juncture, to an account of my own conclusions
on the scale that was used in designing the Plan, I
should like to start with a word of caution. While I hold the
view that the Plan was drawn to a definite scale, and that
this scale was applied consistently throughout the entire

[ILLUSTRATION]

64. PLAN OF ST. GALL. MONKS' VEGETABLE GARDEN

The vegetable growing plots measure two
modules wide, 5 feet (60 inches) and would
require a reach of no greater than 30 inches
from the work space between plots, an
efficient size for hand cultivation. The clear
work space between the cultivated strips, 1-1½
modules wide (45 inches) was adequate for
a gardener with barrow or basket.

The center aisle, 2 modules wide, permitted
two men with their barrows or vegetable
baskets to easily pass each other.

The planning stresses no waste motion, no
scattered lost effort. This was not a garden
in which to play at gardening. It was close
to life, the need to live and the desire to
live. Nowhere in the Plan is the sense of
urgency, the necessity of collaboration and
conservation of resources more dramatically
and concisely expressed than in this simple
composition of eighteen rectangular garden
plots. Adjacent, on the north, where fruit
ripened for the monks' table, was the Monastery
Orchard which served a second purpose
as the Monks' Cemetery (always efficient
even in death) where the monks took their
long final rest.

Modularity was born of sacred numbers.
Each was but a finite and measureable
feature of divine and infinite order communicated
to men from heaven by a vast
scheme of symbolism. The passion for order
still persists, but the explanations are not the
same.

*

For extended treatment of the Monks'
Vegetable Garden see II, 204, 205.

Cemetery and Orchard are treated on page
211, vol. II.

Characters in black squares identify buildings
of the Plan, page xxiv, and III, 14
(Catalogue of Inscriptions).

E.B.

A submodule grid of 1¼ feet is superimposed on the plots of the vegetable garden (red drawing, same size as original; scale 1:192)

breadth and width of the scheme,[359] I do not think anyone
could expect to be able to determine without any shadow of
doubt the precise dimensions of every building, or any piece
of furniture, shown on this scheme. This is impossible for a
number of reasons. Most important among these are that
the Plan is not an original but a copy, and that this copy was
traced, without the aid of any supporting instruments,
through the opaque body of large and rather unmanageable
pieces of parchment that had to be held against a light
surface in order to acquire the requisite transparency.[360]
This was bound to introduce a multitude of minor inaccuracies
and inconsistencies that are incompatible with the
precision of draftsmanship required in the development of
the original scheme.

Moreover, there is clear evidence, as I have demonstrated
elsewhere, that in the process of tracing, original and overlay
changed their respective positions, in several instances
causing a substantial measure of distortion. This is noticeable
especially in the alignment of the claustral structures
with the Church and in the distorted layout of the stables in
the southwestern corner of the settlement.[361]

Despite these malformations, minor or major as they
may be, the Plan of St. Gall retains enough of the precision
of the prototype to permit the conclusion that the original
was based on a consistent and carefully calculated scale, and
to allow us to reconstruct the basic graduations of this
scale.

The primary reason why this problem was not solved in
the past is, I think, that most of the students who took an
interest in this matter were Continental Europeans reared
on the metric system. Being raised in this system, I, too,
could not avoid interpreting the scale of the Plan—as I
presume many others tried before me—by constructing a
straightedge on which the value forty (width of the nave)
was graduated into forty equal units. Applying this scale to
the various buildings of the Plan as well as to the open
spaces between them, I recognized quickly, yet not without
consternation, that a staggering majority of the dimensions
appeared to coincide with intermediate values that did not
make sense in terms of an even numerical progression. I
was puzzled by the frequent occurrence of such values as
2½, 7½, 12½, 17½, 22½, 27½, and so on, and in a special sense
by the heavy recurrent rate of what appeared to be a
standard value, namely, the width assigned to the steps,
benches, and beds. It was larger than 2, yet smaller than 3,
and appeared to make sense only if interpreted as 2½.

I was puzzled by these observations until it occurred to
me that the conditions that they reflected might be related
to the possibility that the inventor of the scheme availed
himself of a scale that was not based on the continuous
sequence of equal numerical values used in the decimal
system, but emerged from the geometrical thinking of the
developmentally older sedecimal system that survives in the
subdivisions of the English inch. I consequently designed a
scale in which the value 40 was internally graduated into
sixteen units, each of a length of 2½ feet, and the entire
riddle of the Plan unfolded itself.

I shall demonstrate the validity of this assertion with a
scale analysis of two areas of the Plan which lend themselves
with particular ease to this type of investigation.

THE 2½-FOOT MODULE (STANDARD MODULE)

Figure 59 shows a scale analysis of the southern transept

arm of the Church of the Plan of St. Gall. The surface area
covered by this part of the Church forms a square, each
side of which is equal to the width of the nave, i.e., 40 feet.
In the second and third drawing shown on this page, this
square is subdivided into sixteen strips, first from north to
south, then from east to west; in the last drawing the two
systems are combined.

The experiment proves that all the internal area divisions
of the southern transept arm are conceived as
multiples of a 2½-foot square. The passageway that gives
access to the crypt is three units wide and sixteen units long
(7½ × 40 feet), the platform on which the altar of St.
Andrew stands is three units wide and ten units long
(7½ × 25 feet). The steps and benches have a standard
width of one unit (2½ feet) and vary in length between five,
six, and ten units (12½ feet, 15 feet, and 25 feet). The
intervals between the steps and benches likewise can be
brought into a system of logical relationships, if interpreted
as multiples of a 2½-foot square.

An analysis of the adjacent area of the Dormitory of the
Monks (fig. 60.A) enables us to establish this point with

even greater persuasiveness. The complicated layout of the
beds in this building is inconceivable without the use of a
carefully constructed system of auxiliary construction lines.
It is easily understandable if it is conceived as being developed
within a grid of 2½-foot squares (demonstrated in fig.
60.C). The overall analysis of Cloister and Church suggests
that the building was meant to be sixteen 2½-foot units wide
and thirty-four 2½-foot units long (40 × 85 feet). Each bed
is one unit wide and three units long (2½ × 7½ feet), with

[ILLUSTRATION]

65. PLAN OF ST. GALL. KITCHEN AND BATHHOUSE OF THE ILL

A 1¼-foot module grid is superimposed on this detail from the facsimile red print (scale 1:192, original size).

the exception of a small number of beds near the two gable
walls which had to be shortened to leave sufficient room for
the entrances and exits located in these walls. A glance at
the drawings shown in figure 60.B discloses that the boundaries
of the beds do not in all cases coincide with the
boundaries of the underlying squares. The beds that lie at
right angles to the long wall straddle the grid lines with
their center axis. This suggests the possibility of the use of
an even smaller module, which we shall discuss later.

The superimposition of the square grid on the original
drawing (fig. 60.B) reveals the means by which the draftsman,
in copying this building, extended its length by one
unit beyond what it was meant to be through an accumulation
of small errors. The center group of beds in the northern
half of the Dormitory has a length of twelve 2½-foot
modules. The corresponding group of beds in the southern
half of the building is thirteen 2½-foot modules long. It is
obvious that they were meant to be of identical size. Figure
60.B shows with great precision those places where the
draftsman took on these additional increments of space
(first and second transverse row in the southern half of the
building). This was probably due to two slight and almost
imperceptible shifts in the relation of the original parchment
to the tracing sheets. By the time the draftsman had
reached the end of the second row of beds, he had inadvertently
picked up an excess of an entire module. This lengthened
the Dormitory from thirty-four to thirty-five standard
modules, or from 85 feet (length of the original) to 87½ feet
(length of the copy).[364]

In analyzing the dimensional layout of this as well as any
other building of the Plan it is important that the overall
dimensions of each respective structure be ascertained by
its relation to neighboring or superordinate units before an
attempt is made to decipher its internal relationships.

THE 40-FOOT MODULE (LARGE MODULE)

This module controls the proportions of the Church and
the layout of the Claustrum (fig. 61). The transept and
nave of the Church, being of equal width, by necessity form
a square at their area of intersection. As is the case in
certain Romanesque churches of Normandy and the Rhineland
two centuries later, the dimensions of this square
determine the layout of the remaining portions of the
church. Thus on the Plan of St. Gall the transept of the
Church forms an oblong composed of three times the area
of the crossing unit. The nave is a space composed of
four and one-half such units, while three more units of
identical size are added to the east of the transept; the forechoir,
the sacristy, and the library. It should be noted that
in the nave the squares are arranged in such a manner that
the corners coincide with the axis of each column. The 40
feet assigned to the width of the nave must for that reason
be interpreted to relate not to the clear span between the
bases of these columns, but to the distance from axis to axis
of each corresponding pair of columns.

That the Church of the Plan of St. Gall is laid out
according to a system of squares has been observed by

many previous students of the Plan, but a fact that appears
to have been entirely overlooked is that the entire aggregate
of buildings forming the Claustrum is developed in a
similar manner.

A glance at figure 61 shows that the body of the Church
can be inscribed into a grid of 40-foot squares (three units
wide and nine units long), and the claustral structures that
abut the Church to the east can be entered into an adjacent
grid of identical squares (three units wide and five and one-half
units long). I have no doubt that this is the manner in
which the drawing was started. But attention must be
drawn to the fact that the alignment of the drawing with the
grid is not perfect. There are two discrepancies—not large,
yet conspicuous enough to cause some concern.

One of these is that the aisles of the Church are not 20
feet wide, as one should expect them to be in the light of
their explanatory titles (latitudo utriusque porticus pedum xx);
instead they measure 22½ feet. The other is that in certain
places the Dormitory and the Refectory extend over the
southern boundaries of the 40-foot grid of the Claustrum
by as much as 5 feet. I believe that these deviations are the
result of purposeful modifications undertaken as the drawing
progressed from its initial conception into its final
stages; and I shall discuss this point in detail later.

THE 160-FOOT MODULE (SUPER MODULE)

The discovery that the Church and the Claustrum were
designed ad quadratum raises the question of whether the
site plan for the entire monastery may not have been
developed from the dimensions of the crossing square. To
answer this question is not easy, because the Plan of St.
Gall fails to inform us about the location of the walls that
separate the monastery from the secular world. We do not
know where the grounds of the monastery begin and where
they end. It is probable, however, that this problem may be
solved by a simple proportional speculation.

Measured from west to east—or more precisely, from the
westernmost fences of the agricultural service structures
west of the Church to the easternmost lines of the building
masses east of the Church—the monastery grounds are
sixteen times the width of the nave of the Church (640
feet), a round and very convincing number, in which the
figure four plays a determinant role (fig. 62). By contrast,
the distance between the outermost lines of the building
masses sited along the southern edge of the monastery and
the outermost lines of the building masses on the northern
side amounts to 11½ times the 40-foot width of the nave of
the Church (fig. 62). The proportion 11½:16 is not a likely
medieval relationship. A more convincing proportion would
be 12:16 (or 3:4). There is some evidence, not easily discarded,
which suggests that in the south and north the
monastery grounds were meant to extend beyond the outer
building masses, since the fences of some of the buildings
located along the southern and northern border of the
monastery site run out into the space which lies beyond
these structures, and end only at the end of the parchment.
Two such fences, running north, may be seen on either side
of the Outer School; another runs south in extension of the
west wall of the House for the Workmen (fig. 62). There
are other considerations of a practical nature which would
require a buffer zone between the outer building lines and
the monastery wall. The water-driven machinery of the
Mill and Mortar houses are dependent on flues and sluices
that can only have run to the south of these buildings, and
a similar safety margin of space would have been desirable
in the north for servicing the privies.

A buffer zone of 10 feet added to the building masses, on
either of the two long sides of the Plan, would take care of
these necessities and would result in a meaningful overall
proportion (12:16 or 3:4) for the Plan (fig. 62). The
acceptance of such an overall modular scheme would,
moreover, help us to settle two other puzzling aspects of
the Plan.

It would explain the location of the Church. It has never
been clarified why the Church lies where it does on the
Plan. It is obvious that it had to be off-center. Had it been
placed in the center of the Plan, the southernmost buildings
of the Claustrum would have been moved to the southern
edge of the monastery, leaving no room for the subsidiary
claustral structures, such as the Monks' Bake and Brew
House, the Mill, and the Mortar. But what determined the
exact distance by which the axis of the Church was to be
off-center?

If we assume that the monastery site was calculated as an
oblong, sixteen 40-foot modules long and twelve 40-foot
modules wide, the entire monastery site could be conceived
as having been inscribed into a grid of twelve supersquares,
each formed by four 40-foot squares, and therefore measuring
160 × 160 feet (fig. 63). Within the linear frame of
reference established by such a grid the difficult problem
of the axial position of the Church—incomprehensible in
terms of the layout of the Roman castrum, with which it has
frequently been compared—would find a surprisingly
simple explanation. The axis of the Church would coincide
with the first, the axis of the Refectory with the second of
the two longitudinal lines of the grid.

The same grid would also explain the transverse division
of the monastery into its four principal building sites:

The western and eastern group of buildings are each
inscribed into a surface area formed by three 160-foot
squares; the central block of buildings extends over six.

[ILLUSTRATION]

DIAGRAM I THE SEQUENCE OF PROGRESSIVE DICHOTOMY USED IN THE SCHEME OF MEASUREMENTS
EMPLOYED IN THE DESIGN AND DRAWING OF THE PLAN

The standard module, 2½ feet, is obtained by successively halving the large module (40 feet) four times. The value of the exponent, column B, indicates the number
of times that the number 40 has been halved. The procedure shown here that yields successively smaller units of measurement, decreasing from 40 feet to
2½ feet by successive halving is "reversible," and is reversible by the same pattern of geometric progression shown here, but in the "opposite" direction yielding
progressively larger values.

Thus larger modules, multiples of 40 feet, such as 160 feet and 640 feet, are evolved from the same standard module and using the same pattern of development.

This is illustrated on the opposite page in Diagram II.

In Diagram II one can visualize the grand symmetry of the scheme of measures by which the design of the Plan was ordered and controlled. For example, 640
is symmetrically disposed with respect to 2½ about the sacred number 40 taken as a pivot or point of origin. In the pattern of such a formula, the infinitely great
and the infinitely small participate with equal significance, in a scheme, it seemed, of divine order. The crossing square, four equal sides each of 40 feet, indeed
defined a holy space.

Forty, the number of greatest value in the series of NUMERI SACRI, was chosen by the designer of the Plan of St. Gall as that dimension in feet
for the crossing square of the Church, the holy space unsurpassed in meaning and felicity to all inhabitants of the monastery.

It was clearly discernible from tracing drafts, in our study of the Plan, that 160 feet, four times forty, was the major module of the Plan.

This is the largest measure which is a common multiple of the Plan. Four units of this module, or 640 feet, is the length of the Plan, and three
units of this module, or 480 feet, is the width of the Plan.

The reason that the 160-foot module, four times the 40-foot dimension of the crossing square, was chosen as a module may be understood by
perusing Diagrams I and II, giving attention to the numerical sequences in columns A, B, C, in each figure. Diagram I portrays a
progression of halving starting with the 40-foot module and DESCENDING to 2½ feet. Diagram II starts out with the 40-foot module, extends the
geometric series in the opposite upward direction by doubling.

The values obtained by doubling, from 40 to 160, correspond at each level of ascent, to the smaller values obtained by the descent from 40 to
2½ feet. The bar elements of Diagram II illustrate the progression graphically: however, it is Column B that cogently reveals the homogeneity
of the numerical relationships as a scheme that established the intrinsic pattern of measurements used in the Plan of St. Gall.

[ILLUSTRATION]

DIAGRAM II THE SUPERMODULE, 160 FEET, ITS DERIVATIVES, 640 FEET AND 480 FEET, AND ITS
RELATIONSHIP TO THE LARGE MODULE

† 640 is the "height" or east-west dimension of the Plan

* 480 feet, the "width," or north-south dimension of the Plan, is an element in this geometric progression. It is derived by taking the sum of the two elements
of the progression 320 & 160, or 3 × 160. With sacred numbers 3 and 4 as multipliers and 160 as a multiplicand, 480 and 640 emerge as the dimensions, in feet,
of the Plan. Sacred numbers, NUMERI SACRI, are treated extensively under I.17, page 118; see also remarks, caption, page 109.

We noticed that, out of the scared number 40, the values of 2½, 10, 40, 160, 640 are generated by exponential values of 4, 2, 0, -2, -4.
Although the more sophisticated notation of Column B was probably not common knowledge in the 9th century, the notation of Column C was
understandable. There is no magic in this simple observation. But it is apparent that the multiplier 4, operating on 40 and yielding 160 was not
chosen by caprice. A module less than 40 facilitated the arduous work of design.

The number 480, 3 times 160, is not one of the natural steps of the progression between 2½ and 40, as shown in DIAGRAM II. This strongly
suggests that the CAUSA PRIMA of the dimension system of the Plan was the longitudinal axis of the Plan of the Church, extended to east and
west to satisfy designing a plan of paradigmatic significance and future influence. The axis of the Church was extended one module of 160 feet to
the east (of the front line of the altar of St. Paul) and one module of 160 feet to the west of the entrance to the covered walk of the west paradise.
This established the length of the Plan, four modules of 160 feet or 640 feet. One module of 160 feet north of the axis and two modules of 160 feet
south of the axis gives three modules of 160, or 480 feet, the width of the Plan. That the dimensions of the Plan are in the proportion of 3 to
4 was more than good theology. The numbers 3, 4, and 5 are the key to accurate construction of a rectangle in land surveying and in building
construction.

E. B.

[ILLUSTRATION]

THE CAROLINGIAN MEASURE AND SCALE USED IN DESIGNING THE PLAN

On the basis of the calculations listed below we compute the length of the foot used in designing the Plan to have these equivalents:

In English and U.S. standard measure: 1′ ⅝″.

In metric measure: 32.07cm

This computation can only be understood as an approximation of the real Carolingian foot that the draftsman of the Plan himself used. The computation
must be corrected, first by the diminution in size to which the parchment was subjected through shrinkage throughout the ages of its existence, and second,
minor distortions caused by shrinkage of photographic elements in development, or of the paper on which the facsimile was printed, during drying.

Our computation of the "foot of the Plan" as reflected in the Löpfe-Benz facsimile is based on an analysis of the longest clearly measurable dimension shown
on the drawing, namely the span extending from the center of the arcade columns that stand at the entrance wall of the church to the center of the columns
that form the easternmost boundary of the crossing square. This span encompasses five and one-half 40-foot squares and consequently represents a length of
220 "Plan feet". Owing to uneven shrinkage or irregularities in the drawing this distance varies slightly depending on whether it is measured along the axis
of the northern, or of the southern row of nave arcades. Using an engine-divided scale of good manufacture with 16 divisions to the inch based on the U.S.
standard foot (identical with the British standard foot) we arrive at the following figures:

231 + 232/2 = average value = 231.5 units (measure on south row = 232 units of 1/16 inch, measure on north row = 231 units)

231.5/220 = 1.05227 feet—12⅝ inches—32.067 cm

This is the measure of the foot of the Plan.

[computation: 12 inches = 30.480 cm.

⅝ inch = 1.587 cm/32.067 cm]

THE 1¼-FOOT MODULE (SUBMODULE)

There is good reason to assume that in certain installations
the inventor of the scheme made use of a submodule by
halving his standard module of 2½ feet, thus arriving at the
smallest module of 1¼ feet. I refer to this unit as a "submodule"
because it is used sparingly, in contrast to the
2½-foot unit which is used as a standard module throughout
the length and width of the Plan. I have pointed out that
2½ feet is one sixteenth of 40, the width assigned to the
nave of the Church; 1¼ is one thirty-second of this measure.
The peculiar values 2½ and 1¼—strange to anyone accustomed
to working with a metric scale—will ring a more
familiar tone if it is remembered that these units correspond
to 30 and 15 inches.

The Plan contains a number of installations which cannot
be explained in any other manner than on the assumption
that they have been constructed on a 1¼-foot module. We
have already encountered it in our analysis of the Dormitory

(fig. 60). The most convincing evidence for the use of the
submodule, however, is in the Monks' Vegetable Garden
(fig. 64).

The Garden covers a surface area that is twenty-one
standard 2½-foot units wide and thirty-three standard
2½-foot units long (52½ × 82½ feet). It consists of two rows
of planting beds, nine on either side, made accessible by a
carefully designed system of paths: three running lengthwise,
ten crosswise. The planting beds are 5 feet wide and
20 feet long. The width of the crosspaths by which they are
separated is less than 5 feet but more than 2½ feet. The
only logical way to relate nine planting beds 5 feet in width
to ten paths the width of which is less than 5 and more than
2½ feet within the available surface area, is to assume that
the draftsman conceived this layout within a grid of squares
of one-half the value of his standard square, i.e., a submodule
of 1¼ feet. This module would allow him to
develop the respective width of the planting beds and the
paths with absolute precision, lengthwise in the simple
sequence of

and crosswise in the sequence of

The 1¼-foot module is also used in the Kitchen and Bath
houses of the Novitiate and the Infirmary (fig. 65). These
buildings are each nine by eighteen of the 2½-foot modules.
They are internally divided into two coequal squares of
nine by nine 2½-foot modules, one containing the Bath
House, the other the Kitchen. The hearth in each of these
two installations forms a square that is composed of four
2½-foot modules. To place a square of four 2½-foot modules
concentrically into the interior of a square of eighty-one
2½-foot modules is possible only within the framework of a
1¼-foot grid. In such a grid each side of the Kitchen and
Bath House would be graduated into eighteen units of 1¼
feet. The position of the hearth could be struck off with
absolute precision in the sequence 7 · 4 · 7; the position of
the bath tubs, with their diameter of three submodules, in
the sequence 2 · 3 · 2 within the squares of seven submodules
left in the four corners.

There are four or five more buildings on the Plan—not
counting several smaller areas here and there—in which the
submodule appears to have been employed (Abbot's
House, House for Distinguished Guests, cloisters of the
Infirmary and the Novitiate, and possibly the Refectory),
but to interpret how exactly it was used in each case is
difficult because the module is so small. A distance of 1¼
feet on the Plan amounts to not much more than twice the
thickness of the stroke of the quill with which the Plan was
drawn. Since the lines were traced without the aid of a
straightedge, even the slightest irregularity in the movement
of the hand would tend to blur the intent of the
original scheme. Therefore, rather than weakening the
argument by interpreting details which may be susceptible
to different solutions, I should like to confine myself to
establishing that this module was used by focusing on
those areas in which its existence can be clearly demonstrated.