The Plan of St. Gall :: :: University of Virginia Library

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:

A western zone, accommodating the houses for livestock
and their keepers and two houses to take care of the
knights and servants who travel in the emperor's following;

A central zone, of twice the surface area of the western
zone, accommodating the Church, the Claustrum, and
all of the buildings that lie to the north and south of this
complex;

An eastern zone, coequal in surface area with the western
zone, accommodating the Novitiate and the Infirmary,
the Cemetery, and several other installations.

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]

University of Virginia Library

THE 160-FOOT MODULE (SUPER MODULE)

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

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

THE CAROLINGIAN MEASURE AND SCALE USED IN DESIGNING THE PLAN

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

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