University of Virginia Library

II.3.10

SQUARE SCHEMATISM

"Square schematism" is a principle of medieval church
design by which the constituent spaces of the church are
calculated as multiples of a basic spatial unit, usually that
of the crossing square. The origin and evolution of this
concept is still one of the great mysteries of medieval
architectural history. The Church of the Plan of St. Gall
represents a crucial stage in the conceptual development of
this principle. The importance of this fact has been blurred
because no consensus of opinion had been obtained, in
previous inquiries, with regard to even the simple question
of whether or not the design of the Church of the Plan had,
in fact, been developed within a system of squares; let alone
the infinitely more complex problem of the historical roots
and the deeper cultural significance of this fascinating
principle of articulating space. I, for one, am convinced
that these questions cannot be solved from within the
field of architectural history. The modular mode of thinking
that underlies this schematism is a general cultural
phenomenon that manifests itself in other spheres of life.
On the following pages I shall try to isolate some of the
converging historical currents that merge in this concept.

PRESENCE OR ABSENCE OF THE GRID OF SQUARES

On the Plan of St. Gall the square and the grid of squares
are used in two different ways: as a method of mensuration,
and as an aesthetic principle. In the first instance the square
grid offered a convenient method of dividing a given area
internally by defining it as a multiple or fraction of certain
modular master units (2½-foot square, 40-foot square, 160foot
square).[282] In the other case, the square grid was used
as an active principle of architectural composition. It is this
latter type alone with which we are now concerned. Reinhardt
categorically denied its presence on the Plan of St.
Gall.[283] Similar views were expressed in 1945 by Samuel
Guyer,[284] but convincingly challenged in 1952 by Albert
Knoepfli[285] in a drawing which shows a grid of 10-foot
squares superimposed upon the Plan of the Church.[286] My
own analysis of the scale and construction methods used in

[ILLUSTRATION]

172. COLOGNE. CAROLINGIAN CATHEDRAL OF SS PETER AND MARY

Like Fulda (fig. 169) and doubtlessly under the same influence, i.e., of Old St. Peter's in Rome (fig. 170), the transept is located in the west. As in
Fulda and in the other Carolingian churches discussed here, the use of modules imparts to the layout of the spaces an aesthetic character wholly
different from the squat corporeality of their Early Christian prototypes.

designing the Plan corroborated this view.[287] In view of the
visual evidence submitted by Knoepfli, as well as my own
analysis of the system of squares shown in figures 61 and
173, I do not see how the validity of this contention could
ever again be questioned.

MEDITERRANEAN OR NORTHERN ROOTS:
A DIVISION OF MINDS

Because of its geographical distribution primarily in the
territory of the Franks, Saxons, and Normans, Georg
Dehio considered the square schematism to be essentially
a "Germanic" contribution.[288] Samuel Guyer,[289] in a complete
reversal of this contention declared this "geometrical
clarity" to be a mark "of the Mediterranean way of thinking,"
and "one that had its roots in classical antiquity."[290]
The square schematism of the Plan of St. Gall, he maintained,
was not one of the new and creative contributions
to medieval architecture that it had been assumed to be,
but "transmits to the West in a rather muddled manner the
thought of the qualitatively superior art" of the Early
Christian period.[291]

These statements are of questionable historical validity—
and the argument does not gain in power when one finds it
supported by such sweeping generalities as "A civilization
in process of just awakening from the darkness of an
a-historical past" and "as yet suspended in a state of
unstable hovering between unconsciousness and awakeness"
could not possibly have produced aesthetic concepts
"of such distinct and clear rationality. . . . The period of
Charlemagne had never the significance ascribed to it so
fervently in recent times. . . . In the time of Emperor
Charlemagne the thoughts of Late Antiquity and Early

[ILLUSTRATION]

173. PLAN OF ST. GALL. PLAN OF MONASTERY CHURCH

SHOWN AT SCALE 1:600

The Church of the Plan of St. Gall is chronologically the last of a triad of Carolingian transept basilicas of monumental dimensions owing
their size to the tide of spiritual and cultural exhilaration that seized the Frankish clergy in the wake of Charlemagne's coronation as emperor,
on Christmas Eve of the year 800, in the basilica of Old St. Peter's in Rome.

Unlike Cologne (fig. 172) and Fulda (fig. 169) which were occidented in imitation of Old St. Peter's, (fig. 170) the Church of the Plan was
oriented. Like Cologne and Fulda, on the other hand, and in contrast to St. Peter's, the Church of the Plan was constructed on a square grid,
in the most elaborate and most consistent application of it, since it encompassed, in addition to the Church itself, the entire claustral complex
and in fact the entire monastery site (figs. 62 and 63).

[ILLUSTRATION]

174. ROME. SANTA MARIA MAGGIORE (432-440)

LOOKING NORTH AND SOMEWHAT EAST TO THE APSE

Despite its coffered Renaissance ceiling (added in 1500, substituting for the original open-timbered roof) this view of Santa Maria Maggiore
conveys persuasively the stylistic quality of the great Early Christian basilicas composed of huge, block-shaped, and internally undivided
voids.

The concept differs fundamentally from that of the square-divided Carolingian churches of Neustadt, St. Riquier, Fulda, Reichenau-Mittelzell,
Cologne, and that of the Plan of St. Gall (figs. 167-69; 171-73), as well as from the bay-divided and arch-framed spaces of the Romanesque
and Gothic (Hildesheim, Speyer, Jumièges; figs. 188-90), the cellular composition of which has primary roots in the Carolingian modular
reorganization of the Early Christian scheme.

For another magnificent view of the interior of a great Early Christian basilica see fig. 81, St. Paul's Outside the Walls, Rome.

[ILLUSTRATION]

175. FEDDERSEN-WIERDE, BREMERHAVEN, GERMANY

175: AISLED HOUSE OF A CHIEFTAIN, WARF-LAYER 11B, 1ST-2ND CENT. (authors' reconstruction)

176: PLAN (after Haarnagel, 1956, pl. 3)

The house belongs to the second settlement horizon of an artificially raised dwelling mound (Warf) which was occupied, on successively higher
levels, from the 1st to the 4th centuries. The house was 28.5 × 7.5m on an east-west axis. The living portion with hearth and the section for livestock
were, respectively, 9m and 16m long. An entrance in the middle of the eastern end wall was primarily used by cattle. (Also see figs. 315-316, II, 58.)

Christianity were taken over in a manner so superficial as
to be incapable of taking any deep root or of being developed
any further."[292]

I propose that we confine ourselves to specific issues
rather than argue the case in such global terms.

INCREASING PROPENSITY FOR MODULAR
SPACE DIVISION IN PRE-CAROLINGIAN AND
CAROLINGIAN ARCHITECTURE NORTH OF
THE ALPS

The emergence of the square schematism in medieval
architecture depended on two crucial innovations in the
interrelation of the component spaces of the basilican
church:

1. The nave and the transept of the church had to be
given the same width, and

2. The width of the aisles had to be fixed to one-half
the width of the nave.

Without the first, the crossing could not form a square;
without the second, the modular division of the nave could
not be carried into the aisles. Both of these features
occurred separately in Early Christian times, but they were
not integrated then into a programmatic architectural
system.

An example of a church with nave and transept of equal
width is the Justinian basilica of the Nativity at Bethlehem
(if Hans Christ's interpretation of its plan is correct).[293] In
several Christian churches of Ravenna—all without transepts—the
width of the aisles is fixed at one half, or approximately
one half, the width of the nave. Yet as we survey
Early Christian church architecture as a whole, we must
conclude that its truly distinguishing feature is not the
presence, but rather the absence of any fixed proportions.
Nevenka Petrović[294] has made an illuminating study of the
proportions in churches of Ravenna and the adjacent
littoral of the Adriatic sea. In attempting to demonstrate
that these churches were laid out according to a system of
squares, as she set out to do, she has de facto illustrated the
fundamental difference between the layout of these later
Early Christian churches and the system of squares employed
in medieval architecture. The salient feature of the
Church of the Plan of St. Gall and its Ottonian and
Romanesque successors is that the squares control the
spacing of the arcades and therefore express the modular
layout of the plan in the elevation of the columns. The
divisions of Petrović's grids (fig. 166), by contrast, have no
relation whatsoever to the position of the arcade columns.
True, in some of the proto-medieval churches of Ravenna,
the length and width of the church exist in a state of

[ILLUSTRATION]

178.

Great Cruciform page

size of original about 33·8 × 24·1cm.

[ILLUSTRATION]

LINDISFARNE GOSPELS

179.A

179.B

LONDON, British Museum, Cotton Nero D. IV, fol. 2v

[by courtesy of the Trustees of the British Museum]

Stages of layout

modular interdependency, but since this module does not
control the spacing of the columns, it is aesthetically of no
consequence.

I tend to agree with George Dehio that the square schematism
is essentially a "Germanic" contribution to Western
architecture for two reasons: first, because it is found
primarily in regions of relatively strong Germanic concentration,[295]
and second, because it is in these areas also that
we may detect its developmental antecedents. An early
medieval church exhibiting an incipient tendency toward
the use of the square as a module was Fulrad's church of
St. Denis, begun after 754 and consecrated in 775 (fig.
167).[296] Its basic layout, if Formigé's interpretation is correct,
was developed within a grid of 6-foot squares which,
in contrast to San Giovanni Evangelista at Ravenna (fig.
166), determined not only the overall dimensions of nave
and transept, but also the interstices of its arcades. The
transept was seven 6-foot units wide, and thirteen long; the
nave was five units wide and fifteen long. The distance from
center to center of arcade columns was two units, and in the
middle part of the transept two cruciform piers establish a
square of five by five units. As yet we cannot speak of
square schematism, because the dimensions of the crossing
square are not mirrored anywhere else in the building, and
in particular not in the intercolumniation of the arcades. A
church that comes closer to this ideal is the Saviour's
Church of Neustadt-on-the-Main, after 768/69 (fig. 167).
The plan of this church together with other cruciform
churches of similar design built in early medieval times,
such as Pfalzel near Trier, and Metlach (both before 713),
may have formed a connecting link between square-divided
Carolingian basilicas of the ninth century and certain
cruciform churches of the fourth and fifth centuries, typical
examples of which are shown in fig. 144-146 and 148-149.
A grandiose variant of this church type, built as early as
380 by Emperor Gratian in his residential city of Trier,
rose in territory that later was part of the very core of the
Frankish kingdom—for every Carolingian to see! (Its
masonry survives to this day, incorporated in the fabric of
the Romanesque church that superseded it.) This is the
only pre-medieval church type where nave and transept
are of equal width, their intersecting bodies forming a
square—and one might indeed regard the fully developed
square schematism of the Carolingian period as a transference
to churches of basilican plan of a principle already
experimented with in pre-medieval times in the highly
specialized context of these Early Christian cross-in-square

[ILLUSTRATION]

180. LINDISFARNE GOSPELS

LONDON, British Museum, Cotton Nero D.IV, fol 2v

Square panel above arm of cross on cruciform page shown in fig. 178

• A. Photo of panel

• B. Photo of square grid visible on corresponding portion of
  fol. 4r.

• C. Square grid with outlines of cross and lozenge pattern
  (first stage of construction)

• D. Final stage of pattern (authors' interpretation)

churches.[297] The first Carolingian church to mark the developmentally
significant moment of the adoption of the
square schematism in a building of unequivocally basilican
design was the abbey church of Centula, 790-799, if
Irmingard Achter's reconstruction of this building is
correct (fig. 170).[298] Because of the scarcity of archaeological
data available on this important building, such an assumption
can neither be fully accepted nor convincingly
rejected. For the same reason it is impossible to ascertain
whether the interstices of the nave arcades were aligned
with these modules.

Modular adjustment between width and length of the
component spaces is clearly visible, however, in the abbey
church of Fulda (802-817).[299] Its nave, measured from the
base of its western to that of its eastern apse, was exactly
four times its width (fig. 169). The dimensions of the
transept were identical with those of the nave. In the vast
body of literature devoted to Fulda—whose authors never
weary of citing the dependence of its design on that of Old
St. Peter's—this crucial aesthetic novelty has never been
pointed out, much less set into proper historical perspective.
We know nothing about the intercolumniation of
Fulda.

On the other hand, it is not possible to interpret Old
St. Peter's as having been developed within a grid of
identical squares—neither each volume by itself, nor any
volume in relation to a neighboring unit or to the whole of
the building mass. The architect who planned St. Peter's
employed instead a constructional system as classical in
concept as the modularity of the Carolingian churches
shown in figs. 144ff is medieval (see Born's analysis, fig.
170). He calculated the length of the longitudinal body of
the church by making use of the diagonal of a square with a
side equal to the width of the church, and developed the
overall length of the church in the same manner, with the
aid of the diagonal of the rectangle obtained by the preceding
method. This configuration, known as a √2
rectangle, is irrational, since the diagonal of a square is not
in any integral relationship to its sides (1: √2 = 1:1.414)
and therefore cannot be defined as an aggregation of an
integral modular value.

Hildebold's church of Cologne (ca. 800-819) was
composed wholly of equal squares: three in the transept,
four in the nave, one in the fore choir (fig. 172). If the
elevation of its nave walls was identical with that of the
church dedicated in 870, the piers of the arcades that
carried the clerestory walls would not have been in alignment
with this system.

The abbey church of Reichenau-Mittelzell, built by
Haito (806-816) is also developed within a modular grid of
squares, but the grid is irregular, and its existence, for that
reason, has been questioned. In evaluating this problem it
is important to distinguish the existence or nonexistence of
the concept of squares at Reichenau from the regularity or
perfection of its execution. The irregularity, in the angular
deviation of the walls from the grid (especially noticeable in
the eastern part of the church) is caused by special topographical
conditions. But no doubt can be entertained that
the concept exists. The shape of the fore choir and of the two
transept arms are almost a mirror image of the shape of the
crossing square, but the squares of the nave are slightly
oblong. Yet the principle of divisions is clearly there, and
the boundary between the two oblongs of the nave is
marked by piers, whose design differs from the columns
standing midway between them. In this feature St. Mary's
Church at Reichenau goes a step beyond even the Church
of the Plan of St. Gall, which has no such alternation in its
main supports.

In Hildebold's church of Cologne (fig. 172) the system
of squares finds clear expression in the west transept and
in the eastern fore choir, both of which are formed of squares
of identical size: three in the transept, one in the fore choir.
The nave is composed of four squares of like dimensions.
We know nothing about its elevation. If it was identical
with that of the church that was dedicated in 870, the piers
of the arcades which carry the clerestory walls would not
have been in alignment with the system of squares.

In the Church of the Plan of St. Gall the square schematism
attains its purest Carolingian form of expression (fig.
173). The basic unit is the 40-foot module of the crossing
square. The transept is formed of three such squares, the
fore choir of one, the nave of four and one-half; and the
dimensions of the crossing square are echoed even in the
Library and Vestiary. In St. Gall, moreover, the interstices
of the columns are in rhythmical alignment with the
squares. It is incomprehensible to me how this fact should
ever have been questioned. What the designer of this
church had in mind were arcades cutting deep into the
masonry of the nave walls (fig. 110) with their supports so
spaced as to give bodily expression to the sequence of
squares on which the Plan was based. This schematism is
a conscious and willed aesthetic principle. It is a fundamentally
different concept from that which produced the
low, narrowly spaced columnar orders of the Early Christian
basilicas of Rome (figs. 141 and 174). Contrary to what
Guyer, Reinhardt, and Reinle believe, it is an ingenious
anticipation of the square schematism of the Romanesque.

What are the historical preconditions of this propensity
for modular organization of space? Some clearly are functional.

[ILLUSTRATION]

181.

Cruciform page preceding the Gospels of St. Luke

size of original about 33·8 × 23·1cm.

[ILLUSTRATION]

182. LINDISFARNE GOSPELS

LONDON, British Museum, Cotton Nero D. IV, fol. 138r

[by courtesy of the Trustees of the British Museum]

Diagram illustrating use of square grid in constructing the layout for
the opposite illustration

Others may have to be traced to vernacular architecture.
For still others we shall have to reach, beyond the
boundaries of architectural history, into the field of book
illumination, where strong expression of modular modes
of thinking can be observed over a century before they
assert themselves in church building. Yet others, and perhaps
the most important of all, may have to be sought in
deeper and more general cultural levels.

NEW LITURGICAL NEEDS
CONTRIBUTING TO MODULAR SPACE DIVISION

I have already drawn attention to a number of contributing
factors that tended to facilitate this development in a functional
sense: the need for an extension of the altar space,
leading to the interposition of a new spatial unit between
transept and apse; the framing of the crossing by means of
arches, creating a square division in the transept, that would
lend itself to being extended to the nave; and most of all,
perhaps, the multiplication of altars, demanding a subdivision
of the spaces of nave and aisles into a sequence of
devotional stations (figs. 164 and 165). We add to this a
feature (which Irmingard Achter stressed in her discussion
of the Carolingian Abbey Church of Centula): circular
towers such as the towers which surmounted the crossing
and the westwork of this church require as base a square-shaped
underpinning. All of these innovations contributed
to the development of a modular scheme, but none of them
alone (and perhaps, not even all together), might have
led to the creation of the modular space division of the
medieval church as a binding architectural principle. There
are other forces to be taken into account.

MODULAR SPACE DIVISION: AN INTRINSIC
FEATURE OF PREHISTORIC, PROTOHISTORIC, AND
MEDIEVAL WOOD CONSTRUCTION

In an article dealing with the origins of the medieval bay
system,[300] I have pointed out that modular design has been
from the remotest periods an intrinsic feature of northern
wood construction. The stability of the timbered Germanic
house required that its roof-supporting posts be joined
together at the top: lengthwise by means of plates, and
crosswise by means of tie beams. This divides the space of
the house into a modular sequence of timber-framed bays
(figs. 175 and 176). Recent excavations have made it clear
that this construction type came into existence around 1200
B.C., and for the next two thousand years it served as an
all-purpose house in the Germanic territories of Holland,
Germany, England, and Scandinavia as well as in all those
areas of Central and Western Europe that were primarily
settled by Germanic peoples.[301] In timber this concept is
old; in stone it is new. In timber it develops as a logical
construction method from the natural properties of the

[ILLUSTRATION]

Canon Tables (183.A)

The Ada Gospels is the first great highlight of the classicizing phase of
illumination of the so-called Court School. It consists of an earlier part
(fols. 6-38) containing the canon tables (fols. 6v-11v) which combine the
decorative tradition of the Hiberno-Saxon school (figs. 178-182) with a tendency
to treat the arcades of the tables in a more architectural manner.

Size of leaves of the manuscript in the present cropped state is 36 × 24.5cm.

Figures 183.A and 183.B are reduced about 12.5 percent.

Originally the leaves were larger.

The later part of the Ada Gospels consists of the remainder of the text, and
portraits of the four evangelists (fols. 15v, 59v, 85v, 127v), one of which is
illustrated in fig. 184 (see overleaf).

[ILLUSTRATION]

183.C ADA GOSPELS (EARLY 9TH CENT.)

DIAGRAM SHOWING USE OF SQUARE GRID IN THE
CONSTRUCTION OF THE CANON TABLES SHOWN IN
183.A AND 183.B (see overleaf)

TRIER, Municipal Library, MS. XXII, fol. 6v

material. In masonry it is an intrusive feature, imposed
upon the material as a willed aesthetic principle—and
therefore ushers in a conflict between style and building
material which, in its ultimate phase, the Gothic, led to a
complete denial of the natural properties of stone. I have
suggested that the modular arrangement of space, which
begins in Carolingian Church architecture, gathers increasing
strength in the Ottonian period and reaches its peak of
expression in the Romanesque and Gothic (fig. 177), has
one of its roots in the fact that these churches were constructed
by men in whose collective memory "to build"
had been synonymous with building in modular sequences
of space.

The validity and importance of this explanation cannot
be appreciated until it is understood that the determining
factor in analyzing the origins of square schematism is not
that it is based on the shape of the square, but that it
establishes a system of binding modular relationships. In
distinguishing between the système des carrés of the Romanesque
and the système des barlongs of the Gothic, we have
lost sight of the fact that both of these systems are members
of the same family. Whether the module is square or
rectangular is determined by secondary conditions, sometimes
functional, sometimes constructional, sometimes
stylistic, and on occasion, even by purely arbitrary reasons.
The house of the Germanic chieftain of the first and second
centuries A.D., which is shown in figures 175-176, employs
both the square and the rectangular module, the former in
the living area, identifiable by the hearth; the latter, in the
section of the house where the cattle are stabled, identifiable
by the manure mats.[302] Here the shape of the module is
conditioned by strictly functional considerations: the roof-supporting
trusses are spaced at intervals of 6 to 7 feet, just
as much space as is needed to stable two head of cattle. In
the living section of the house, on the other hand, the
trusses are set further apart to give greater freedom of
movement. The distinction is very old and can be observed
in Bronze Age houses of the same construction type, dating
from around 1200 B.C., recently excavated by Waterbolk in
Elp, Holland.[303]

In the Carolingian monastery churches discussed in the
preceding pages, the square is the more reasonable form
to be adopted—at least in the liturgically most important
areas—the choir and the transept— which lend themselves
to square division with notable ease. In the nave, this was
more difficult to obtain, since here the square division
conflicted with the narrow intercolumniation inherited
from the Early Christian prototype churches. It required
a strong personality to move the columns apart to the novel
and daring distance of 20 feet, as was done in the Church
of the Plan, and thus to express the module in the bodily
sequence on the columns. The designer of the Church of
Cologne may have struggled with similar ideas (fig. 172), but
abandoned the scheme in actual construction (figs. 15-16).

[ILLUSTRATION]

183.B

[ILLUSTRATION]

183.D ADA GOSPELS

DIAGRAM SHOWING USE OF SQUARE GRID

TRIER, Municipal Library, MS. XXII, fol. 8v

MODULAR AREA DIVISION: AN INTRINSIC
FEATURE IN THE LAYOUT AND DESIGN
OF ILLUMINATED PAGES IN HIBERNO-SAXON
AND CAROLINGIAN MANUSCRIPTS

The modular bay division that governed the construction
of the Germanic house from the first millennium B.C.
onward was not the only source for the appearance of
modular relationships in Carolingian church architecture. It
may, in fact, take second place when weighed against
another influence, which reflects an attitude of mind more
than a constructional necessity. An organization based on
modules is one of the distinguishing features of the layout
of the illuminated pages of Hiberno-Saxon and Carolingian
manuscripts.

Figures 179.A and 179.B show how the artist of the Lindisfarne
Gospels set out to decorate the large cruciform page
that forms the frontispiece (fol. 2v) to this remarkable book
(fig. 178).[304] The principal motif is a square-headed cross
framed by a narrow band and decorated internally with a
key pattern. In the field between the arms of the cross and
the outer frame of the page, there are four panels with step
patterns, two square ones on the top, two of oblong shape
at the bottom. The background is filled with an intricate
design of interlace. The page is framed by a strip of interlaced
birds, held in by narrow bands which terminate at
each of the four corners in an ornamental knot.

An analysis of the construction method used in setting
out the design of this page shows that all the basic divisions
are multiples of the width of the framing bands. The basic
values are 5 · 6 · 7 · 12 (fig. 179.A). The squares of the cross
measure 12 · 12; the panels in the fields above and beneath
the arms of the cross are 10 · 10 and 10 · 25. I feel certain
that a system of linear coordinates, such as is shown in
figures 179.A and B, was laid out on the page, by means of
either lines or prickings before the artist entered the
decorative details. In certain places where the design was
very intricate, such as the panels above and under the arms
of the cross with their complicated step patterns (fig. 180.A),
the illuminator actually drew out the lines with the point
of a fine stylus. This is visible on the opposite side of the
sheet (fol. 2r) as a grid of delicately protruding ridges (fig.
180.B).[305]

I have shown in figures 180.C and D how this system was
worked out. First, the illuminator divided the square
internally into sixteen subordinate squares by the method
of continuous halving. Then he divided each subordinate
square into nine base squares through internal tri-section.
This furnished him with all the desired linear co-ordinates
for the lozenge, cross, and step patterns with which these
squares are decorated (fig. 180.A). The same or similar

[ILLUSTRATION]

184.A St. Luke

The Ada Gospel portraits of the four evangelists framed by arcades
(fols. 15v, 59v, 85v, 127v) depend stylistically on a Late Antique
manuscript tradition combining the sculptural corporeality of Roman
figure style with touches of Byzantine mannerism.

Revived in the art of the Frankish illuminators of the Court School,
this tradition merged with the northern concept of organization of
space. This first encounter of the two traditions is not reflected in the
portrayal of the Ada evangelists, but visibly controls the layout of
the surface in which their images are placed. Later, in a synthesis of
southern corporeality and northern abstraction that parallels the
same development in architecture, these concepts will produce a
figure style that, despite strong dependance on classical prototypes, is
distinctly medieval (see fig. 185).

[ILLUSTRATION]

184.B ADA GOSPELS (EARLY 9TH CENT.)

DIAGRAM SHOWING USE OF SQUARE GRID IN CONSTRUCTION
OF ARCH FRAMING

TRIER. Municipal Library. MS XXII, fol. 59v

methods were used in all other ornamental pages of the
manuscript, and also in the layout of the canon tables (fol.
10r-fol. 17r).

Figures 182.A, B, and C give an analysis of the design
of the great cruciform page on fol. 138v that precedes the
Gospel of St. Luke (fig. 181).[306] This page has as its main
motif a cross with T-shaped arms, filled in with a background
of interlaced patterns; the spaces around the cross
are filled with an animal interlace. The entire decoration of
this page is laid out on a system of squares, each side of
which is four times the width of the framing band. The
page measures thirteen units across and seventeen units up
and down. The transverse axis of the cross is laid out in
the sequence:

the vertical axis in the sequence:

The protruding knots at the corners and in the prolongation
of the two intersecting axes of the page are inscribed
into a marginal area seven units wide.

These principles of modular book design so typical of
Hiberno-Saxon art were inherited by the continental
Carolingian illuminators. Figures 183.C and D are a design
analysis of two of the canon tables of the Ada Gospels, fol.
6v and fol. 8v (figs. 183.A and B).[307] The layout of these
tables varies. Some have four arcades, others have three.
As in the Lindisfarne Gospels all the internal subdivisions of
these pages are calculated as multiples of the width of the
framing bands. In both tables the design is suspended in a
square grid composed of 4 × 4 base units.

On fol. 6v (figs. 183.A and C) the bases of the columns
and their interstices are calculated in the sequence:

the column shafts and their interstices in the sequence:

The columns are inscribed into a grid of 16 × 19 squares,
the arches into a 9 × 19-square grid.

The canon arch on fol. 8v (figs. 183.B and D) has only
three columns. It is based on the same grid pattern. The
bases of the columns are calculated in the sequence:

the column shafts and their interstices in the sequence:

Figures 184.A and B show that the same method of construction
is used in the layout of the arch which frames the
figure of St. Mark on fol. 59v of the Ada Gospels. The basic

[ILLUSTRATION]

185. CODEX AUREUS OF ECHTERNACH

MADRID, Escorial, Cod. Vitr. 17, fol. 2v

[by courtesy of the Patrimonio Nacional]

Emperor Konrad and Empress Gisela prostrate themselves before
Christ in Majesty. School of Echternach, 1043-1046. The Gospel
book was presented to Speyer between 1043 and 1046 by Henry III
(1038-1056) who (folio 3v) is portrayed with Agnes, his consort, in
the act of transmitting the manuscript to Mary, patron saint of the
cathedral. Both illuminations are high points in the synthesis of a
figurative style rooted in Antiquity, with a medieval propensity for
planimetric order and linear simplicity pervading both figurative and
geometric components of each picture (rectangle, lozenge, circles,
semicircles). Byzantinizing mannerisms (cf. fig. 184) are dropped;
the figures have acquired the magnificent blocklike stance that
characterizes much of the contemporary sculpture.

unit is a square, three times the width of the framing bands.
The columnar section is a square, 20 × 20 units; the arch
section, an oblong of 9 × 20 units.

The square grid affects the layout of the page, but not the
design of the figure of the Evangelist. This latter is clearly
patterned after a Byzantine model. The conflict between
the corporeal emphasis of the classical design, and the
tendency of the northern medieval illuminator to subject
the borrowed image to linearism and geometricity provoked
a developmental dialectic in which the ability to absorb
classical influences with increasing strength, in successive
stages, is preconditioned by a partial rejection and successful
transformation of those absorbed in a preceding phase.
In the period of the Romanesque, as a consequence of this
dialectic, solutions are obtained in which southern corporeality
and northern abstraction enter into a state of
balance (fig. 185). In like manner in the field of architecture,
southern masonry tradition fuses with northern frame
construction in a marriage in which the two component
traditions are matched with consummate perfection (fig.
186).

The square schematism is the primary organizing agent
in this development. It helps to disassemble the large
corporeal spaces of the Early Christian basilica, and to
arrange its parts in modular sequences that could be
vaulted. It determines the take-off points for the rising
shafts and arches that were needed to carry the vaults.

MODULAR AREA DIVISION:
AN INTELLECTUAL PRINCIPLE AFFECTING THE
CONCEPTUAL ORGANIZATION IN THE
RELATIONSHIP OF CHURCH AND STATE

It has become a commonplace of historical reference to
speak of the "anthropomorphic" character of Greco-Roman
and Late Antique art and of the "corporeal"
quality of their figurative and spatial composition; and it
has been stressed time and again that this quality grows
out of a way of thinking that interprets man and his metaphysical
environment "in the image of man," a concept so
embedded that even Christianity could not rout it. We
have not yet found any way of describing or explaining
adequately the way of thinking that impelled the medieval
illuminators to submit the classical prototypes to relentless
abstraction and caused the medieval architects to break up
and reassemble their spaces in controlled volumetrical
sequences.[308] Until we have, we shall not be able to understand
fully the meaning of such a phenomenon as the
square schematism of medieval art or, for that matter, any
other schematisms conceptually related to it. Square
schematism is an intellectual principle by which formerly
existent, yet isolated or only loosely connected parts are
brought into an ordered modular relationship. It is a
principle of intellectual alignment that strikes far beyond
the reality of architecture or book illumination into the
realm of literary and musical composition—as Charles W.
Jones and Richard D. Crocker have shown in recent
studies[309] —reflect a cultural attitude that may have had a

[ILLUSTRATION]

186. SPEYER CATHEDRAL (1082-1106)

[after Dehio, GESCHICHTE DER DEUTSCHEN KUNST,
4th ed., I, 1930, plate vol., figure 63]

About 1030, Emperor Konrad II (1029-1039) began to replace the
Merovingian cathedral with a new building (Speyer I) whose crypt
(dedicated in 1041) became a sepulchral sanctuary for the imperial
house. The nave walls of this structure were articulated by a
continuous sequence of engaged shafts rising from the floor to the
head of the walls. The roof was timbered. The aisles by contrast were
covered with shaft-supported and arch-framed groin vaults.

During the reign of Emperor Henry IV (1056-1106, or more
precisely from about 1082-1106), the design of the aisles was
transferred to the nave by the superimposition upon each alternate
tier of a second and heavier shaft, and their connection lengthwise
and crosswise by means of arches capable of carrying vaults. The
view shown above represents the cathedral in the form it had attained
at this point (Speyer II).

direct effect upon even the organization of the relationships
of Church and State, where similar tendencies can be observed
at about the same time. An illuminative reflection of
this mode of thinking is to be found in Walahfrid Strabo's
Libellus de Exordiis, written between 840 and 842. Here
secular rulership and ecclesiastical government are brought
into a system of modular relationships in which each of the
two respective hierarchies is formed by a series of parallel
offices:

Like the "disengaged crossing" or the "extended altar
square" many of the component parts of this system are
old. But the manner in which they were drawn together
into a system of homologous parts presaged a development
which, two to three centuries later, led to the accomplished
and intensely sophisticated metaphysical visions of scholastics.
They envisioned the universe as a triad of structurally
related hierarchies (fig. 187)—each being an identical image
of the other as well as of the system as a whole—that
possessed identical subdivisions into triads of ranks, and
in each of these triads each subordinate rank corresponded
in substance to its equivalent part in every other triad.[311]

SETBACK AND RE-EMERGENCE

On the preceding pages I have shown that the square
schematism appeared in western architecture neither as

[ILLUSTRATION]

187. WILLIAM OF AUVERGNE. LIBER DE UNIVERSO (1230-1236)

HIERARCHIES OF HEAVEN, STATE AND CHURCH

[Author's diagrammatic interpretation]

Components of this concept are Early Christian; their integration into an all-embracing metaphysical scheme is medieval. Similarities in the institutional
organization of Church and State were apparent in the 4th century after the Church began to model its administrative structure after that
of the State. Carolingian awareness of this fact is attested by the passage of Walahfrid Strabo quoted above, p. 231.

Dionysius the Pseudo-Areopagite (5th-6th cent.) speculated that the celestial hierarchies of angels and the orders of the Church were parallel. This
concept became a central theme of Carolingian theology after a manuscript of Dionysius (presented to Pepin I by Pope Paul in 758) had been
translated into Latin by Hilduin of St. Denis. (For more detail see Glossary, s.v. Hierarchy.)

[ILLUSTRATION]

HILDESHEIM. ST. MICHAEL'S CHURCH (1010-1033)

188.B

188.A

Alternating piers and columns at modular intervals is a leitmotif of Ottonian architecture, but has sporadic Carolingian antecedents in Reichenau-Mittelzell
(figs. 117, 134, 171), Werden (Vorromanische Kirchenbauten, 1966-71, 372ff), and the basilica of Solnhofen (see V. Milojcic,
Ausgrabungen in Deutschland, II, Mainz, 1975, 278-312).

abruptly and nor with as few historical preconditions as was
formerly thought. This raises the question: why, once
conceived, did it so suddenly disappear, not to re-emerge
until almost two centuries later?

The answer to this, I think, is relatively simple. The
square schematism, in the highly sophisticated and accomplished
form, which it attained in the layout of the Church
of the Plan of St. Gall, was born within the conceptual
framework of a building that had an overall length of no
less than 300 feet and for that reason could readily be
divided internally into a sequence of 40-foot squares. When
in the revisionary textual titles of the Plan it was suggested
that the church be reduced to a length of 200 feet and that
the columnar interstices be shortened from 20 to 12 feet,[312]
the modular order of the original layout was demolished.
There is no evidence to suggest that this reduction in size
was conditioned by structural or aesthetic considerations.
The change occurred as has been shown,[313] at more or less
the same time—and probably for the same reasons for
which—the abbot of Fulda was deposed for overtaxing the
spiritual and economic resources of his monastery with the
construction of a church considered by his monks as being
outrageously large. In this historical climate the dimensions
of the Church of the Plan of St. Gall, as laid down in the
drawing, could no longer be considered prototypal. The

[ILLUSTRATION]

JUMIÈGES, ABBEY CHURCH (1040-1067)

189.B

The red overprinting supplied by the authors on
Lanfry's fine drawing indicates where certain scars
in the original masonry give evidence of a structural
feature now vanished. This is by some interpreted as
a simple engaged column rising from floor to
clerestory wall-head level, by others as the seat of
abutment masonry of diaphragm arches. The
controversy requires thorough re-examination through
a masonry study made from scaffolds giving access to
full height of nave wall.

As long as such a study is lacking, and until a
structural engineering analysis is made, Ernest Born
and I prefer to keep the controversy alive, Born
favoring the former and I the latter interpretation.

W.H.

189.A

SEINE-INFÉRIEURE, FRANCE

Masonry scars in its clerestory walls (189.C, 189.D) prove that the nave of this Early Romanesque church was spanned by diaphragm arches
rising from engaged columnar shafts attached to every second pier of the nave (begun not before 1052). The square schematism and system of
alternating supports of Jumièges clearly derive from Ottonian architecture (fig. 188).

Columnar shafts introducing modular division into the nave walls first appeared in the cathedrals of Orléans (990) and Tours (ca. 990-1002)
and gained a hold in Germany, after the principle had been established in Speyer I (1030-1061). Jumièges goes further than Speyer through
use of diaphragm arches that carry modular division of nave walls transversely across the space. Diaphragm arches had previously been used in
the abbey church of Nivelles (1000-1046) and the cathedral of Trier (1016-1047). After Jumièges (1052-1067) they are found in other
Norman churches: St. Vigor-de-Bayeux (ca. 1060), Cérizy-la-Foret (ca. 1080), St. Gervaise-de-Falaise (ca. 1100-1123), and St. Georges-de-Boscherville
(after 1114). They become fashionable even in distant Italy: San Pier Scheraggio in Florence (ca. 1050-1086), Lomello (1060?)
and the magnificent San Miniato in Florence (ca. 1070-ca. 1150).

In all these churches the diaphragm arches were placed at intervals too large to allow vaulting between them. This step, the last in development
of the medieval bay system, was made in Speyer II (fig. 190).

[ILLUSTRATION]

189.C SOUTH WALL OF NAVE

Southwest view (toward the Seine and the quarry site for the stones
of Jumièges, showing clerestory windows.

Originally the nave of the church was covered by an open timber
roof, which in 1688-92 was concealed under a vaulted wooden
ceiling supported by sculptured brackets and foliated capitals inserted
on sill level of the clerestory windows.

On this occasion scars were left in clerestory walls through the
removal of some feature, which some believe to have been a
diaphragm arch (Pfitzer, Michon, Horn) and others a simple
engaged column (Martin Du Gard, Lanfry, Born).

[ILLUSTRATION]

189.D DETAIL

A close view shows one of the masonry scars left on the inner face of the
clerestory walls when the original feature for which it formed a seating was
removed, to make room for a vaulted 17th-century ceiling. It is the narrowness
and shallowness of these scars, as well as the height and thinness of the
clerestory walls, that induced earlier scholars to discard the assumption of
diaphragm arches.

Against this view it can be argued that for roughly two-thirds of their total
height, the nave walls are externally buttressed by the gallery vaults of the
church; and that along the lines where the scars occur, the clerestory is externally
reinforced by engoged buttresses rising from the galleries to clerestory wall-head
level. For a good summary of the controversy, see Michon-Du Gard, 1927.
47-54.

[ILLUSTRATION]

SPEYER CATHEDRAL (1082-1106)

190.B

190.A

[redrawn by Ernest Born after plans by
Dehio, Geschichte der Deutschen Kunst, 3rd ed., plate vol. I, figs. 68-69;
Kubach and Haas, 1972, pl. 9; and Conant, 1959, 75, fig. 22]

The great conceptual leap from Early to High Romanesque architecture was made by introducing continuous sequences of arch-framed vaults
springing from shafts that reached from floor to head of clerestory walls. Modularity, now embodied in an armature of architectural members
pervading and framing space in all directions, thus acquired its fully medieval form. The Ottonian "box-space" was transformed into the
bay-divided medieval space. The Gothic changed the vocabulary, but not the fundamental concept of space.

A basilica of magnificent longitudinal sweep and breathtaking verticality (70m. long, over 30m. high), Speyer was the first full embodiment of
this principle of composing churches in continuous sequences of clearly definable modular units of space.

grandiose scale of the original concept had received a
shattering blow in the neo-asceticism of the monastic reform
movement, and, in consequence, was abandoned.

The political chaos that followed the reign of Louis the
Pious offered no opportunities for a return to the earlier
concepts. Their renascence had to await the political and
economic consolidation that was brought about in Germany
by the house of the Saxon kings, and in France by the rising
power and importance of the dukes of Normandy that
peaked in the conquest of England.

The steps that lead to the re-emergence of square
schematism in Ottonian and Norman architecture are well
known and need not be reiterated. They are marked by
such highlights of medieval architecture as St. Michael's
Church at Hildesheim, 1010-1033 (fig. 188); the Abbey
Church of Jumièges, 1040-1061 (fig. 189); and the second
stage of the imperial cathedral of Speyer, ca. 1080-1106
(figs. 186 and 190).

St. Michael's at Hildesheim had a total length of 230 feet
and was internally composed of a sequence of seven
modules 30 feet square plus an apse with a radius of 20 feet
(fig. 188).[314] One could not wilfully construct a more convincing
mirror-image of the modular square division of the
Church of the Plan of St. Gall (figs. 61 and 173).

I do not know of the existence of any accurate measurement
studies of the Abbey Church of Jumièges (10401067).
But from the plans of Martin du Gard[315] and of
Lanfry[316] one gains the impression that it might have been
based on a modular sequence of 35-foot squares, four of
those composing the nave, one the crossing, one the fore
choir, and one half the apse, for a total of six and one-half
squares.

Whether or not the renascence of these modular concepts
at Hildesheim and Jumièges has any direct connection with
the Plan of St. Gall is impossible to say. The discussion of
this subject has suffered from the fact that until very
recently the square schematism even of the Church of the
Plan of St. Gall had been questioned.[317] Yet the similarities
can hardly be overlooked. As in the Church of the Plan of
St. Gall (fig. 61), so in Hildesheim and in Jumièges the
general dimensions of the principal spaces were calculated
as multiples of the crossing square. In both of these churches
this modular division was aesthetically underscored by a
rhythmical alternation of light supports with heavy supports,
the latter marking the corners of the module, the
former rising in the interstices between them. The system
has two isolated Carolingian precursors in the abbey
churches of Werden (dedicated 804)[318] and Reichenau-Mittelzell
(consecrated in 816)[319] but becomes a governing
principle of style only in the Ottonian period, starting with
the abbey church of Gernrode (961-965)[320] and leading
from there in successive steps of refinement through the
magnificent series Hildesheim[321] —Jumièges—Speyer. A
feature of primary developmental implications—completely
overlooked in all authoritative studies on the Abbey Church
of Jumièges—were the great diaphragm arches that spanned
the nave crosswise, rising from shafts attached to every
alternate pier.[322]

Aesthetically this is a first attempt to visually connect the
alternating support articulation of the nave walls with the
aid of a bold transverse member reaching full width across
the space of the nave as well as full height into the roof of
the structure. The diaphragm arch has been variously derived
from Roman,[323] Syrian,[324] Mohammedan,[325] and
Italian[326] sources; but its prototype is much closer at hand;
in the masonry arches that frame the area of intersection in
churches with nave and transept of equal height, and
establish in the transepts of these churches a modular cross
division of space that precedes that of the nave by centuries
(Church of the Plan of St. Gall, 816-17; Hildebold's
Cathedral of Cologne, after 800 and before 819; and perhaps
even the abbey church of St. Riquier, 790-799).[327]
The ultimate prototype of the diaphragm arch is, of course,
the triumphal arch of the Early Christian basilica[328] and

the testing ground for its migration from the transept into
the longitudinal body of the church are the aisles, where
precocious modular cross division by means of transverse
arches appear as early as the beginning of the ninth century
(Werden-on-the-Ruhr, dedicated by Bishop Ludger in 804
and Reichenau-Mittelzell, consecrated by Bishop Haito in
816).

The transept of the Cathedral of Speyer looks as though
it might have been conceived as a triad of 50-foot squares.[329]
The spacing of the piers in the original building (Speyer I,
constructed between 1030 and 1061) did not perpetuate
these dimensions; and when the nave, between 1080 and
1106 (Speyer II) was covered by groin vaults, mounted on
arches rising from shafts attached to every alternate pier,
this resulted in a sequence of oblongs rather than squares.
This variance in modular shape and size is an impurity of
minor importance; the epochal historical advance achieved
in Speyer was that the modular division of the ground floor
was here, for the first time, embodied in an all-pervasive
system of shafts and arches that divided the space lengthwise
and crosswise as well as in its entire height into a
modular sequence of clearly definable cells or bays. Once
this point was reached, the walls between the rising shafts
and arches could be perforated—and were in fact transformed
progressively into that intensely skeletal armature
of shafts and arches that led to the formation of the Gothic.

The self-contained and divisive vaults that covered the
bays of Romanesque and Gothic churches—firmly set off
against each other by their strong relief of framing arches
and ribs—were bound to strengthen the modular organization
of the spaces they covered. Yet they cannot by any
stretch of imagination be interpreted as a technical precondition
of that concept. Modular area division—as has
been made abundantly clear by the examples here cited—
preceded modular vault construction by centuries and
reached far beyond the realm of architecture into the layout
of the decorative pages of Christian service books. It has its
roots in a cultural frame of mind, not in technical conditions.

[ILLUSTRATION]

190.X GENOELS-ELDEREN DIPTYCH

190.Y

Shown same size
as original

BRUSSELS. MUSÉES ROYAUX D'ART ET D'HISTOIRE

[by courtesy of the Musées Royaux]

The monumentality of architecture in concept, execution, and fabric
may tend to overwhelm the scale of, and make distant, those objects that
men once handled and used in their daily pursuits. Tools, books, jewelry,
harness trappings, weapons, liturgical objects—with few exceptions they
are gone from us. The survivors, many of them precious then, as now,
lie in museums, remote from the purposes of their makers and rendered
exotic by their scarcity. Thus, the integration in spirit of such intimate
objects with monuments of architecture is somewhat difficult to achieve.
The many handicrafts that provided embellishment to daily life in a
monastic community such as was proposed by the Plan of St. Gall, has
been but lightly touched upon in this study. That works of art and
adornment were important to the community is undisputed. The Plan
has accommodations for making weapons and associated equipment,
saddlery and presumably other harness tack, and goldsmithing. Silversmiths,
lapidaries, and enamellers may have worked with armourer and
swordsmith. These crafts were housed with other facilities for more
ordinary work, in a pair of buildings in the southwestern tract of the
presumed site. Lay artisans were intended to reside in the community,
as is evidenced by comprehensive housing provided in the Plan.

Crafts that enhanced the praise of God by ornamentation of books,
vestments, and liturgical objects to assist in worship, were proper
activities for monks. Most notable were manuscript copying and
illumination, and ivory carving was likely among them. It is not
referred to specifically on the Plan of St. Gall, probably because its
execution did not require special facilities such as forges, smelters, and a
welter of noisy tools. The work of the ivory carver, silent and delicate,
often closely connected with all aspects of bookmaking, could be done
in a scriptorium, in company with scribes and illuminators.

The illustrated book cover is closely related to illuminations of the
Godescalc Gospels (781-783), earliest of the Court School manuscripts.
It has the same flatness of relief, the same delicate linearity, clearly
distinguishing it from the softly rounded forms and classicizing drapery
style of the later ivories of this school. The model must have been an
Early Christian ivory of Coptic or Syrian origin and representing a
style widely diffused in Merovingian Europe.

The front cover of the diptych shows Christ standing on the asp and
basilisk, flanked by two angels. The back cover displays the Annunciation
(upper register) and Visitation (lower register). Both covers are
pieced from several ivory plaques of different sizes. The work is
perforated and may have been mounted on a foil of gold leaf. The eyes
are inlaid lapis; interlace and step-patterns of the frames are clearly
influenced by insular art and stand in strong contrast to the perspective
illusionism of the two scenes. For references, see Braunfels, KARL DER
GROSSE, WERK UND WIRKUNG (exh. cat.), No. 534, pp. 345-46.

[ILLUSTRATION]

191. PLAN OF ST. GALL. MONKS' CLOISTER, THE CHURCH AND ADJACENT BUILDINGS

When St. Cuthbert built himself a hermitage on Farne Island, where he spent the last eleven years of his life in solitary retreat, he surrounded his
living space "with a wall higher than a man standing upright," and further increased its relative height "by cutting away the living rock so that
the pious inhabitant could see nothing except the sky from his dwelling, thus restraining both the lust of the eyes and the thoughts and lifting the
whole bent of his mind to higher things" (Bede, ed. Colgrave, 1940, 214-17). The Plan of St. Gall achieves a like effect for an entire community
in the sophisticated layout of the cloister with its egress and ingress governed by a body of rigid laws, the open inner court being the monks' only
access to nature and sun—a controlled and ordered island of nature with judiciously selected and carefully tended plants: PARADISUS CLAUSTRALIS.