renaissance gothic: pictures of geometry and narratives of ornament

1.1 Stephen Weyrer, Nave and Choir vaults, Church of St George, Nordlingen, c. 1500.

Photo: author.

& ASSOCIATION OF ART HISTORIANS 2006

P I C T U R E S O F G E O M E T R Y A N D N A R R AT I V E S O F O R N A M E N T I N R E N A I S S A N C E G O T H I C

RENAISSANCE GOTHIC: PICTURES OF

GEOMETRY AND NARRATIVES OF

ORNAMENT

E T H A N M A T T K AV A L E R

What is to be made of sixteenth-century Gothic? More than fashionably late, it is

often regarded as a lithic manifestation of the Middle Ages, exceeding its bounds.

For non-specialists, a sense of trespass on Renaissance territory has long made it

difficult to accept these Late Gothic creations as legitimate products of their own

culture.1 Many scholars of the sixteenth century still have difficulty in finding a

place for the transept facades of Senlis Cathedral, the looping-rib vaults at An-

naberg in Saxony, or the whole of Segovia Cathedral, Gothic structures that all

slightly postdate Michelangelo’s frescoes for the Sistine ceiling.

Gothic architecture witnessed a burst of creative development at the end of

the fifteenth century, a dramatic renewal of an authoritive manner of design. In

many cultural centres of Europe there arose at this time highly refined and fertile

Gothic idioms. Nurtured by prominent patrons and prestigious artists, these

thrived until around 1540, decades after Italianate forms had entered the local

repertory.2 Gothic monuments from this period have generally ceded to con-

siderations of Italianate developments, partly a consequence of a Burkhardtian

enshrinement of the Renaissance as the birthplace of the modern world. But such

disfavour is a fate meted out to many so-called late stages of period styles.

Dominant modes of periodization before the twentieth century favour a con-

veniently linear progression, an orderly sequence of artistic manners, each of

which supersedes its predecessor and is held to embody a distinct world-view.3

Although stylistic pluralism is recognized, it rarely challenges this governing

schema. The Late Gothic of c. 1500, however, was not only the preference of much

of society’s elite, it also employed significant new forms and design strategies.

By the second decade of the century Gothic and Italianate inventions might

appear side by side as indices of the multiple stylistic solutions then possible, a

situation that pertains to most capitals of northern Europe.4 Well-known artists

such as Jan Gossaert in the Netherlands,5 Pierre Chambiges in the Paris region,6

ART HISTORY . ISSN 0141-6790 . VOL 29 NO 1 . FEBRUARY 2006 pp 1–46& Association of Art Historians 2006. Published by Blackwell Publishing, 19600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

Roland Le Roux in Normandy,7 Bernard Nonnenmacher in Alsace,8 Erhard Hey-

denreich in Bavaria,9 and Benedikt Ried in Bohemia worked concurrently in both

manners.10 Yet a certain self-consciousness about design practices had existed for

some time. Francois Bucher and Paul Crossley have argued that even after Ger-

man architects were called down to work on Milan Cathedral at the end of the

fourteenth century, an awareness of alternative Italian practice had spread

through the German lands.11 The elite Gothic of the sixteenth century was, in

part, a system under siege. No longer an inevitable recourse, it had become a

choice, a preference over Italianate manners. Although custom and decorum

might dictate the use of Gothic for certain projects, an awareness of other options

impaired the perception of these structures as signs of universal authority. Gothic

designers adopted various strategies to refurbish their accustomed mode, to

render it more effective, especially as a medium for religious experience.12

During the late fifteenth and early sixteenth centuries Gothic architecture

witnessed a thorough revision of spatial properties throughout northern Europe.

In the German lands13 measures were taken to unify the space in voluminous hall

churches such as the cathedral of Freiberg.14 In the Netherlands the famous

Church of our Lady at Antwerp expanded into a seven-aisle basilica, providing an

enormous interior for urban worshippers.15 And in France porches and facades

were constructed, often for transepts, reframing older structures: the well-known

south porch to the church of Notre-Dame at Louviers in Normandy, for example,

offered a strikingly new architectural experience for those entering the building.16

But the imaginative and novel use of ornament was an equally important

enterprise for architects of the later fifteenth and earlier sixteenth centuries.17 In

fact, the term ‘flamboyant’, which now refers generally to a Late Gothic stage in

French architecture, derives from a particular ornamental feature: the flame-like

tracery forms found in certain French churches around 1500 – classic examples

decorate the gables, rose window and facade of the Church of the Trinity at

Vendome, built around the beginning of the new century.18 In the sixteenth

century the architect Lorenz Lecher referred to Late Gothic forms as Zippernwerkh,

a word likewise related to the language of ornament that seems to derive from

a name for irregular tracery shape.19 In the Netherlands, architects such as

Rombout II Keldermans and Loys van Boghem devised a comprehensive orna-

mental system of distinctive tracery motifs that imparted a sense of unity to the

larger structures, while signalling important features or moments in the en-

semble.20 And in the southern and eastern German lands, elaborate figured

vaults became the focus of the church interior: inventive vault designs based on

geometric motifs proliferated in workshop drawings and executed buildings.21

The expansive patterns overhead were complemented by tracery compositions

that decorated balustrades to galleries, music lofts, choir screens, pulpits, choir

stalls and other works of micro-architecture, all of which occupied significant

sites in these buildings. In many important churches ornamental fields displaying

geometric figures were an inescapable feature of the interior.


2 & ASSOCIATION OF ART HISTORIANS 2006

The relatively little attention that has been paid to these issues is due partly

to a long-standing dismissal of ornament as extraneous to the essential properties

of architecture and to a prejudice against replete decoration as a sign of deca-

dence and decline. Even such a sympathetic critic of Late Gothic as Francois Bu-

cher categorizes as ‘overrich’ the porches at Louviers, Albi and Strasbourg.22 And

he refers to the florid vaults in the western chapels at Ingolstadt as ‘the last stand

of a dying style . . . based on a disciplined geometric grid which explodes into

fireworks of incredible technical and design sophistry’.23 This is symptomatic of a

pervasive modernist aesthetic that conceives of ornament as necessarily opposed

to structure and inevitably antithetical to the functional elements of buildings.24

Recent attention to ornament as a system, however – from Islamic carving to

twentieth-century architecture – has shown how it can actively engage the viewer

and serve as an effective agent of self-representation and cultural change.25

Much Gothic architecture built around 1500 was relatively free of carved or-

nament, as a cost-saving measure for poorer parishes and a potential aesthetic

preference. In Germany, church exteriors are often quite plain, and in the north-

west, simple quadripartite vaults were still the rule,26 as they were in France and

the Netherlands. In Paris, the Late Gothic parish churches, such as St Gervais, have

generally spare and sober interiors with little fanfare to announce their presence

in the urban community.27

This essay, however, addresses those structures that exploited ornamental

embellishment and explores certain potential functions that decorative

devices may have fulfilled. Geometric vault and tracery designs were complex

artistic phenomena that answered several needs. Once the invention of geometric

patterns became securely embedded in lodge practice as an area of competition

and achievement, it was applied to religious and secular edifices alike. Yet, when

located in churches, these ornamental projects might help to convey the sacred

character of the encompassing building. Given a consonant frame of mind, the

beholder might intuit such inscriptions as a sign or index of the celestial realm of

pure ideas that existed above the world of human experience.

Debate about geometric symbolism is not new in the literature of Gothic ar-

chitecture. Otto von Simson, Nigel Hiscock and others have detected cosmological

significance in the use of geometry to plan certain medieval churches.28 This ar-

ticle, however, does not consider such a procedural application of geometry,

largely hidden from view in the actual building. Rather, the present study in-

vestigates the presentation of geometry as a visible symbol in discrete tracery

carvings and rib configurations that are set apart for the beholder. Further, in

many cases ornamental forms undergo a kind of development within the space of

the church that allows for a narrative reading. This progression of decoration

could confirm arch narratives in the culture, such as the passage from earth to

heaven.

The arguments raised here are necessarily speculative. There are few written

texts from the early modern period that refer to Gothic ornament at all, and the


3& ASSOCIATION OF ART HISTORIANS 2006

potential functions identified here would most likely have been fulfilled at a

subconscious level, without a full awareness on the part of the viewer. And yet

these ornamental features are so common and conspicuous in religious buildings

that they call for an explanation. This article treats prominent geometric orna-

ment as a potential reference to the language of divine conception, a marking

that helped to sanctify religious structures. Narratives of geometric forms are

then considered, and finally distinctive geometric designs are viewed from the

perspective of craft as badges of authorship. The discussion focuses on Gothic

creations in the German lands, where these decorative forms occur with parti-

cular frequency. They are also found in France and the Netherlands, though on

fewer monuments. As always, their appearance depended on many factors; their

relative absence in other regions is not a significant obstacle to the theories

presented here. That they occur at all demonstrates the ubiquitous potential for

this use of ornament. Indeed, the Late Gothic in France exhibits several instances

of narrative development, a perspective addressed in the latter part of this essay.

Although certain examples cited here are extreme manifestations of these phen-

omena, they bring to full visibility general tendencies in the period, goals com-

mon to many architects and designers.

P I C T U R E S O F G E O M E T RY

In areas corresponding to modern-day Germany, Austria and the Czech Republic

especially, Late Gothic architects inscribed conspicuous geometric designs on the

interiors of their churches. Towards the end of the fifteenth century intricate

and inventive patterns of broken geometric figures became increasingly common

in prominent locations: nave and chapel vaults, balustrades to galleries, church

furnishing and decorative cladding. Such compositions, ever more complicated,

soon became an independent field of endeavour in lodge practice, as Bucher has

observed. The numerous exercises in geometric construction that have survived

attest, among other things, to the availability of paper as a support, which en-

abled this kind of competitive enterprise – most Gothic drawings, indeed, date

from the later fifteenth and sixteenth centuries.29 Some of these drawings are so

complex that the structures that they depict could never be built; they stand as

demonstration pieces of a mode of design removed from practical concerns.30

When geometric patterns were set in church interiors as carved tracery or figured

vaults, however, they might be read as emblems of the building’s sacred status.

These configurations may be construed as pictures of geometry. They are

contained by railings and mouldings that act as frames, defining an image and

isolating it for regard. This is not a matter of geometric planning, a process

common to architecture of nearly all cultures. It is not the same use of geometry

that contributed to the plotting of a Gothic choir. These designs are discon-

tinuous with the rest of the structure. They stand apart as illustrations of basic

geometric figures that have undergone a series of operations. Such detached

patterns can signify the science of geometry itself, or, more specifically, geometric



1.2 Stephen Weyrer, Choir vaults, Church of St George, Nordlingen, c. 1500. Photo: author.



construction, which conveys the role of creative intelligence. On one level the

master craftsman thus proclaimed his skill. Yet the architect could also act as a

temporary stand-in for the ultimate creator. Ornament thus helped to convey the

sacred natures of religious structures, offering a commentary on their relation-

ship to divine authority.

These geometric designs were most impressive when displayed on church

vaults that extend like canopies over entire chapels, choirs and naves. The art of

vault construction progressed dramatically during the fifteenth century and as-

sumed ever greater importance in church design. There is continually less em-

phasis placed on wall articulation; many German churches built around 1500

exhibit flat, unbroken mural surfaces. Simple cylindrical or octagonal piers re-

place the earlier compound piers with multiple shafts that slowly channelled the

eye upward.31 Attention is now directed immediately to the decorative pattern of

ribs in spectacular figured vaults, which become increasingly divorced from basic

structural requirements.32

A typical example of this genre is found in the Church of St George at Nord-

lingen, begun in the early fifteenth century but vaulted around 1500 by Stephen

Weyrer in consultation with the Augsburg architect Burckhard Engelberg (plate

1.1).33 Over the choir, Weyrer has deployed single- and double-curved ribs (curved

both in plan and in elevation), creating a complex assembly of lines and arcs

across the crown of the vaults (plate 1.2). These ribs form a distinctive figure in

each bay, a hexagon containing a four-pointed star. Further, the ribs of the

polygon protrude slightly at intersections like wooden beams, a detail that opti-

cally detaches them from their surroundings and emphasizes their identity as a

motif.34 Decorative display is paramount. The vaults above the nave introduce a

different arrangement: a dense net composed of triangles, lozenges and rhom-

boids (see plate 1.1). As before, geometric shapes and patterns are set in bounded

fields and presented for viewing.35

The fashionable figured vault designs of around 1500 seem to have been ex-

ceedingly well known throughout the German lands.36 Their popularity was so

great that they spread to the smallest village churches: in some cases inexpensive

ribs made of stucco were used to imprint geometric designs on otherwise spare

surfaces. At Weigersdorf in Lower Austria, plaster mouldings of intersecting

squares, semicircles and quarter-circles are attached to the shell above the nave.

Although individual motifs are easily recognized within the space of the church,

the orderly arrangement of perfect geometrical shapes is visible only on the

ground plan.37

The pictorial aspect of these late figured vaults is central to their creation and

reception.38 There remains an inevitable dialectic between the design on paper

and the projection of the vault over three dimensions, but the drawing is often

prime, a discrete area of activity and competition. Once conceived on the drawing

board, geometric compositions were applied to many types of architectural or-

nament. There are sometimes close connections between the designs for tracery



1.3 Interior with ceiling of SS. Peter and Paul, Lavant, 1516. Photo: Lucas Madersbacher.



and for ribbed vaults, despite practical considerations of engineering that

regulated vault construction.39 A drawing in Vienna (Akademie der Bildenden

K .unste, no. 17091) shows a geometric pattern often used for the openwork

of balustrades, as found on German, French, Austrian and Czech structures.40 The

new venue has been signalled, however, by indicating the joins of the rib sections.

The design clearly appealed as a two-dimensional image, since actual cons-

truction would have obscured the regularity of the geometric configuration.

Not surprisingly, certain drawings are framed in ways that suggest their self-

1.4 Augsburg craftsmen, Pulpit of Church of St George, Nordlingen, 1499.

Photo: author.



sufficiency as objects of study rather than their function as aids in further stages

of production.41

A perfectly flat wooden ceiling, such as that of the Church of SS. Peter and

Paul at Lavant in the Tirol, offered the perfect opportunity to translate drawing

into building without distortion (plate 1.3).42 Fixed to the ceiling, which is dated

1516, are rows of intersecting ogival arches, which are superimposed over a grid of

crossing diagonal bars that form large squares. The church at Lavant shows the

priority placed on geometric patterning divorced from any technical function and

hypostatizes tendencies that are less fully realized at countless other sites.

Complementing their vaults, church interiors were frequently appointed with

balustrades and railings containing geometric tracery. This carving from around

1500 differs from earlier decoration in its greater prominence and complexity of

design, its predilection for incomplete and interpenetrating forms. The Church of

St George at Nordlingen contains several examples of such tracery. The pulpit,

executed by Augsburg craftsmen in 1499 (plate 1.4),43 is attached to a winding

stair that is fronted by intricately crafted openwork. This framed geometric

1.5 Stephen Weyrer, West gallery and pulpit, Church of St George, Nordlingen, 1499 and

1506–08. Photo: author.



composition is characterized by fragmented, interlacing circles, ordered around a

latticework of foci. While individual elements are recognizable, the logic of the

entire design remains hidden, a perceptual puzzle. The pulpit railing relates

to the balustrade on the west gallery, designed by Stephen Weyrer in 1506

(plate 1.5).44 This, too, is a composition of broken arcs and circles, an additional

field of geometric figures that impresses itself upon the viewer.

Another prominent embodiment of this manner of design is the chapel wall

and closure about the west choir of Augsburg Cathedral (plate 1.6), an imposing

barrier that greets visitors as they enter through the building’s principal portal.

The structure comes from Burckhard Engelberg’s workshop and was completed

about 1501.45 An openwork balustrade crowns a frieze carved with rows of con-

tiguous half-circles. The various arcs all touch at a shared point on their cir-

cumference, disclosing that there are three distinct sizes, though once this

essential property is detected, it is easy to see that the half-circles increase in

diameter by regular increments of the smallest radius. Order and proportionality

are conveniently read, even if precise numerical relationships are obscured by the

tight, repetitive pattern.

Older august structures such as the cathedrals of Strasbourg and Freiburg

were fitted with galleries in the new style,46 which soon spread to the corners of

the Hapsburg empire. In the parish church at Niederlana in the Tirol the ex-

tensive west gallery is adorned with a balustrade containing open tracery in the

form of three-quarter circles filled with lobed triangles and other geometric

1.6 Burckhard Engelberg, Closure about west choir, Augsburg Cathedral, c. 1501. Photo: author.



motifs (plate 1.7).47 The distinctive composition is continued along the sides of

the nave in a frieze of blind tracery.

Brazenly non-functional, these carvings could convey the very idea of geo-

metry. They could engage the beholder in acts of puzzle-solving, encouraging

attempts to discover the operations used to generate the design. Much in this

manner, J .ugen Julier has detected perspectival games or riddles in the complex

geometric construction of works of Late Gothic micro-architecture, such as the

baptismal font at Strasbourg Cathedral; he considers the designers of these ob-

jects to be expressing a form of architectural humour or irony, deliberately defy-

ing the expectations of the observer.48 Playing with habits of perception also

became an important preoccupation for Netherlandish Gothic designers c. 1500.

There are puzzle-like aspects to many of the complex frames of Netherlandish

carved altarpieces, such as that at Lombeek, which seem intentionally confusing

and disorienting in their irregular subdivision. These works encourage the viewer

to discover the underlying system of proportions in order to restore a sense of

order.49 The solving of puzzles and riddle-like forms is not uncommon in late

medieval texts. Such demands are placed on the reader of works such as Guil-

laume de Deguileville’s The Pilgrimage of Human Life.50

S A C R E D S I G N S

The tradition for associating geometry and geometric figures with the divine

spans more than a millennium. Early medieval writers on this subject remained

an important intellectual source for the late Middle Ages; their popularity in the

1.7 Hans Hueber(?), West gallery and nave wall, parish church, Niederlana, 1483–92.

Photo: author.



later fifteenth and sixteenth centuries is confirmed by numerous publications of

their works and by references to their theories in the treatises of younger theo-

logians. Augustine and Boethius famously praised geometry as a means of cog-

nition, as an instrument for understanding God’s creation, and extolled the ideal

nature of geometric forms.51 A major strain of this writing was clearly platonic,52

based, above all, on Plato’s Timaeus, the dialogue best known to medieval authors,

which describes the creation of the world in terms of geometric figures.53 This

belief in the metaphysical nature of geometry, number and proportion continued

to resonate in the late Middle Ages. Alan of Lille, the twelfth-century theologian

who enjoyed considerable popularity in the fifteenth century, reveals his debt to

1.8 Guillaume de Deguileville, Le Pelerinage de la vie humaine, Paris, 1500.

Book illustration. New Haven: Yale University, Beinecke Library.



the platonic tradition when he claims that ‘Every mathematical name is less

improperly said of God than is a concrete name.’54 And treatises on geometry

continued to extol regular two-dimensional figures and polyhedrons as the es-

sential forms of the universe.55

Several writers of the fifteenth century considered geometric terms and

shapes characteristic of the ideal, abstracted language of divine thought and the

mechanism of creation. Among the most prominent was Nicholas of Cusa, for

whom the curve and the straight line were indicative of the dual nature of the

universe; the circle was the ‘perfect figure of unity and simplicity’.56 In De docta

ignorantia, Nicholas follows the platonic tradition in describing how God fash-

ioned the world using geometry along with arithmetic, music and astronomy.57

His notion of the divine and infinite ‘absolute maximum’ is likened to the inter-

action of geometric forms: ‘just as the sphere is the act of the line, triangle and

circle, so the Maximum is the act of all things.’58 In fact, Nicholas expresses God’s

relationship to created matter in geometric terms:

[God], therefore, is the final cause of all. But since beings are finite their attraction to Him as

their end necessarily differs from one to another. Some are attracted through the intermediary

of others, in much the same way as the line is to the sphere through the triangle and circle, the

triangle to the sphere through the circle, and the circle directly to the sphere’.59

We find a similar strain in the writing of Charles de Bovelles, for whom geometry

was a guide in measuring the qualities of the Trinity.60

These platonic concepts found their way into popular devotional texts,

a measure of their broad currency. Exemplary is Guillaume de Deguileville’s

The Pilgrimage of Human Life, composed shortly before 1350, which continued to

enjoy a significant vogue in the fifteenth and sixteenth centuries and was pub-

lished in French and Spanish editions.61 In the first book, a geometric figure is

introduced as an image of divine legacy. Christ’s ‘testament of peace’ is illustrated

by a right-angle ‘carpenter’s square’ – ‘a jewel formed and shaped by my father’. A

diagram is provided in the text, and the reader is instructed to label its parts

(plate 1.8). Geometric properties, critical to the design, guarantee its truth and

authority:

If anyone would like to know its form, I will provide the exact design to those of good under-

standing. Take a carpenter’s square and set it with one end up and the other end down, with the

corner at a right angle. Then place an A right at the corner joining the two sides, an X on the

upper end, and a P on the lower end, as shown in the figure. You can then easily recognize its

form and see its name written clearly there with the three letters I have mentioned. These three

letters show that those who have been left the gift of this jewel must have peace in three ways

. . . They ought to be moved strongly toward this by the fact that they are on the same plane,

neither higher nor lower. When I created, shaped and formed them, I placed them at the same

degree.62



The general tendency to seek analogy to divine concepts in geometric terms is far

more important than specific allusion. It is a habit of thought, deeply entrenched,

that is revealed in both learned and popular texts. A belief in the cosmic sig-

nificance of numerical relationships, and of music and geometry as their embo-

diment, was so widely held and resonant that it remained a constant potential

reference.63 Moreover, the well-known image of God as a geometer using a com-

pass to create the world survived into the late Middle Ages.64

Platonic currents in late medieval culture thus encouraged a reading of

geometric figures as archetypal identities, as perfect and essential forms. Redu-

cing objects to mathematical properties purged them of the specifics of their

material manifestation and approached the divine blueprint. Nicholas of Cusa

expresses this concept when he speaks of ideal forms descending to enjoy a

limited existence in matter.65 He is clearest on this point in the dialogue De ludo

globi, in which one speaker asserts, ‘Thus materialized, no form is true, but rather

only an image of the truth of true form, since the truth of form is separated from

all material.’66

Because tracery compositions were studies in the system of mathematical

proportions that was considered a gift of God, they might be received as a register

of forms in the perfection of their idea before their materialization in the world.

When presented in fragmentary state as tracery, as broken or incomplete circles,

these figures could convey a departure or descent from this highest state. They

signal the notion of becoming, the process of corruption that necessarily accom-

panied material embodiment. An intimation of this transformation is found in

Michael Pacher’s St Wolfgang Altarpiece, completed in 1481.67 Above the scene of

the Coronation of the Virgin floats the dove of the Holy Spirit. The form of this

bird, with its wings outstretched, clearly mimics the crossing lines of tracery

immediately behind and above it. The gently curving ogival arches of the balda-

chin seem to comprise a geometric matrix from which the material form of the

dove is generated. In allowing itself to be represented as a dove, the Holy Spirit

condescends to assume the mantle of perceptible form.

Of all geometric shapes, the circle was generally considered to be the most

perfect. A fundamental source was again the Timaeus, which praised the sphere,

not distinguished from the circle, in a passage included in Calcidius’s commen-

tary. Notably, Augustine had also defended the perfection of the circle, testimony

that was adopted in early medieval tracts on geometry.68 A belief in the sacred

nature of this figure remained very much alive in the fifteenth century, especially

in the writings of Nicholas of Cusa, who praised the circle as the ‘perfect figure of

unity and simplicity’, a prelude to his ‘analogy of the infinite sphere and the

actual existence of God’.69 For Nicholas, as for many before him, stars naturally

moved in circles, the archetypal figures of the universe.70 Indeed, in its perfec-

tion, the circle was clearly divine, confirmed by the fact that ‘God is a circle with

its centre everywhere and circumference nowhere’, and ‘Christ is the centre of all

circumferences.’71



1.9 Vault of Mariakapelle, parish church, Schorndorf, c. 1500. Photo: author.



This idea was also represented in more popular literature of the late Middle

Ages, attesting to its wide dissemination. A prominent example is Bartholomaeus

Anglicus’s famous encyclopaedia, which, though written in the thirteenth cen-

tury, was frequently published in both Latin and vernacular editions around

1500.72 In his chapter on heavenly bodies, which acknowledges the authority of

the Timaeus, Bartholomaeus asserts that a spherical, circular shape was most

appropriate for the world as a sign of the ‘perfection of all things’.73 More sig-

nificantly, the circle is directly associated with the divine act of creation in his

later chapter on the figures of the senses.74

The proliferation of looping-rib vaults in the early sixteenth century, the so-

called Bogenrippen- and Schlingrippengewolbe, may be examined in this context of

sacred geometry.75 Architects in the German lands,76 in Spain,77 and occasion-

ally also in France,78 employed double-curved ribs that inscribe meandering,

curvilinear pathways beneath the masonry shell. At Kutna Hora in Bohemia and

at Annaberg in Saxony, to cite two well-known cases, the ribs form a series of

interpenetrating round outlines across the vaults, which are especially shallow

and allow for extensive graphic elaboration.79 In the centre of each bay rests a six-

pointed star that resembles a flower with six petals, a quasi-representational

motif that is embedded within a broad geometric pattern. The mark of the

compass is even clearer in the vaults of the Chapel of St Catherine in Strasbourg

Cathedral, a late example of the genre by Bernard Nonnenmacher, which displays

interlacing three-quarter circles.80 Stars are painted on the webbing, affirming

the long-standing association between church vaults and the heavens.81 But even

without the celestial allusion, the ideal circular patterns of these vaults could

convey notions of the divine plan.82 Cosmological implications are still easier to

read in the vault of the large Mariakapelle at Shorndorf in W .urttemberg, where

the ribs form a continuous net of complete, intersecting circles (plate 1.9).83 The

entire vault represents an extensive Tree of Jesse; busts of Old Testament kings

and prophets appear at the junctures of the circles, while Jesse himself reclines

above the entrance wall. Here God’s programme conforms with the most perfect

geometric form.

H I E R A R C HY A N D A N A G O G I C A L R E L AT I O N S

Artistic representations of divided terrestrial and celestial worlds are common in

the fifteenth and sixteenth centuries. Although the two regions are sometimes

shown as contiguous, they signified discontinuous realms, related to each other

mystically or anagogically. Charles de Bovelles nicely describes this bifurcated

model in stating, ‘the intelligible world is double: one of substance and the other

of reason; one above the firmament and the other below.’84 And for Nicholas of

Cusa, ‘the visible universe [was] a faithful reflection of the invisible.’85 Such

anagogical relationships were hierarchal and vertical, ‘leading to higher things’

(ad superiora ducens).



Significantly the arrangement and placement of geometric decoration was

hierarchic. In retables, the baldachins, those complex assemblies of linear geo-

metric parts, rest above the range of human figures. On buildings, geometric

patterns are usually set above areas occupied by viewers or inhabitants of the

architectural space; they occur most frequently in triforia, window tracery,

tympana, gables and crests to porches. Both a division and essential connection

between earthly and heavenly realms is expressed in paintings like Jean Belle-

gambe’s Triptych with the Last Judgement (c. 1520–25).86 The Paradise wing shows the

celestial palace of the heavenly Jerusalem as a skeletal Late Gothic structure

composed of geometric tracery forms. Situated in the upper corner of the panel, it

is distinct from the substantial terrestrial edifice that serves as a gathering point

on earth for the journey to heaven.

The understanding of a universe split between material form and idea is

implicit in a number of figural reliefs and altarpieces from this period. A lower

area is occupied by carvings of humans or divine beings, either present iconically

or acting out a story, while an upper register is given over to a presentation of

geometric shapes. One example of this format is the Epitaph for Wolfgang and

Sigmund von Keutschach, appended to the exterior wall of the pilgrimage church

at Maria Saal in Carinthia (plate 1.10).87 In the large lower field Christ and God the

Father crown the Virgin Mary, while the dove of the Holy Spirit hovers with

outstretched wings at the top. A thin layer of clouds divides this figural relief

from an upper field displaying three intersecting semicircles and a series of rev-

erse arcs. A moment’s observation discloses a correspondence between the two

halves of the relief, since the three semicircles agree in number and place with

the three actors in the figural field below. The crossing of arcs at the centre

(topped by a fleuron) creates a shape roughly comparable to the dove of the Holy

Spirit, an analogy fortified by the common ascription of a celestial, ideal charac-

ter to circles and their family of geometric figures. The semicircles in the relief

can be seen as inscriptions of mathematical ideas and, as such, represent a higher

plane than the material representation of the figures, even given their divine

status.88 As in Michael Pacher’s St Wolfgang Altarpiece, there is an opposition

between objects of experience and conceptual geometric forms.

It was possible for these images to serve as instruments for the activation of

memory and meditation. The church, with its figured vaults and panels of geo-

metric tracery, thus made permanent and emphatic a locus of ideas associated

with the nature of the world and the double-order plan of the cosmos. The pro-

portionate circles, arcs and line segments spanning vaults could bring to mind

notions of ideal pattern and proportion. These features could thereby induce a

process of measuring, actively engaging the beholder in a specific manner of

thinking that might lead to productive and directed meditation. Mary Carruthers

has discussed a related phenomenon, one that involves the dynamic appreciation

of space rather than fixed surfaces. She describes the experience of visitors

walking through Cistercian churches, with their sober mural expanses, alter-



1.10 Hans Valkenauer(?), Epitaph for Wolfgang and Sigmund von

Keutschach, c. 1511. Red marble. Maria Saal: parish church.

Photo: author.



nating columns and open spaces – the physical procession generating a pattern of

light and shadow that might reinforce certain thinking habits. The Late Gothic

vault with its configuration presented a stable pattern. Yet in a similar way, it

could lead the viewer to meditate; it might be considered as a ductus, a guide, an

aid of passage, or an inducement, a device facilitating access to meditation.89 The

vault, and pictorial geometry in general, could be considered a ‘cognitive ma-

chine’, following Carruthers’s description of the habits and mechanics of medi-

tation. A clear instance of this technique as applied to geometric figures is found

in the example cited above from that popular devotional text The Pilgrimage of

Human Life. The right-angle carpenter’s square provided in a diagram becomes a

cognitive tool for engendering a meditative state. The reader is directed to study

its geometric properties, which determine the relationship between various ideas

that are identified with its parts.90

This is not to suggest that Gothic tracery had some stable, conscious and

verbally articulated significance. Rather, in its present application, it could signal

that a certain manner of understanding was relevant. It could suggest to the

viewer a particular way of relating visual appearance to conceptual structure.

Under proper conditions, formal configurations that were homologous with a

division between earth and heaven might be intuited as embodiments of this

paradigm. The stone offered a physical structure, a matrix upon which similarly

ordered ideas could be projected. Seeking God, pursuing signs of the celestial

realm, was a probable activity for a visitor to a church, and carvings of geometric

shapes offered a ready reminder of established notions of the divine and its

register in the world.

Architecture, actual or represented, could thus refer to metaphysical rel-

ationships through homology. It offered material confirmation of ordering

systems and consequently privileged certain types of relationships over others;

in the words of Theodor Adorno, it permitted ‘that which [was] about to slip away

to be objectified and cited to permanence’.91 The viewer identifies the screen or

altarpiece as an object of experience while simultaneously recognizing agree-

ment with a significant conceptual structure. Art can thus give presence to vague

and transitory impressions in the form of a stable sensory phenomenon; its

aesthetic truth would be its potential for disclosing an accepted truth.92

N A R R AT I V E S O F O R N A M E N T

The ornamental articulation of these Late Gothic buildings and furnishings often

encourages a narrative reading that imposes a sense of order on geometrical

figures. As the viewer experiences the elevation of certain church facades, the

arrangement of baldachins in Gothic altarpieces and the vault patterns in suc-

cessive bays of a nave or choir, decorative motifs may seem to undergo gradual

change.93 In place of human characters there are geometric shapes that become

objects of protracted regard.94 If conventional plots are lacking, these figures may

undergo sequential transformations that lead towards an ultimate state. Arche-



typal forms are identified and differences reconciled, often by combining prop-

erties of two different motifs in subsequent figures.95 This kind of mathematical

story-telling may come to seem natural enough. Indeed, Hayden White has argued

that narrative is the privileged mode of understanding in Western civilization,

that historians tend to organize their data into narrative patterns when giving

them meaning.96 Narrative tendencies, however, are not of recent vintage, for

medieval writers like John of Garland (thirteenth century) had already classified

most narrative as hermeneutic (ermeneticon).97

Vertical progression is one of the privileged dynamics in this model of in-

terpretation, though it might by complemented by other axes of reading.98 As

saints rise to heaven so religious edifices ascend towards a metaphorically higher

and more blessed state. This is the standard arrangement of tabernacles, ex-

emplified by those at Ulm, Nuremberg and Louvain.99 The lower ranges com-

monly encase statues or figural groups which advance in scriptural order from

level to level, culminating in Eucharistic images of Christ. Looking up, the viewer

notes that structural members are gradually reduced to a single pinnacle: unity

out of multiplicity or chaos.

Aspects of twentieth-century narrative theory may be useful in raising to full

awareness what would have been a pre-conscious mode of understanding for

sixteenth-century viewers. It is essential to recognize that geometric transfor-

mations are performances of mathematical operations on a given figure. Each

resulting new shape is as much a register of such an operation, an act, as it is a

distinctive entity in itself. Such a process is articulated in the writings on nar-

rative by Vladimir Propp and by A. J. Greimas. In his study of Russian folklore,

Propp classifies fairy tales not according to specific characters but according to

the generic acts that advance the plot. Characters provide agency but are classi-

fied in terms of the functions they perform, the essential components of the tale.

He observes that stories begin with a situation establishing norms, followed

by the introduction of a conflict which is gradually resolved.100 Greimas, too,

considers characters as registers of narrative transformation rather than as sig-

nificant entities; he terms them actants rather than acteurs. He further discusses

the way in which a series of plot actions can be read as a single argument, a

sentence directed towards a specific point or goal. ‘A story’, he maintains, ‘is a

discursive unit which ought to be considered as an algorithm, that is, as a suc-

cession of state-actions oriented toward an end. . . . In order to have meaning, a

story must be a significant whole; it manifests itself, therefore, as a simple se-

mantic structure.’101 This teleological aspect of narrative is also applicable to an

understanding of Gothic ornament, which can progress towards a resolution of

apparent oppositions in the juxtaposition of forms.102

Narrative understanding is invited by the great tabernacle in Ulm M .unster,

built during the 1460s and completed by 1471 (plate 1.11), the largest work of

micro-architecture in the Late Gothic world. Achim Timmerman refers to the

structure as a ‘complex geometrical argument’, and indeed there is something



1.11 Tabernacle, Ulm, M .unster,

completed c. 1471. Photo: author.



almost rhetorical about it.103 A programme of Old Testament prophets and pa-

triarchs is encased in the tabernacle, offering a scriptural basis. But its enormous

impact is greatly enhanced by its intricate architectural articulation, its multi-

plicity of tubes and struts that are winnowed and simplified as the tabernacle

rises. A series of intersecting arches provides connections between the tubes and

pinnacles, leading the eye from the outset along numerous paths. The vertical

elements are linked at various points by inverted ogival arches which unite pairs,

reducing them to a single upward extension. The statue of Moses is surrounded

by a set of pinnacles of different dimensions (plate 1.12). The outer ones end

abruptly, but are linked by flying buttresses to three inner uprights that reach

higher. These, in turn, are linked by bell figures, surmounted by fleurons, which

ascend still farther but which eventually come to an end and mark a false path on

the way to the top. Buttresses, struts, bell shapes and arches create intersections,

detours and proper channels to the culmination of the tabernacle, the single

pinnacle at the top.

The ascent of the Ulm tabernacle is given a ready theological gloss, for it is

set against a fresco of the Last Judgement, painted on the wall to the choir.104 The

top of the structure stands opposite the palace of the heavenly Jerusalem in the

fresco, associating a narrative of salvation with its course. The Ulm tabernacle can

be read like an intricate sentence with oppositional clauses and a predicate.

Doubleness is unified, oppositions are resolved, and a conclusion is ultimately

reached. The eye is led along the lines of the tabernacle, noting true and false

pathways. Geometric figures – the intersecting arches and bell figures – transform

the plot, addressing states of absence or abundance. They might loosely be

compared to the actants in the narrative theory of Greimas, figures of change in

the story line.

Late Gothic church facades are sometimes designed to be read in similar ways.

Here a vertical orientation is essential to the ascription of meaning. An instance

of this manner of composition is the north transept facade of Evreux Cathedral,

designed by Jean Cossart and completed by 1517 (plate 1.13).105 The facade is or-

ganized around three large triangular gables: the lowest surmounts the portal,

the middle tops the rose window, and the final member of the trio crowns the

gallery between the two towers. All three gables are paired with circles or semi-

circles in different ways. Directly above the portal, a (semi-)circle is entirely en-

closed in the lowest gable. In the centre of the facade, the rose window transforms

the gable, expanding and curving its sides while making the top ogival. At the

highest gable, between the towers, circular contours have broken through and

now frame the triangle. The facade seems to demonstrate the escalating im-

portance of the circle over the triangle. The direction is again upward, from the

ground to heaven.

Certain vaults of the period also allow of a narrative reading. At the pil-

grimage church at Krenstetten in Lower Austria curved and straight ribs form a

series of distinct and self-contained figures on the vaults (plate 1.14). The ren-



1.12 Detail with Moses, Tabernacle of Ulm, M .unster, completed c. 1471. Photo: author.



1.13 Jean Cossart, North transept facade, Evreux Cathedral, completed by 1517. Photo:

author.



1.14 Vaults of Crossing and

Choir, parish church,

Krenstetten, c. 1520.

Photomontage: author.



ovations of the 1520s raised the height of the choir by some five metres and in-

cluded a new crossing, an area accessible to the laity which offered an excellent

view of the fascinating ceiling.106 At Krenstetten the vault seems to be detached

from its supports and isolated as an object of regard. Its independence is implied

by the idiosyncratic capitals that channel pier mouldings into the shell without

connecting them with the ribs above; meanwhile, other ribs descend and cross at

these capitals, bypassing the piers.

In the bays over the crossing the vault displays three pairs of elongated ovals –

formed by double contiguous squares closed at the ends by half-circles.107 The

bays over the choir reveal a different pattern. First, the paired ovals contract to

circles in the choir’s westernmost bay. These are followed by a central cross with

curving arms, replacing the doubled forms and progressively obscuring any recog-

nizable figure; a few fragmented and indistinct shapes fill the remaining space to

the choir wall. Nonetheless, this eastern zone conveys the impression of geo-

metric order. Arc and straight line are still the building elements, though the

overall pattern is enigmatic. This use of geometry resembles a sort of writing that

can be recognized as language but which cannot be read – perhaps a bit like the

Islamic inscriptions in certain mosques that are progressively stylized until they

are no longer legible but continue to signify as holy utterance.108 Throughout the

vaulting at Krenstetten there is a perceptible progression from double ovals to

double circles to the elimination of all doubling and, finally, to opacity at the east

end of the choir.109 At Krenstetten the geometric rib configurations might be

perceived as a type of metalanguage or, rather, as a material register of one. In the

choir, the most sacred part of the church, the language is too complicated to be

recorded comprehensibly in stone. It is not possible to give a definite reading of

the Krenstetten vaults, only a likely path of inquiry and reflection. The designs

here imply notions of difference, development, hierarchy and the limits of com-

prehension.

Much in this manner, the succession of baldachins in Netherlandish carved

altarpieces can be read as a type of story, an abstract addendum to the narrative

conveyed by the scenes of human figures. The Altarpiece of the Joys of the Virgin

at Brou (plate 1.15), probably executed by artists from Brussels about 1517, is

particularly conducive to this approach. Each of its many compartments is

crowned by an elaborate composition in open and blind tracery. In this alabaster

retable the arrangement of figural scenes supports a vertical orientation; the

horizontal axis at each level is minimized by the towering central compartment

of the Assumption of the Virgin, which breaks through the horizontal divisions. The

principal ornamental figures or actors in the carved canopies are the bell shape,

the trefoil and the standard round arch (plate 1.16). Varieties of these forms can

further be distinguished – ogival, suppressed and corbel – and their alternating

occurrence in openwork, blind tracery and drop tracery could be classified as

modes.110 All these configurations appear extensively throughout the church and

thus help to present the retable as part of a larger entity.



1.15 Netherlandish artists, Altarpiece of the Seven Joys of the Virgin, c. 1517. Brou: St Nicolas

de Tolentino. Photo: author.



As the figures of Mary, Joseph and the Christ Child recur in successive frames,

so, too, do the abstract geometric figures in the large tracery plates that top each

scene, with the pattern shifting at each of the three storeys. At the lowest level,

the four compartments are set apart in black touchstone and surmounted by an

entablature that continues as a string course around the interior of the chapel.

Because scenes from a continuous Marian programme are included, it makes

sense to regard this part as a foundation for the corpus rather than as a kind of

predella. In the ornamental carving above the Annunciation and Visitation, each

filling two bays, trefoils in blind tracery appear above a suppressed arch sup-

porting drop tracery. The two narrow side bays present compressed trefoils with

bell-shaped figures resting on regular arches, all executed in blind tracery (see

plate 1.16). On the second storey the lateral compartments of the Nativity and

Adoration of the Magi have converted the trefoils to openwork with bells delineated

in the drop tracery. The pattern changes again in the following register. The

decorative canopies to Christ Appearing to His Mother and Pentecost are cut in the

form of corbel bells, while blind tracery above completes a trefoil and an envel-

oping suppressed arch. The trefoils reassert themselves in ogival form, however,

in the baldachin that screens the central Assumption of the Virgin at the top.

There are oppositions between bell and trefoil, between concave and convex

forms, and between open and blind tracery. But there are also indications at

1.16 Netherlandish artists, detail of ornamental forms above the Annunciation and the side com-

partment, Altarpiece of the Seven Joys of the Virgin, c. 1517. Brou: St Nicolas de Tolentino. Photo:

author.



subsequent levels of a partial synthesis of elements, which permits an under-

standing of process over time. The ornamental carving above the low Nativity

includes both trefoil and bell found in the disparate compartments of the base-

ment. The third storey conflates bell and trefoil into a corbel bell framing Christ

Appearing to His Mother. The trefoil has once again become dominant above the

Assumption at the top, yet its ogival form betrays a relationship to the underlying

variations. The original distinctions between figures have been minimized or

eliminated through a process of assimilation.

The Brou altarpiece is designed to suggest that it expresses a truth more

comprehensive than that conveyed through the human figures alone, yet one

congruent to them. Culturally conditioned preferences for closure and union

conditioned response to similarities in tracery from storey to storey as a process

towards reconciliation of difference. The same disposition affects the reception of

the figural scenes. Mary and the apostles are human, familiar and of the earth;

their lives have significance and purpose only with respect to the will of God,

which cannot be represented in experiential or mundane terms. The Assumption

of the Virgin is a passage from human to divine, from being to meaning. The

architectural frame, with its sequential geometric patterns, may seem to express

the power and desire governing this resolution, supernatural signs of transfor-

mations in nature.

Much of what we see involves the erasure of disparity or divergence as re-

gistered in geometric forms. It is worth observing that the elimination of differ-

ence, a reconciliation of opposites, is a common goal in late medieval and early

modern culture. There are many parallels in the literature of the period. Here the

eradication or suppression of difference can signal a programme of ideological

legitimation in the subtext, which depends on narrative for its realization.111

Chretien de Troye’s Erec et Enide, for instance, presents the unknown knight as a

threat, less on account of his belligerence than for his refusal to divulge his

identity; he is difference as much as potential evil. Forced to reveal his name and

status, the knight is reintegrated into the common aristocratic social structure

and loses his malevolent character.112 Oneness consistently represents ethical and

practical ideals. In the English translation of Froissart from the early sixteenth

century, the clear and distinct speech of English diplomats contrasts with Bur-

gundian ‘double of understandige’.113 That ‘parfyt vnyoun’ of opposing forces is

also the ideal in John Lydgate’s verse. In the Troy Book war ensures that ‘Yngeland

and Fraunce/May be al oon, withoute variaunce.’114 The essential unity and in-

tegrity of Henry V becomes his identifying marker. Praised as ‘ay in oon withoute

chaunge’ in John Pages’s Siege of Rouen, the king is free of all French ‘dob-

lynesse’.115

The act of understanding as both the enactment of narrative and the re-

cognition of congruence is suggested by the Saluzzo Altarpiece (plate 1.17) with its

distinct and separate figure groups and complicated baldachins.116 Carved in oak

and polychromed in Brussels about 1515, its gilded ornament is as remarkable



1.17 Brussels workshop, wing of Saluzzo altarpiece, Broodhuis, Brussels, c. 1515. Photo: author.



and occupies as much space as the scenes from the life of the Virgin beneath. The

canopy that surmounts the Marriage of the Virgin and the Annunciation is particu-

larly extensive and impressive in design, a complex structure of ogival, round and

rampant arches, buttresses and struts, all carefully cut and fitted. The arches

ascend towards the centre as they connect with supporting members in adjacent

bays. Some routes end abruptly or deviate from the common goal. A few of the

familiar shapes appear, normalizing the pattern: ogival trefoils appear at the

sides, though bent at a right angle along their central axis, while a diminutive

bell arch is suggested in the middle near the top.

This structure had the potential to evoke a specific range of responses. The

baldachin could be seen as a strange suspended labyrinth with continuous and

broken paths. The viewer of the sixteenth century might well begin to retrace

the tracery as if mentally travelling through one of Joachim Patinir’s con-

temporaneous landscape paintings.117 The performance need not be exhaustive

to convey the sense of play, of infinitely complex order only partly perceptible.

Forced to assimilate the tabernacles to the realm of human actors, a viewer might

think of the visible world as a finite index of the divine matrix. The ornamental

fields change from compartment to compartment, much as the figural scenes do,

and there is once again a relation between the canopies that establishes a second

order of narrative. The baldachins in the lateral wings are the most intricate,

whereas those in the adjacent compartments are designed around larger geo-

metric figures that orientate the viewer more easily. The baldachin in the central

chamber is higher and simpler still, thus imitating the progression in the in-

dividual tabernacles.

The value placed on such variation is actually to be found in a contract of 1507

between the Brewers’ guild of Louvain and Jan Borman, the famous sculptor from

Brussels. Borman and assistants were required ‘to make the middle tabernacle

entirely different [from those in the side bays] though as expertly as indicated in

the plan (patroen)’.118 The commission from the Louvain brewers reveals a great

deal about the appreciation for this branch of architectural ornament. When it

came to carving the wooden tabernacles, Borman turned to a specialist in min-

iature wood masonry, Jan Petercels, who, in turn, was required to follow a

drawing supplied by Matthijs Keldermans, a member of the prestigious family of

architects and sculptors from Mechelen. It should be noted that the brewers en-

trusted the design and execution of these tabernacles to acknowledged experts of

their own choosing.

It is important for our purposes that these various essays in geometric design

often occur in combination with the imitation of vegetal forms. Buttresses may

seem to take root, pinnacles to flower, and curtain arches to crawl like vines along

facades.119 At Breisach, for instance, the body of the high altar has its customary

architectural baldachin replaced by leafy branches that closely imitate the cus-

tomary framing trefoil.120 The wood seems to return to its live origins, perhaps

drawing on notions of the potentia absoluta (total power) of God in creating the



world – yet again there are indications of change, of metamorphosis. The intricate

broken patterns of geometric shapes and the vegetal elaboration of more ex-

pected tracery forms can be seen as departures from a precise, mathematically

stipulated norm and assume meaning when seen in contrast to this perfect

standard. The ideal is shown in the breach. The juxtaposition of geometric figures,

intact and flawless, with renderings presented as incomplete or transformed into

plant-like effigies again suggests degeneration or adulteration.121

O R N A M E N T A N D I D E N T I T Y

One might say that the presence of these carved fields was overdetermined, for

they addressed several different needs and desires. This emphasis on the geo-

metric design was soon institutionalized in lodges and guilds, becoming a

recognized field of competition.122 The importance placed on sophisticated

geometric patterns allowed particularly inventive compositions to point to the

designers as a sort of imaginative signature. In Nuremberg Adam Kraft presents a

spectacular example of complex tracery for the balustrade to his tabernacle in the

Church of St Lawrence; this virtuoso openwork is placed directly above a kneeling

figure of the artist himself and stands as a supplementary sign of authorship

(plate 1.18).123 It seems to emerge from his head as the product of his ingenium and

takes its place between the coats of arms of the patron on the dais. Burckhard

Engelberg likewise placed inventive patterns on his balustrades which were si-

milar to micro-architecture in Augsburg, Ulm and other cities.

These idiosyncratic designs betray a certain kinship with older masons’

marks, the simpler geometric figures cut in quarried blocks that ensured credit

and accountability for less prestigious labour. During the fifteenth century ma-

sons’ marks were placed on coats of arms, divorced from practical concerns, and

transformed into emblems of identity. Jorg von Halspach, the architect of the

Church of Our Lady in Munich, is typical of many elevated craftsmen in this res-

pect. His epitaph, which stands against the west entrance of this church, prom-

inently displays his mark as the charge on his escutcheon.124 Adam Kraft’s in-

ventive tracery could likewise be associated with the artist beneath and functions

as a sort of trademark or badge of identity.

The potential use of inventive decorative motifs as personal or institutional

devices owed much to a gradual abatement in the use of heraldic imagery under

Burgundian and Hapsburg rulers: as Emmanuel Bourassin and others have re-

lated, traditional coats of arms depended on prohibitively complex rules and were

inconveniently inflexible. Although heraldry remained a critical language of

honour and territorial alliance for royalty and the high nobility, it slowly ceded

place to more fluid imprese, mottoes and other emblematic devices, signs more

readily adaptable to the changing role of the elite during this dynamic period,

and more easily tailored to individual needs.125 Often these supplementary in-

signia accompanied coats of arms; at other times they replaced them. On the

tomb of Margaret of Bourbon at Brou, for example, an angel supports a shield that



carries only the initials of Margaret of Austria and her late husband, Philibert of

Savoy, joined by a love knot.

With the atrophy of stable heraldic display, improvisation became more ac-

cepted, and tracery figures might be charged informally with associations of

office, status and possession. For whatever combination of factors, elaborate

geometric patterns were prominently imprinted on devotional space. The ques-

tion is not what such forms must have signified but rather what avenues of

thinking they would have supported for those attentive to devotional concerns.

Indeed, these carvings also appear on secular buildings, though they are far more

numerous in religious structures. It may be that the multivalence of this type of

design was necessary to permit its broad adoption. Devotional applications,

however, were especially promising.

It is likely that the printing press heightened sensitivity to geometric con-

figurations. Publishing not only spread knowledge of alternative traditions but

also encouraged a change in the way that the act of thinking was understood and

expressed. Scanning became an essential skill as the quantity of information

available increased dramatically, and greater attention was paid to the visual

presentation of texts because it facilitated their assimilation.126

Academics were more inclined to use diagrams when explaining the inter-

relationships between logical propositions. The complexity of these matrices and

the technical skill required to pen them legibly restricted their benefit in

1.18 Adam Kraft, Base of Tabernacle, Church of St Lawrence, Nuremberg, 1493–96. Photo: author.



1.19 Netherlandish artists, Nativity, Altarpiece of the Seven Joys of the Virgin, c. 1517.

Brou: St Nicolas de Tolentino. Photo: author.



manuscript, whereas printing nurtured the use and re-use of geometric designs,

as is found in the work of the first generation of post-Gutenberg writers. Spatial

organization became an ever more prevalent manner of conceptualization.127

The question of the individual, of creation and authority, inevitably relate to this

issue. Writing, composing, adapting, copying in scriptoria, publishing and editing

all helped determine the idea of the text, the process of reading and the model of

knowledge.128 Spatial and specifically geometric paradigms became increasingly

common.

By the second decade of the sixteenth century Late Gothic had become a

mode, a preference over an alternative Italianate manner. It may be argued that

the increasingly conspicuous presentation of geometric tracery was in part a

polemical assertion of local practice, a response to the waning power of a tradi-

tional symbolic language. At this time a register of this conflict is found in the

alabaster retable for Margaret of Austria’s church at Brou (see plate 1.15). The

Altarpiece of the Joys of the Virgin, its many episodes simultaneously apparent,

presents a spatial mapping of time that approximates a divine perspective; in the

mind of God all events occur in an eternal present.129 Such a transcendent order

is implied by the jube-like form that ascends within the lateral compartments.

This Gothic structure plays no role in the sacred story. It stands tall in each of the

figural scenes, unnoticed by the human actors and conflicting with the other

architectural props, which are foreshortened and clearly in an Italianate mode. In

the Nativity the ethereal frame emerging behind Joseph is given priority over the

antique triumphal arch to the right (plate 1.19). Italianate and Gothic forms co-

exist, a juxtaposition that reveals the Gothic to be transcendent and superior. In

the Adoration of the Magi the Gothic pier rises directly behind the seated Virgin

with no relationship to the Italianate building to the left. Recessed within the

shadows of the individual chambers, this cryptic superstructure unites the dis-

parate scenes while imputing purpose and authority to their sequence.130

As geometric designs appeared in easily visible, bounded and less conven-

tional sites, they were able to reinforce an immediate and sensory intuition of

transcendent authority. This development partly coincides with a period of self-

reflection on the part of Gothic designers, as Boucher and Crossley have defined it.

It leads up to a moment when Gothic decoration had become a mode, a language

of conscious choice, rather than an inevitable recourse. And it comes at a time

when numerous political and religious institutions were undergoing radical

change, and when the knowledge of possible alternatives to many unquestioned

matters was quickly disseminated through print. These geometric patterns show

how Gothic ornament of the late fifteenth and sixteenth centuries assisted in

interpreting larger and far more complicated structures, in mediating the ex-

perience of architecture.



Notes

1 Francois Bucher, ‘Fifteenth-century German

architecture, architects in transition’, in Ar-

tistes, artisans et production artistique au moyen

age, Colloque international, ed. Xavier Barral I

Altet, 3 vols, Paris, 1987, vol. 2, 416. Bucher,

insists that ‘the Gothic style began to lose its

patronage around 1500’, a situation that would

not arise for several decades.

2 J. Biazostocki, ‘Late Gothic: disagreements

about the concept’, Journal of the British Archae-

ological Association, 3rd series, 29, 1966, 76–105;

Ulrich Coenen, Die sp.atgotischen Werkmeis-

terb.ucher in Deutschland als Beitrag zur mittel-

.alterlichen Architekturtheorie, Aachen, 1989; U.

Germund, Konstruktion und Dekoration als Gestalt-

ungsprinzipien im sp.atgotischen Kirchenbau: Unter-

suchungen zur mittelrheinischen Sakralbaukunst,

Manuskripte zur Kunstwissenschaft in der

Wernerschen Verlagsgesellschaft, 53, Worms,

1997; F.-J. Sladeczek, ‘Was ist sp.at an der

Sp.atgotik? Von der Problematik der kunst-

geschichtlichen Stilbegriffe’, Unsere Kunst-

denkm.aler, 42, 1991, 3–23.

3 On the issue of period style, see L. Besserman,

The Challenge of Periodization: Old Paradigms and

New Perspectives, ed. L. Besserman, New York and

London, 1996, 3–27; K.-G. Faber, ‘Epoche und

Epochengrenzen in der Geschichtsschreibung’,

Zeitschrift f .ur Kunstgeschichte, 44, 1981, 105–13; M.

Gosebruch, ‘Epochenstile – historische Tat-

s.achlichikeit und Wandel des wissenschaftli-

chen Begriffs’, Zeitschrift f .ur Kunstgeschichte, 44,

1981, 9–14; F. Schalk, ‘ .Uber Epoche und Historie’,

in Studien zur Periodisierung und zum Epochen begriff,

eds H. Diller and F. Schalk, Akademie der Wis-

senschaft und deutschen Literatur in Mainz,

Abhandlung der Geistes- und Sozialwis-

senschaften, Mainz, 1972, no. 4, 12–38; R.

Suckale, ‘Die Unbrauchbarkeit der g.angigen

Stilbegriffe und Entwicklungsvorstellungen.

Am Beispiel der franzosischen gotischen Ar-

chitektur des 12. und 13. Jahrhunderts’, in Stil

und Epoche Periodisierungsfragen, eds F. Mobius

and H. Sciurie, Dresden, 1989, 231–50; G. Po-

chat, ‘Der Epochenbegriff und die Kunst-

geschichte’, in Kategorien und Methoden der

deutschen Kunstgeschichte 1900–1930, ed. L. Ditt-

mann, Stuttgart and Wiesbaden, 1985, 129–67.

4 In Prague, Hungary and Poland the juxtaposi-

tion of modes occurred earlier. Benedikt Ried’s

Italianate windows of 1493 decorate the ex-

terior of the Vladislav Hall in the Castle of

Prague, contemporary with the innovative

Gothic vaulting inside. See J. Biazostocki, The Art

of the Renaissance in Eastern Europe, Oxford, 1976,

15–16.

5 E.M. Kavaler, ‘Renaissance Gothic in the Neth-

erlands: the uses of ornament’, Art Bulletin, 86,

2000, 228–31; Larry Silver, ‘The ‘‘Gothic’’ Gos-

saert: Native and Traditional Elements in a

Mabuse Madonna’, Pantheon, 44, 1987, 58–69.

6 M. Durand and P. Bonnet-Laborderie, Senlis et

son Patrimonie: la ville en ses forets, Beauvais, 1995,

44. The south transept dates from the 1530s.

For a negative assessment of Pierre Chambi-

ges’s design for the south transept of Senlis, see

C. Wilson, The Gothic Cathedral: The Architecture of

the Great Church 1130–1530, London, 1990, 254–5.

For his Gothic work at Beauvais, see S. Murray,

Beauvais Cathedral: Architecture of Transcendence,

Princeton, 1989, 134–5; on Pierre Chambiges’s

Italianate contributions to Saint-Germain-en-

Laye and other chateaux for Francis I, see W.

Prinz and R.G. Kecks, Das franzosische Schloss der

Renaissance, Berlin, 1985, 108, 438–9, 456, 461–4.

7 Yves Bottineau-Fuchs, ‘Maıtre d’oeuvre, maıtre

d’ouvrage: les Le Roux et le chapitre cathedrale

de Rouen’, in Artistes, artisans et production ar-

tistique au moyen age, Colloque international, ed.

X. Barral I Altet, 3 vols, Paris, 1987, vol. 1, 183–

95; G. Lanfry, E. Chirol and J. Bailly, Le Tombeau

des Cardinaux d’Amboise, Rouen, 1959, 16–20;

Charles de Beaurepaire, ‘Les Architectes de

Rouen dans la premiere moitie du XVIe siecle’,

Bulletin des amis des monuments Rouenais, 1904,

119–30.

8 T. Rieger, ‘Bernard Nonnenmacher, Maitre

d’oeuvre de la Cathedrale de Strasbourg de

1519–1551, et l’introduction du style Re-

naissance dans l’architecture religieuse alsa-

cienne’, Bulletin de la cathedrale de Strasbourg, 22,

1996, 85–90.

9 H. Kiener in U. Thieme and F. Becker, eds, All-

gemeines Lexikon der bildenden K.unstler von der

Antike bis zur Gegenwart, vol. 16, Leipzig, 1923,

263–4; F.W. Fischer, ‘Die Stadtpfarrkirche zur

Schonen Unserer Lieben Frau’, in Ingolstadt –

die Herzogsstadt – die Universit.atsstadt – die Fes-

tung, eds T. M .uller, W. Reissm .uller and S. Hof-

mann, vol. 1, Ingolstadt, 1974, 345–9; H.-R.

Hitchcock, German Renaissance Architecture,

Princeton, 1981, 32–3.

10 G. Fehr, Benedikt Ried: Ein deutscher Baumeister

zwischen Gotik und Renaissance in Bohmen, Mu-

nich, 1961; Fehr, ‘Architektur der Sp.atgotik’, in

Gotik in Bohmen, ed. K. Swoboda, Munich, 1969,

329–31.

11 Bucher, ‘Fifteenth-Century German Architec-

ture’, 409–19; P. Crossley, ‘The Return to the

Forest: Natural Architecture and the German

Past in the Age of D .urer’, in K.unstlerischer Aus-

tausch: Artistic exchange, Akten des XXVIII Inter-



nationalen Kongresses f .ur Kunstgeschichte,

Berlin, 1993, vol. 2, 71–80.


ture’, 412: See also F. Bucher, ‘Medieval Archi-

tectural Design Methods, 800–1560’, Gesta, 11:

2, 1972, 44. Concerning the concentration on

geometric design on the part of Gothic de-

signers, he writes, ‘The style had entered its

defensive fifteenth-century phase with an al-

most hectic fireworks of forms directed against

the planar purity of Renaissance architecture.’

13 I refer here to regions that were either German-

speaking or strongly influenced by the culture

of such areas; I do not use the term in a poli-

tical sense. In addition to the present-day

nation of Germany, I include Austria, Alsace,

parts of Switzerland and Bohemia (which,

though culturally distinct, commonly impor-

ted architects from Germany). On questions of

cultural and national identity in Central Eur-

ope, see T. DaCosta Kaufmann, Court, Cloister

and City: The Art and Culture of Central Europe

1450–1800, Chicago, 1995, 16–21.

14 N. Nussbaum, German Gothic Church Architecture,

trans. S. Kleager, New Haven and London, 2000

(1985), 192–5. An emphasis on the development

of ‘unified space’ in German hall churches

dates back to Kurt Gerstenberg’s influential

thesis in Deutsche Sondergotik. Eine Untersuchung

.uber das Wesen der deutschen Baukunst im sp.aten

Mittelalter, Munich, 1913, 53–79, 127–31. Nuss-

baum offers an extended critique (157–61) of

Gerstenberg’s theories of vault construction.

15 W.H. Vroom, De Onze-Lieve-Vrouwekerk te Antwer-

pen. De financiering van de bouw tot de beelden-

storm, Antwerp and Amsterdam, 1983, 18–19; J.

van Brabant, Onze-Lieve-Vrouwkathedraal van An-

twerpen: Grootste gotische kerk der Nederlanden,

Antwerp, 1972.

16 R. Sanfacon, L’architecture flamboyante en France,

Laval, 1971, 176–9. Champagne was the one

region in France where hall churches are

prevalent. See R. Nenno, Die sp.atgotischen Hal-

lenkirchen in der S .udchampagne, St Ingbert, 1988.


ture’, 413–16.

18 Francois Cali, L’ordre flamboyant et son temps:

Essai sur le style gothique du XIVe au XVIe siecle,

Paris, 1967, 12–15, 154, illus. 27. The term ‘flam-

boyant’ and its association with flames date

from the seventeenth century. The facade of

Vendome was designed by Jean Tixier, the au-

thor of the spire of the north tower of Chartres

Cathedral.

19 Gerstenberg, Deutsche Sondergotik, 18–19.

20 Kavaler, ‘Renaissance Gothic in the Nether-

lands’, 233–9.

21 Nussbaum, German Gothic Church Architecture,

180–1, 188, 198; Nussbaum and S. Lepsky, Das

gotische Gewolbe. Eine Geschichte seiner Form und

Konstruktion, Munich and Berlin, 1999, 237–70.

22 F. Bucher, ‘The Medieval Architectural Module:

Generating and Ornamental Concept’, in World

Art: Themes of Unity in Diversity, ed. I. Lavin,

3 vols, London, 1989, vol. 1, 225.

23 Bucher, ‘Medieval Architectural Design Meth-

ods’, 48.

24 Bucher concludes his dismissal of sixteenth-

century German vaults with the comment:

‘The Renaissance was to reject these games

with a vengeance, very much as the Bauhaus

was to obliterate Art Nouveau.’ Bucher, ‘Med-

ieval architectural design methods’, 48. For a

discussion of ornament versus structure, see

A.-M. Sankovitch, ‘Structure/Ornament and the

modern figuration of architecture’, Art Bulletin,

80, 1998, 687–717.

25 See the English translation of Alois Riegl’s

fundamental study Problems of Style: Foundations

for a History of Ornament, trans. E. Kain, anno-

tated by David Castriota, Princeton, 1992, and

P. Crowther, ‘More than Ornament: The Sig-

nificance of Riegl’, Art History, 17, 1994, 482–94;

Oleg Grabar, The Mediation of Ornament, Prince-

ton, 1992.

26 Nussbaum, German Gothic Church Architecture,

156, 175, 185.

27 A. Bos, Les eglises flamboyantes de Paris: xve –xvie

siecles, Paris, 2003. Note expecially Saint-

Germain-l’Auxerrois, Saint-Gervais, Saint-Merry,

Saint-Medard and the nave of Saint-Nicolas-

Champs. This unadorned manner, neverthe-

less, permitted sophisticated treatment; to the

choir of the parish church of St Etienne at

Beauvais, the architect Martin Chambiges im-

parted to the piers a subtle undulating contour

that enlivens the interior without decorative

display. See Murray, Beauvais Cathedral, 137–42.

Related principles govern the elevation of sev-

eral parish churches in Troyes and neighbour-

ing southern Champagne; exemplary in this

respect is the choir of the church of St Jean-au-

Marche at Troyes (Murray, illus. 180). For a si-

milar sober style characterizing the parish

church of St.-Maclou in Rouen, see L. Neagley,

‘Elegant Simplicity: The Late Gothic plan de-

sign of St.-Maclou in Rouen’, Art Bulletin, 74,

1992, 395–422.

28 N. Hiscock, The Wise Master Builder: Platonic Geo-

metry in Plans of Medieval Abbeys and Cathedrals,

Aldershot, 2000; G. Strachan, Chartres: Sacred

Geometry, Sacred Space, Edinburgh, 2003; G. Les-

ser, Gothic Cathedrals and Sacred Geometry, 3 vols,

London, 1957, 1964; O. von Simson, The Gothic

Cathedral: Origins of Gothic Architecture and the

Medieval Concept of Order, Princeton, 1974 (1956),

13–42.



29 W. M .uller, Grundlagen gotischer Bautechnik: Ars

sine scientia nihil, Munich, 1990, 18–19. On the

development and distribution of paper in the

fifteenth century, see Lucien Febvre and Henri-

Jean Martin, The Coming of the Book: The Impact of

Printing 1450–1800, London, 1984 (1958), 37–43.

30 Bucher, ‘Design in Gothic Architecture’, 68–9.

31 In certain churches in Lower Austria, such as

Sankt Valentin and Krenstetten, the vaults ap-

pear to make a clean break with their supports.

Box-like ‘capitals’ that connect with the shell

grip the cylindrical piers like a carpenter’s vice,

obstructing any sense of visual continuity. See

G .unter Brucher, Gotische Baukunst in Osterreich,

Salzburg and Vienna, 1990, 200–203, 230–1.

32 On the structural function of ribs and the de-

velopment of figured vaults, see Nussbaum

and Lepsky, Das gotische Gewolbe, 60–8, 234–70;

Nussbaum, German Gothic Church Architecture,

150–1, 180–4, 195–216; J. Acland, Medieval Struc-

ture: The Gothic Vault, Toronto, 1972, 142–4. Star

and simple net vaults had been in use since the

fourteenth century, but complex figured

vaults, often using curvilinear ribs, were de-

veloped during the later fifteenth and six-

teenth centuries.

33 F. Bischoff, Burckhard Engelberg: ‘Der vilkun-

streiche architector und der Statt Augspurg Wercke

Meister’, Augsburg, 1999, 331–4; Nussbaum and

Lepsky, Das gotische Gewolbe, 249, 253–4; E.D.

Schmid, Nordlingen – die Georgskirche und St.

Salvator, Stuttgart and Aelen, 1977, 70–3; W.

Helmberger, Architektur und Baugeschichte der St.

Georgskirche zu Dinkelsb .uhl (1448–1499). Das

Hauptwerk der beiden sp.atgotischen Baumeister Ni-

claus Eseler, Vater und Sohn, Bamberg, 1984, 89–

98. The church of St George at Nordlingen was

begun in 1427 by Hans Felber and Hans Kun

under the direction of the well-respected Kon-

rad Henzelmann. The vaulting, constructed

1495–1505, by Weyrer, is in a way a more so-

phisticated development of the vaulting of the

church of St George at Dinkelsb .uhl, executed

by the younger Nikolaus Eseler during the

1490s. The elder Eseler, who began the church

at Dinkelsb .uhl, was also active at Nordlingen.

34 This protrusion of the ribs, resembling timber

construction, was employed by Burkhard En-

gelberg in the south aisle of the church of Sts

Ulrich and Afra in Augsburg. See Nussbaum

and Lepsky, Das gotische Gewolbe, 252–3. The

motif is also found in the aisles of the Church

of Our Lady at Ingolstadt.

35 A vault displaying a third distinct pattern, also

with double-curved ribs, supports the western

gallery.

36 The designs of vaults erected throughout the

German lands are recorded in drawings pre-

served in numerous collections and sketch-

books. See, for instance, H. Koepf, Die gotischen

Planrisse der Wiener Sammlungen, Vienna, 1969;

M .uller, ‘Einfl .usse der osterreichischen und der

bohmisch-s.achsischen Sp.atgotik in den Ge-

wolbemustern des Jacob Facht von Andernach’,

Wiener Jahrbuch f .ur Kunstgeschichte, 27, 1974, 65–

82. The Strasbourg architect Hans Hammer was

presumably one of many who travelled widely;

he is documented as having journeyed to

Hungary and seems to have visited additional

sites, for he records the designs of vaults from

Erfurt and other locations in his sketchbook.

Some of these drawings show vaults with

double-curved ribs, testimony to the early

knowledge of these designs in Alsace. See F.J.

Fuchs, ‘Introduction au ‘‘Musterbuch’’ de Hans

Hammer’, Bulletin de la cathedrale de Strasbourg,

20, 1992: 12, 52–3.

37 Brucher, Gotische Baukunst in Osterreich, 211;

Walther Buchowiecki, Die gotischen Kirchen Oster-

reichs, Vienna, 1952, 303. The vaulting scheme

comprises two parallel grids of circles and

squares. The choir, which is vaulted in stone

and reveals a less elaborate geometric figure,

dates from the end of the fifteenth century.

38 See M .uller, ‘ .uber die Grenzen der Interpre-

tierbarkeit sp.atgotischer Gewolbe’, 47–69;

M .uller, Grundlagen gotischer Bautechnik, 151–97,

233–40, 247, 257–77; M .uller, ‘An application of

generative aesthetics to German late Gothic rib

vaulting’, Leonardo, 11: 2, Spring, 1978, 107–110.

39 H. Korner, ‘Die ‘‘gestorte Form’’ in der Architek-

tur des sp.aten Mittelalters’, Festschrift f.ur Hart-

mut Biermann, eds C. Andreas, M. B .uckling and

R. Dorn, Weinheim, 1990, 75; Nussbaum and

Lepsky, Das gotische Gewolbe, 177–8; F. Bucher,

Architector, The Lodge Books and Sketchbooks of

Medieval Architects, vol. 1, New York, 1979, 197–9.

40 Koepf, Die gotischen Planrisse, no. 17091.

41 Korner, ‘Die ‘‘gestorte Form’’‘, 76. Drawing no.

17003 in the Vienna Akademie der bildenden

K .unsten is carefully finished but unsuitable as

a plan for construction. Koepf, Die gotischen

Planrisse, 24, illus. 115.

42 E. Schubert, L. Madersbacher, et al., Die Gotik,

Tiroler Ausstellungsstrassen, Milan, 1994, 128–9.

43 Schmid, Nordlingen, 73–4; Dehio, Handbuch der

Deutschen Kunstdenkm.aler, Bayern III: Schwaben,

773.

44 Schmid, Nordlingen, 75–7, Bischoff, Burckhard

Engelberg, 154. The west gallery was built be-

tween 1506 and 1508.

45 Bischoff, Burckhard Engelberg, 294–7. Bischoff

attributes the enclosure to Engelberg himself.

46 In Strasbourg, the gallery, designed by Hans

Hammer, faces the Angels’ Pier in the south

transept of the cathedral. Hans Reinhardt, La

Cathedrale de Strasbourg, Paris, 1972, 143. The

balustrade probably dates from about 1486. For



Hammer’s drawings for the balustrade, see

Fuchs, ‘Introduction au ‘‘Musterbuch’’‘, 61–3. A

similar balustrade of geometric openwork once

faced the organ tribune. In the Cathedral of

Freiburg, up-to-date galleries decorate the in-

terior of the west facade. On the refitting of

older French churches with Late Gothic orna-

mental patterns, see P. Kurmann, ‘A propos des

restaurations effectuees sur les cathedrals go-

thiques a la fin du moyen age’, Annales d’historie

d’Art et d’Archeologie, 25, 2003, 19, 26–9.

47 C. Gufler, Die Pfarrkirche Maria Himmelfahrt in

Niederlana, Laurin Kunstf .uhrer, no. 108, Bozen,

1997, 14–21. The church in Niederlana was built

principally between 1483 and 1492, probably by

Hans Hueber. The parish was wealthy enough

to purchase in 1502 an extraordinary carved

retable from Hans Schnatterpeck of Meran, for

which Leonhard Sch.auffelein painted the outer

wings. See Herbert Schindler, Der Schnitzaltar:

Meisterwerke und Meister in S.uddeutschland, Oster-

reich und S.udtirol, Regensburg, 1978, 125–33.

48 J. Julier, Studien zur sp.atgotischen Baukunst am

Oberrhein, Heidelberg, 1978, 190–1, and criti-

cism by M .uller, ‘ .uber die Grenzen der Inter-

pretierbarkeit sp.atgotischer Gewolbe’, 49–51.

49 Kavaler, ‘Renaissance Gothic in the Nether-

lands’, 240–1. These formal jeux develop as

puzzles the ambiguities inherent in geometric

construction. In the music of the time there

seem to be associated developments, for John

Tucke lists in his contemporary musical trea-

tise the term ambigua, which is defined as the

substitution of a longer tone for a shorter one

or vice versa with consequent rhythmic ambi-

guity. Although the technique is observable in

a number of compositions, the word is not

known in other music treatises, suggesting its

recent coinage and an incipient self-conscious

attention to its principles. See R. Woodley, John

Tucke: A Case Study in Early Tudor Music Theory,

Oxford, 1993, 98–9

50 See Eugene Clasby’s introduction to Guillaume

de Deguileville, The Pilgrimage of Human Life (Le

Pelerinage de la vie humaine), ed. and trans. E.

Clasby, Garland Library of Medieval Literature,

series B, vol. 76, New York and London, 1992, xv.

In literature and music, there are the puzzle-

balades and puzzle-canons of the late fifteenth

and sixteenth centuries, artistic compositions

permitting reconstitution in numerous ways.

See Kavaler, ‘Renaissance Gothic in the Neth-

erlands’, 238–41; J. Beck, ‘Formalism and vir-

tuosity: Franco-Burgundian poetry, music, and

visual art, 1470–1520’, Critical Inquiry, 10, 1984,

646.

51 Origen and Cassiodorus were also prominent

among writers who interpreted geometry as a

divinely ordained cognitive instrument. See

Hiscock, The Wise Master Builder, 114; E.A. Zait-

sev, ‘The meaning of early medieval geometry

from Euclid and surveyors’ manuals to Chris-

tian Philosophy’, Isis, 90, 1999, 530. In De ordine,

Augustine states: ‘From here on [reason] ad-

vanced to the power of eyes, and while con-

templating the Earth and the Sky, it felt that it

liked only the beauty; and in the beauty, the

forms; in the forms, the measures; in the

measures, the numbers. And it scrutinized in

itself whether there existed such a line or

roundness, such a form or figure that corre-

sponded to what the reason contained in itself.

In what the eyes saw it found nothing com-

parable to what the intellect itself conceived.

And these distinct and orderly [forms] it

transmitted to a discipline, which it called

geometry.’ See Augustine, De ordine, 2.15.42, in

Corpus Christianorum, series Latina, vol. 29,

Turnhout, 1970, 130. I borrow Zaitsev’s trans-

lation. This passage was further incorporated

in the Institutiones of Cassiodorus. See Cassiodori

Senatoris Institutiones, ed. R.A.B. Mynors, Oxford,

1937, xxx–xxxi. Cassiodorus remained current

in the fifteenth century, less, though, through

his Institutiones that through his Historia eccle-

siastica tripartite, which was published at Augs-

burg, Cologne, Strasbourg and Paris before

1500. On the later medieval reception of Boe-

thius, see H. Patch, The Tradition of Boethius: a

Study of His Importance in Medieval Culture, New

York, 1935; D. Pingree, ‘Boethius, Geometry

and Astronomy’, in Boethius: His Life, Thought and

Influence, ed. M.T. Gibson, Oxford, 1981, 155–66.

52 The Greek platonists had judged the universe

to be divided into three levels. The upper re-

gion contained solely eternal ideas, whereas

the lower held the changeable matter of the

natural world. The middle level, however,

comprised mathematical and especially geo-

metric forms, a register of communication be-

tween perfect concepts and imperfect natural

objects. A fragment from an early commentary

on Euclid states that ‘Euclid’s intention is

twofold: aimed at the pupil and the nature of

things. . . . At the nature of things, since it is

known that the science of nature and the

splendid learning of Timaeus or Plato demon-

strate geometrically.’ Zaitsev, ‘The meaning of

early medieval geometry’, 522–3, 530–1. In the

De opiticio mundi Philo discusses how God first

made a world of perfect ideas, which he used as

a pattern for the imperfect material world. See

J. Block Freedman, ‘The architect’s compass in

creation miniatures of the later middle ages’,

Traditio, 30, 1974, 424–5; Philo, trans. F.H. Col-

son and G.H. Whitaker, Cambridge, Mass., 1962,

I.iv. 17–20: ‘[God] brought to completion a

world discernible only by the mind, and, with



that for a pattern, the world which our senses

can perceive.’

53 It was probably through other texts, however,

that the idea reached the later Middle Ages.

The passage in the Timaeus describing the gen-

eration of the four elements through regular

triangles was not taken up in Calcidius’s

translation, the principal version of Plato’s text

available until the late fifteenth century. Cal-

cidius’s commentary did treat in distinctly

geometric terms Plato’s notion of the chora, a

preexistent place for things to be created that

allowed the embodiment of ideas. The platonic

interpretation of geometry is fully present,

however, in Proclus’s commentary on Euclid, In

primum Euclidis, definitions 26–9, 166–7: ‘The

Pythagoreans assert that the triangle is the

ultimate source of generation . . . Consequently

the Timaeus says that the ideas of natural sci-

ence, those used in the construction of the

cosmic elements are triangles. . . .’ Even better

known was Aristotle’s reference to Platonic

theory in De caelo, whereas Cassiodorus ex-

plicitly presents geometry as a divine instru-

ment of creation in his Institutiones: ‘. . . for, if

one be permitted to say so, the Holy Trinity

employs geometry when it grants various spe-

cies and forms to its creatures which it has

even now caused to exist; when with venerable

power it apportions the courses of the stars and

causes those which are movable to pass swiftly

along established paths and sets in a definite

position those which are fixed. Whatever is

well ordered and complete can be attributed to

the properties of this science.’ The passage en-

joyed considerable popularity and was in-

cluded by Rhabanus Maurus in the chapter on

geometry in his De institutione clericorum and in

certain other early medieval geometries. See

Aristotle, De caelo, 279 B 33; Cassiodorus, In-

troduction to Divine and Human Readings, trans.

Leslie Webber Jones, New York, 1946, 197;

Zaitsev, ‘The meaning of early medieval geo-

metry’, 540–1; Hiscock, The Wise Master Builder,

115–6. For Cassiodorus, see further B. Bennett,

‘Cassiodorus’, in Dictionary of the Middle Ages,

vol. 3, 1983, 123–4. For philosophical concepts

of place in the Middle Ages and its geometric

determinants, see Zaitsev (545–6), who surveys

the pertinent writings of Macrobius, Boethius

and Scotus Eriugina. On the survival of pla-

tonism in the Middle Ages, see M.T. Gibson,

‘The Study of the Timaeus in the Eleventh and

Twelfth Centuries’, Pensamiento, 25, 1969, 183–

94; R. Klibansky, The Continuity of the Platonic

Tradition during the Middle Ages, Supplement,

Plato’s Parmenides in the Middle Ages and the Re-

naissance: A Chapter in the History of Platonic Stu-

dies, London, 1981; P.G. Ruggiers, ‘Platonic

Forms in Chaucer’, Chaucer Review, 17, 1983,

366–81 Klibansky (28) notes that manuscripts

of Calcidius’s translation of the Timaeus were in

all important medieval libraries. Paul Frankl

goes so far as to assert that ‘Plato sanctified the

equilateral triangle and the square . . . The

medieval esthetic, insofar as it was based on

Plato, took over this identification.’ See Frankl,

‘The secret of the medieval masons’, Art Bulle-

tin, 28, 1945, 58.

54 Alan of Lille, Theologicae regulae, no. 31. Several

of Alan’s works were published in many edi-

tions before and slightly after 1500; the Regulae

appeared in 1492 at Basel from the press of

Jacob Wolff of Pforzheim. See E. J. Butterworth,

‘Form and significance of the sphere in Nicho-

las of Cusa’s De ludo globi’, in Nicholas of Cusa: In

Search of God and Wisdom, Essays in Honor of

Morimichi Watanabe by the American Cusanus

Society, eds G. Christianson and T. Mizbicki,

Leiden, 1991, 89–90; F. Hudry, ‘Introduction’, in

Alain de Lille, Regles de theologie suivi de sermon

sur la sphere intelligible, Paris, 1995, 7–80; Jean

Jolivet, ‘Remarques sur les Regulae Theologicae

d’Alain de Lille’, in Alain de Lille, Gautier de

Chatillon, Jakemart Gielee et leur temps, eds H.

Roussel and F. Suard, Lille, 1980, 83–99. Alan of

Lille strongly influenced Chaucer, who refers

explicitly to Alan’s Anticlaudianus in The House of

Fame (II.985-90).

55 The cosmology of the Timaeus is reflected in

Proclus’s commentary on Euclid, revived in the

fifteenth century, as it is in several sixteenth-

century tracts, such as Wenzel Jamnitzer’s Per-

spectiva Corporum Regularium of 1568, which

mentions the Timaeus in its complete title.

See Wenzel Jamnizer, Perspective corporum reg-

ularium das is ein fleissige f.urweisung wie di f.unff

Regulirten Corper, darvon Plato in Timaeo und Eu-

clides inn sein Elementis schribt, Nuremberg, 1568,

M. J. Kemp, ‘Geometrical bodies as exemplary

forms in Renaissance space’, in World Art:

Themes of Unity in Diversity, ed. I. Lavin, 3 vols,

London, 1989, vol. 1, 238–9. For Proclus’s dis-

cussion of geometry as an expression of divi-

nity, see Proclus, A Commentary on the First Book

of Euclid’s Elements, trans. G.R. Morrow, Prince-

ton, 1970, 16; Hiscock, The Wise Master Builder,

115. On the neoplatonic resonances in Proclus’s

commentary on Euclid, see J. Mueller, ‘Mathe-

matics and philosophy in Proclus’ Commen-

tary on Book I of Euclid’s Elements’, in Proclus:

lecteur et interprete des anciens, actes du colloque

international du CNRS, Paris, October 2–4,

1985, eds J. Pepin and H.D. Saffrey, Paris, 1987,

305–318. On interest in Proclus during the fif-

teenth and sixteenth centuries, see Paul Oskar

Kristeller, ‘Proclus as a reader of Plato and

Plotinus, and his influence in the middle ages

and in the Renaissance’, in Proclus: lecteur et in-

terprete des anciens, 191–211.



56 N. Cusanus, Of Learned Ignorance, trans. G.

Heron, with an introduction by J.B. Hawkins,

New York, 1954, book. 1, chap. 21, 46. On Ke-

pler’s admiration of Nicholas of Cusa for his

mystical elaborations on geometry, see F. Hal-

lyn, The Poetic Structure of the World: Copernicus

and Kepler, New York, 1993, 175–8. Nicholas’s

works were published in a reliable edition by

Martin Flach at Strasbourg in 1488.

57 Nicholas of Cusa, Of Learned Ignorance, book. 2,

chap. 13, 118–19: ‘With arithmetic He adjusted

it into unity, with geometry He gave it a ba-

lanced design upon which depends its stability

and its power of controlled movement: with

music He allotted its parts . . . God has set up

the elements in an admirable order, for He

created all things in number, weight and

measure. Number appertains to arithmetic,

weight to music and measure to geometry.’

Nicholas further insists that ‘mathematics are

a very great help in the understanding of dif-

ferent divine truths.’ By mathematics, he

meant primarily geometry. In order to reach

the divine and infinite ‘absolute maximum’, it

was necessary to deal with ‘finite mathema-

tical figures’. See Nicholas of Cusa, Of Learned

Ignorance, book 1, chap. 11, 26. He continues: ‘. . .

Boethius, the most learned of Romans, went so

far as to say that knowledge of things divine

was impossible without some knowledge of

mathematics.’ He elaborates further: ‘In so far

as they have followed him [Pythagoras], the

platonists and the chief of our own philoso-

phers, like Augustine and later Boethius, have

not hesitated to assert that number was the

essential exemplar in the mind of the Creator

of all things to be created.’ On the importance

of Greek mathematics and platonic literature

in the work of Nicholas of Cusa, see Ernst

Hoffmann, Cusanus-Studien, I, Das Universum des

Nikolaus von Cues, Sitzungsberichte der Hei-

delberger Akademie der Wisserschaften, Phi-

losophish-historische Klasse, 3, 1929–30, 5–34.

58 Nicholas of Cusa, Of Learned Ignorance, book 1,

chap. 23, 51.


chap. 23, 52–3.

60 Charles de Bovelles, Le Livre du sage, ed. and

trans. P. Magnard, Paris, 1982, 198.

61 There exist several fifteenth-century manu-

script editions of this work. See, for instance,

ms. germ. fol. 624, Berlin, Staatsbibliothek zu

Berlin, Preubischer Kulturbesitz. The text was

published repeatedly in the fifteenth and early

sixteenth centuries. A Spanish translation, El

pelegrino dela vida humana, was printed at Tou-

louse in 1490 by Heinrich Mayer. In addition,

French editions were issued at Paris by Bertold

Rembolt and Jean Petit (1500 and 1515) and

Antoine Verard (1511). See also E. Steiner, Doc-

umentary Culture and the Making of Medieval Eng-

lish Literature, Cambridge, 2003, 20.

62 De Deguileville, The Pilgrimage of Human Life,

34–5, v. 2512–79.

63 H. Junecke, Die wohlbemessene Ordnung, Patha-

gorieische Proportionen in der Historischen Archi-

tektur, Berlin, 1982; Hallyn, The Poetic Structure of

the World, 21, 57, 173. Plato’s understanding of

cosmological harmony in music in the Timaeus

was important for Augustine, who posits a si-

milar interpretation in book six of De musica.

Boethius likewise conceived of music as a

measure of divine order in his own treatise, De

musica, which endured as an authoritive text

until the Renaissance. See Hiscock, The Wise

Master Builder, 65, 77–8. For Nicholas of Cusa’s

reference to music as a measure of divine har-

mony, see Of Learned Ignorance, book 2, chap. 1,

68: ‘Consequently the most perfect, faultless

harmony cannot be perceived by the ear, for it

exists not in things sensible but only as an

ideal conceived by the mind. From this we can

form some idea of the most perfect or infinite

harmony, which is a relation in equality. No

man can hear it while still in the body, for it is

wholly spiritual and would draw to itself the

essence of the soul, as infinite light would at-

tract all light to itself. Such infinitely perfect

harmony, in consequence, would be heard only

in ecstasy by the ear of the intellect, once the

soul was free from the things of sense.’

64 Several miniatures from the fourteenth and

fifteenth centuries demonstrate the continu-

ing relevance of this notion for the late Middle

Ages. Again, the Timaeus underlies much of this

imagery in suggesting the picture of God im-

posing form on inchoate matter. But there

were also biblical passages that would have

strengthened this notion in the mind of med-

ieval readers, such as the well-known verse

from the Wisdom of Solomon (11:21) that re-

lates God’s creative process in the following

terms: ‘Thou hath disposed everything accord-

ing to measure, number, and weight.’ The fifth-

century theologian Apponius explicitly related

the passage to geometry in his commentary on

the Song of Songs: ‘The discipline of the geo-

metrical and arithmetical art teaches that ev-

ery creature is built according to measure and

number.’ See Freedman, ‘The Architect’s Com-

pass’, 419–24; J. E. Murdoch, Album of Science:

Antiquity and the Middle Ages, New York, 1984,

330; E. Panofsky and F. Saxl, D.urer’s ‘Melancholia

I’: Eine quellen- und typengeschichtliche Unter-

suchtung, Leipzig and Berlin, 1923, 67–70; Zait-

sev, The Meaning of Early Medieval Geometry, 536.

65 Nicholas of Cusa, The Layman on Wisdom and the

Mind, trans. with an introduction by M.L.

F .uhrer, Ottawa, 1989, 103. Plato and Boethius



are cited by name in this work (65–7, 89). See,

too, Of Learned Ignorance, book 3, chap. 110, 58:

‘An intelligence is above time and unsubjected

to temporal corruption, for by its nature it

embraces within itself incorruptible forms.

Such, for example, are the abstractions of

mathematics – and even of physical things,

which the mind buries in itself and readily

transforms into abstractions or spiritual reali-

ties. All this is to us an indication of the mind’s

own incorruptibility, for the habitat and nat-

ural container of incorruptible things must

itself be incorruptible. Now this intellect has a

natural movement towards the most abstract

truth as being the end of all its desires and its

final and most delectable object. Now this ul-

timate object is in all things, for it is God; and

the immortal and incorruptible human in-

telligence is insatiable till it attains him, for it

is satisfied only with an eternal object.’ A si-

milar notion of the division between material

objects and divine ideas is expressed by Charles

de Bovelles, who writes of ‘the perceptible signs

that make known the divine and most high

trinity’, Le Livre du sage, 191.

66 Nicholas of Cusa, De ludo globi, in N. von Kues,

Philosophisch-theologische Schriften, ed. L. Gabriel,

trans. with commentary by D. and W. Dupre,

Vienna, 3 vols, 1964, vol. 3, 231. Boethius had

expressed a similar distinction between a

higher world of ideas and lower material realm

in De arithmetica (II.31): ‘Thus it is known to us,

that just as it is in this matter, so in the world

are things joined together. Either things are of

the same immutable proper substance, as are

God, the soul, or the mind, or whatever is

blessed with incorporality by its own nature, or

they are of a variable and mutable nature,

which we undoubtedly see is the case in cor-

poreal things.’ See Hiscock, The Wise Master

Builder, 87.

This use of geometry as a concentrated sign

of the higher realm of divine thought is in

keeping with the views of earlier writers such

as the popular Dionysius the Pseudo-Areopa-

gite, whose works were extensively published

with commentaries in the late fifteenth and

sixteenth centuries. In De ecclesiastica hierarchia

(2.III.2) Dionysius typically insists that ‘sacred

symbols are actually the perceptible tokens of

the conceptual things.’ In De coelesti hierarchia

(1.3) he explains, ‘He revealed all this to us in

the sacred pictures of the scriptures so that he

might lift us in spirit up through the percep-

tible to the conceptual, from sacred shapes and

symbols to the simple peaks of the hierarchies

of heaven.’ See Hiscock, The Wise Master Builder,

123. De caelesti hierarchia and De ecclesiastica

hierarchia were published separately in Paris

(1498 and 1515) and Strasbourg (1502). Editions

of collected works containing these treatises

were published at Bruges (c. 1478), Paris (1498

and 1515), Strasbourg (1502 and 1503) and Basel

(1539). The Latin translation is generally that of

Ambrose the Camaldule from the early fif-

teenth century, though in northern Europe

Marcilio Ficino’s newer translation was issued

at Strasbourg in 1503. Commentaries by such

notables as Jacques Lefevre d’Etaples and Ju-

docus Clichtoveus accompanied Dionysius’s

texts.

67 M. Baxandall, The Limewood Sculptors of Renais-

sance Germany, New Haven and London, 1980,

252–4, plate 13.

68 Augustine, De quantitae animae, 12:19, Corpus

Scriptorum Ecclesiasticorum Latinorum, 89,

section 1, part 4, Vienna, 1986, 154:10–13; Cal-

cidius, In Timaeum, ed. J.H. Waszink, Corpus

Platonicum Medii Aevis, Plato Latinus, 4, Lon-

don and Leiden, 1962, 25:20–26:23; Zaitsev,

‘The meaning of early medieval geometry’, 529.

Cicero praised the sphere and circle as the

most perfect and beautiful forms in De natura

deorum, one of Petrarch’s favourite books,

which was frequently printed in the fifteenth

century. See Cicero, The Nature of the Gods, trans.

with an introduction by P.G. Walsh, Oxford,

1997, xlii, I: 63–4, II: 47–9.


chap. 21, 46; chap. 23, 51. For Nicholas’s refer-

ences to the circle and sphere as divine forms

of the cosmos, see H. Lawrence Bond, ‘The

journey of the soul to body in Nicholas of Cu-

sa’s De ludo globi’, in Nicholas of Cusa: In Search of

God and Wisdom, 81–3.


chap. 11, 108–10.

71 Nicholas of Cusa, De ludo globi, vol. 3, book 2,

294–5; Bond, ‘The Journey of the Soul to Body’,

81–2. The idea is taken by Nicholas from earlier

theological treatises such as the Liber XXIV

Philosophorum. See Clemens Baeumker, Beitr.age

zur Geschichte der Philosophie und Theologie des

Mittelalters, 25 (1928), 208. The tradition of

sacred association with the circle is set out in

Georges Poulet, The Metamorphosis of the Circle,

Baltimore, 1966, xi–xxvii; Freedman, ‘The Ar-

chitect’s Compass’, 421.

72 First published in Latin at Basel in 1470, and

printed in numerous Latin and vernacular

editions into the seventeenth century.

73 Bartholomaeus Anglicus, De proprietatibus re-

rum, Westminster, c. 1495, chap. 10, sig. 8-recto:

‘Thenne as Marcianus sayth, the worlde is

an unyversall gaderynge togider of thynges

whiche ben made.and all rou[n]de as it were a

spere other a belle. For the utter partye of the

worlde hathe shape and liknesse of a spere & of

a cercle. And as Marcianus sayth there was noo



shape neyther lkyeness so covenable to the

worlde as a rounde lykness and shape.and that

for perfeccyon of all thynges. And for the ly-

kenesse that the worlde hath in everlastinge

beynge with his werker that is wythoute ende

and without begynnynge.’ Plato’s Timaeus is

mentioned by name at the end of this passage,

which treats God’s imparting form to inchoate

matter. Martianus Capellus’s De Nuptiis Mercurii

et Philologiae was one of the most popular Latin

texts on logic during the Middle Ages. See

Hiscock, The Wise Master Builder, 62.

74 Bartholomaeus Anglicus, De proprietatibus re-

rum, Frankfurt, 1601, book 19, chap. 127, 1235:

‘universitatis etiam conditor, scilicet Deus in

circulo designator.’ See Freedman, ‘The Archi-

tect’s Compass’, 421.

75 Barbara Baum .uller, Bogenripper- und Schlin-

grippengewolbe der Sp.atgotik in Bayern und Os-

terreich, Munich, 1989.

76 Numerous vaults using double-curved ribs

were constructed in the German lands. The

choir of the Church of St James at Wasserburg,

an early instance from around 1450, has ribs of

stucco that inscribe large circles in the crown

of the vaults. Well-known examples of masonry

vaults of this type are found in churches in

Annaberg and Chemnitz in Saxony; Kutna Hora

and Most in Bohemia; Nuremberg (formerly

the Augustinerkirche) and Passau in Bavaria;

Freistadt, Weistrach and Konigswiesen in

Lower Austria, and Cologne in the Lower Rhi-

neland (the sacristy to the Carthusian Church

of St Barbara). See Nussbaum and Lepsky, Das

gotische Gewolbe, 259–68; Hiltrud Kier, Gotik in

Koln, Cologne, 1997, 31–4.

77 Spanish vaults with curvilinear ribs are found

in Salamanca (the New Cathedral and espe-

cially San Esteban), Zaragoza, Jaca and many

other cities. See Nussbaum and Lepsky, Das go-

tische Gewolbe, 299–307.

78 Though much less common than in Germany,

these vaults are found, for instance, over the

crossing of the Church of St Jean at Chaumont,

in the Chapel of the Virgin in the Parisian

church of St Germain-l’Auxerrois, in the Chapel

of Notre-Dame-les-Joies in Noyen Cathedral,

and in various smaller chapels at Senlis and

Beauvais. See H. Zerner, L’Art de la Renaissance en

France: L’invention du classicisme, Paris, 1996, 44;

A. Bos, Les eglises flamboyantes de Paris: xve -xvie

siecles, Paris, 2003, 111, 171; C. Wilson, The Gothic

Cathedral, 257. In Alsace, they are found in the

Chapel of St Catherine in Strasbourg Cathe-

dral, the Church of Saint Jean at Wissembourg,

the Chapel of St Adelaıde de Seltz and the

Mount of Olives behind the collegiate church

of Saverne. See Rieger, ‘Bernard Nonnen-

macher’, 86–7; C. Grodecki, ‘La galerie du Mont

des Oliviers et la Bibliotheque de l’eveque

Guillaume de Honstein a Saverne (1539–1541)’,

Bulletin de la Societe d’Histoire et d’archeologie de

Saverne, 77, 1972, 1–8.

79 The vault of the nave of St Barbara at Kutna

Hora was designed by Benedikt Ried and begun

in 1512. Ried modified the basilican plan, rais-

ing the aisles above the side galleries and

uniting them with the nave. The vaulting at

Annaberg was constructed between 1517 and

1525. See Fehr, Benedikt Ried, 1961, 36–40;

Nussbaum, German Gothic Church Architecture,

210–15; Nussbaum and Lepsky, Das gotische Ge-

wolbe, 262–5. In Austria incomplete circular

forms characterize the vault designs: for in-

stance, at Weistrach and Konigswiesen.

80 Rieger, ‘Bernard Nonnenmacher’, 85–7. The

vaults were begun in 1542 and completed by

1546. For the drawing for the vaulting, a ‘pla-

cement plan’, see Bucher, ‘Design in Gothic

architecture’, 62–3.

81 Sculpted stars are affixed to the vaults of the

ambulatory of Cologne Cathedral, for instance,

and painted gold stars on a blue background

decorate the vaults of the upper church of St

Chapelle in Paris. See Nussbaum and Lepsky,

Das gotische Gewolbe, 164–5.

82 W. Leedy, Fan Vaulting: A Study of Form, Technol-

ogy, and Meaning, London, 1980, 33–4. Leedy

suggests a similar cosmological interpretation

for the circular patterns of English fan vault-

ing, first constructed in the fourteenth century

but significantly revived during the late fif-

teenth and sixteenth centuries.

83 Bucher, ‘Medieval architectural design meth-

ods’, 47–8; Nussbaum and Lepsky, Das gotische

Gewolbe, 317. Complete circles are also inscribed

in church vaults at Bad Wimpfen am Berg and

in the sacristy of the church at Annaberg.

84 Charles de Bovelles, Le Livre du sage, 5, 155.

85 Nicholas of Cusa, Of Learned Ignorance, chap. 11,

25: ‘All our greatest philosophers and theolo-

gians unanimously assert that the visible uni-

verse is a faithful reflection of the invisible,

and that from creatures we can rise to a

knowledge of the Creator, ‘‘in a mirror and in a

dark manner’’, as it were.’

86 Kavaler, ‘The Jube of Mons and the Renaissance

in the Netherlands’, Netherlands Art Historical

Yearbook, 45, 1994, 359, illus. 11. Bellegambe’s

triptych is in Berlin: Staatliche Museen zu

Berlin, PreuXischer Kulturbesitz, Gem.alde-

galerie, inv. no. 641.

87 L. Schultes in Geschichte der Bildende Kunst in Os-

terreich. III, Sp.atmittelalter und Renaissance, ed. A.

Rosenauer, Munich, 2003, 341, no. 123. The

epitaph, of Salzburg provenance, has been at-

tributed to Hans Valkenauer and was originally



in the interior of the church. The relief is dated

c. 1511.

88 The intersection of the semi-circles might sug-

gest the action of crowning Mary, as, in both

cases, there is a merging of distinct entities.

89 M. Carruthers, The Craft of Thought, Meditation,

Rhetoric, and the Making of Images, 400–1200, New

York and Cambridge, 1998, 202–204, 227–31,

254–70.

90 De Deguileville, The Pilgrimage of Human Life,

34–5.

91 T.W. Adorno, .Asthetische Theorie, Frankfurt, 1993,

114: ‘Denn in Kunst wird das Entgleitende ob-

jecktiviert und zur Dauer zitiert.’

92 For Adorno, art allows us to seize the sig-

nificant insight, that truth that would other-

wise be lost among the multitude of references

evoked. Artistic truth must encompass both the

acknowledgement of irreconcilable antagon-

ism in the world and the paradoxical tendency

towards a utopian reconciliation. This is a po-

tential that is realized by the viewer. Albrecht

Wellmer, attempting to demystify Adorno’s

writing, focuses on truth in art as a perceptual

effect rather than its being an intrinsic quality.

For Wellmer, aesthetic truth can only be me-

taphorical. It arises from the simultaneous re-

ception of the art work as a symbolic construct

with internal criteria of aesthetic validity, and

as an object of experience which is judged ac-

cording to non-metaphorical categories of

truth. According to this model, the observer

must perceive some essence of reality in the

work of art while simultaneously viewing the

work as reality showing itself through this

medium. Yet because the revelation is part re-

cognition, it must confirm something pre-

viously known. As Wellmer argues, ‘We can

only recognize the ‘‘essence’’ which ‘‘appears’’

in the apparition if we already know the es-

sence as something which does not appear.’ A

perceived structural similarity between the

known idea and its manifestation as art work, a

like relationship between parts and the whole,

would account for this identity, despite the

radically different ways in which the two are

expressed. See Adorno, 182–7, 251; Albrecht

Wellmer, ‘Adorno’s Aesthetic Redemption of

Modernity’, Telos, 62, 1984–5, 92, 105–109; T.

Huhn, ‘Adorno’s Aesthetics of Illusion’, Journal

of Aesthetics and Art Criticism, 44, 1985–86, 181–9;

L. Zuidervaart, Adorno’s Aesthetic Theory. The Re-

demption of Illusion, Cambridge, Mass., 1991,

288–9; C. Norris, ‘Utopian Deconstruction:

Ernst Bloch, Paul de Man and the politics of

music’, in Music and the Politics of Culture, ed.

Christopher Norris, New York, 1989, 333–4.

93 Narrative readings are not limited to religious

edifices; the running decoration on secular

buildings, such as the town hall in Ghent, is

transformed at significant sites; the progress of

passers by establishes expectations of con-

tinuity that are either met or denied. In this

respect, there is a relationship with the tem-

poral appreciation of musical melody See L.

Meyer, Emotion and Meaning in Music, Chicago,

1956, 88–127; Kavaler, ‘Renaissance Gothic in

the Netherlands’, 234–7.

94 See Michael Fried’s discussion of the abstract

sculpture of Anthony Caro, which, despite its

non-representational nature, conveys some-

thing of the human body, movement and lan-

guage of gesture through its ‘syntax’. Michael

Fried, Art and Objecthood, Chicago and London,

1998, 28–30, 161–2.

95 The fundamental studies on narrative by

Propp, Levi-Strauss and Greimas have been

helpful in suggesting patterns of response to

non-representational carving, as have investi-

gations into the semiotics and ideology of

music, notably J.-J. Nattiez, Music and Discourse.

Toward a Semiology of Music, trans. C. Abbate,

Princeton, 1990; F. Escal, Espaces sociaux, espaces

musicaux, Paris, 1979; Celestin Deliege, Invention

musicale et ideologies, Paris, 1986; Norris, ‘Uto-

pian Deconstruction’, 305–37; A. Williams,

‘Music as immanent critique: stasis and devel-

opment in the music of Ligeti’, in Music and the

Politics of Culture, 187–225. On the history of

interpretation of Gothic architecture, see Paul

Crossley, ‘Medieval architecture and meaning:

the limits of iconography’, Burlington Magazine,

130, 1988, 116–21.

96 Hayden White, Metahistory: The Historical Imagi-

nation in Nineteenth-Century Europe, Baltimore,

1973, 1–42.

97 Jean Pepin, ‘L’Hermeneutique ancienne’, Poe-

tique, 23, 1975, 291–300; E. Vance, ‘Pas de Trois’,

in Interpretation of Narrative, eds M. J. Valdes and

O. J. Miller, Toronto, 1978, 122–34; The Parisiana

Poetria of John of Garland, ed. and trans. T. Lawler,

Yale Studies in English, vol. 182, New Haven,

1974, 101.

98 Many carved altarpieces from Antwerp and

Brussels, for instance, are commonly bi-axial.

Here the hierarchic order is displayed verti-

cally, while the narrative sequence is shown

horizontally.

99 This is also true for other potentially narrative

arrangements. At Beauvais, for example, Mar-

tin Chambiges designed bells, trefoils and

groups of mouchettes and souflets to be steadily

transformed as they ascend the facade. See

Murray, Beauvais Cathedral, 135–6; C. Wilson, The

Gothic Cathedral, 252–6.

100 Vladimir Propp, Morphology of the Folktale, trans.

L. Scott, Austin, 1990, 25–8, 35–6, 42–52, 84–6,

92. The conflict can take the form of an ab-



sence, interdiction, or violation of an inter-

diction, for instance. Lack or desire and trans-

ference by means of a donor are among the

‘moves’ that perpetuate the narrative, which

concludes with an act of conciliation or trans-

cendence.

101 A. J. Greimas, Du Sens: essais semiotiques, Paris,

1970, 187. I borrow from Vance’s translation of

this passage ‘Pas de Trois’, 132.

102 Contrasting geometric figures can appear in

conflict, resolved by subsequent conflations of

their differing properties. This achievement of

unity out of difference also has strong ideolo-

gical connotations. For Levi-Strauss, narrative

can bring about a poetic or creative resolution

of active social conflict by symbolically re-

conciling differences. See Structural Anthro-

pology, trans. C. Jacobson and B. G. Schoepf,

New York, 1963, 206–31; Levi-Strauss, Tristes

tropiques, trans. John Russell, New York, 1963,

176–80; Frederic Jameson, The Political Un-

conscious: Narrative as a Socially Symbolic Act,

Ithaca, 1981, 77–9.

103 A. Timmermann, ‘Staging the Eucharist: late

Gothic sacrament houses in Swabia and the

Upper Rhine: architecture and iconography’, 2,

unpublished PhD dissertation, University of

London, Courtauld Institute of Art, 1996, 94–8.

104 Timmermann, ‘Staging the Eucharist’, 94.

105 A. Gosse-Kischinewski and F. Gatouillat, La ca-

thedrale d’Evreux, Evreux, 1997, 25, 65–6.

106 Brucher, Gotische Baukunst in Osterreich, 201–202;

W. Buchowiecki, Die gotischen Kirchen Osterreichs,

98; P.B. Wagner, Pfarr- und Wallfahrtskirche zu

Unserer Lieben Frauen Himmelfahrt in Krenstetten,

Niederosterreich, Christliche Kunstst.atten Os-

terreichs, no. 309, Salzburg, 1997, 3–13.

107 Such a clear pattern of shapes, immediately

readable, is unusual. The marked emphasis on

basic squares and circles as templates of design

suggests some familiarity with ratios common

in Italy. See Wagner, Krenstetten, 12.

108 See Grabar, The Mediation of Ornament, 48–50,

88–9. Grabar cites the tenth-century writer al-

Tha’alibi as claiming that ‘the worst of writing

is the writing of angels because it must be il-

legible to humans.’

109 The vaults in the nearby church at Sankt Va-

lentin in Lower Austria represent a different

manner of narrative development. The vaults

over the nave show a regular progression of

bands bearing distinctive geometrical motifs –

lobed lozenges within squares – alternating

with bays of thick net vaults. The vaulting over

the choir, by contrast, portrays a bewildering

array of incomplete figures, paired rows of

strange shapes composed of various arcs over a

diamond grid. The final bay resolves this dou-

bleness and fragmented quality in a single,

central radiating star with seven curving rays.

See Brucher, Gotische Baukunst in Osterreich,

202–203.

110 The lace-like drop tracery has additional para-

digmatic forms: double cusped rings sus-

pended from the keystone and single rings at

the corners, linked to other points by a single

filament of alabaster.

111 Jameson, The Political Unconscious, 82–3, dis-

cusses the subtext as the place both of social

conflict and ideological opposition. Social dis-

sonance may be expressed through contra-

diction, whereas ideological opposition is

expressed in antinomy or paradox, which ap-

peals to the narrative of the text for resolution.

112 Jameson, The Political Unconscious, 118–9; Eric et

Enide, 1042: ‘Sire, Yidiers, li filz Nut, ai non’. See

also Jean Lemaire, Oeuvres de Jean Lemaire de

Belges, ed. J. Stecher, vol. 3, Louvain, 1883, 98–

134. In his Concorde des deux langages, Jean Le-

maire undertakes to marry the two vernaculars

of poetic renown. In triplets customary of Ita-

lian verse he constructs a ‘Temple de Venus’,

whereas a French ‘Temple de Minerve’ is fash-

ioned in Alexandrines. On this latter site he

hopes for an ‘amoureuse concordance’.

113 The Chronicle of Froissart, trans. John Bourchier,

vol. 6, London, 1906, 113–14; Froissart, Oeuvres,

ed. A. Kervyn de Lettenhove, vol. 15, Brussels,

1871, 114–15; L. Patterson, ‘Making identities:

Henry V and Lydgate’, in New Historical Literary

Study, eds J.N. Cox and L.J. Reynolds, Princeton,

1993, 83. The passage deals with problems at

the negotiations between John of Gaunt and

Richard, Duke of York, with Philip of Burgundy

and Jean, Duke of Berry in 1394.

114 John Lydgate, Lydgate’s Troy Book, ed. Henry

Bergen, part 3, New York, 1975 (1906), 870;

Patterson, ‘Making identities’, 80.

115 The Brut, or the Chronicles of England, ed. Friedrich

W. D. Brie, part 2, Early English Text Society, OS

136, London, 1908, 410; Patterson, ‘Making

identies’, 85.

116 M. Buyle and C. Vanthillo, Vlaamse en Brabantse

retabels in Belgische monumenten, Brussels, 2000,

148–9.

117 For an interpretation of Patinir’s landscape

paintings as Andachtsbilder, see R. L. Falkenburg,

Joachim Patinir Landscape as an Image of the Pil-

grimage of Life, trans. M. Hoyle, Amsterdam and

Philadelphia, 1988.

118 J. Crab, Het Brabants Beeldsnijcentrum Leuven,

Louvain, 1977, 323–4, no. 21 (1507): ‘endo alsoe

opgaene met zynen tabernaculen ende met-

selrien ende welfsel gelyc den patroen dat

uutwyst ende gelyck Mathys Keldermans deser

stadt meester metsere den gront vanden selven

patroen getrocken heeft . . . de drie tabernacu-

len sal hy beteren te wetenne den middelsten



geheel veranderen endo noch alsoe goet maken

dan hy int patroen staen.’ Crab (nos 21, 22, 24)

cites three contracts for altarpieces in which

Jan Petercels appears as a specialist in the fab-

rication of wood tabernacles.

119 Several contributions of the 1960s address the

vogue for vegetal imagery between 1470 and

1520. See Karl Oettinger, ‘Laube, Garten und

Wald. Zu einer Theorie der s .uddeutschen Sak-

ralkunst 1470–1520’, in Festschrift f .ur Hans Sedl-

mayr, Munich, 1962, 201–228; Joachim B .uchner,

‘Ast- Laub- und Masswerkgewolbe der endenden

Sp.atgotik: Zum Verh.altnis von Architektur,

dekorativer Malerei und Bauplastik’, in Fes-

tschrift Karl Oettinger, eds Hans Sedlmayr and

Wilhelm Messerer, Erlangen, 1967, 265–301;

B .uchner, ‘ .Uber die decorative Ausmalung

sp.atgotischer Kirchenr.aume in Altbayern’, in

Mouseion Studien aus Kunst und Geschichte f.ur O. H.

Forster, Cologne, 1960, 184–93; Margot Braun-

Reichenbacher, Das Ast- und Laubwerk: En-

twicklung, Merkmale und Bedeutung einer sp.atgo-

tischen Ornamentform, Erlanger Beitr.age zur

Sprach- und Kunstwissenschaft, 24, Nurem-

berg, 1966. Ten years earlier, E.-H. Lemper

completed his thesis on the subject (unavail-

able to me): Das Astwerk Seine formen, sein Wesen

und seine Entwicklung, diss., Liepzig, 1950. See

also Crossley, ‘The Return to the Forest’, 71–80;

Hubertus G .unther, ‘Das Astwerk und die The-

orie der Renaissance von der Entstehung der

Architektur’, in Theorie des arts et creation artis-

tique dans l’Europe du Nord du XVIe au debut du

XVIIIe siecle, Actes du colloque international

organize les 14 a 16 decembre 2000 a l’Uni-

versite Charles-de-Gaule – Lille, Lille, 2002,

13–32.

120 Baxandall, The Limewood Sculptors, 23, 30–2,

299–300; H. Metz, Der Breisacher Altar, Konig-

stein im Taunus, 2000.

121 On the phenomenon of vegetal decoration and

its relationship to architectural carriers, see

Kavaler, ‘Nature and the Chapel Vaults at In-

golstadt: Structuralist and Other Perspectives’,

Art Bulletin, 87, 2005, 230–48.

122 Bucher, ‘Fifteenth-Century German Archi-

tecture’, 415.

123 On Kraft’s tabernacle, see C. Schleif, Donatio et

Memoria Stifter, Stiftungen und Motivationen an

Beispielen aus der Lorenzkirche in N .urnberg, Mu-

nich, 1990, 16–75; H. Bauer and G. Stolz, En-

gelsgruX und Sakramenthaus in St Lorenz zu

N .urnberg, Konigstein im Taunus, 1989, 8–12.

124 P. Pfister and H. Ramisch, Der Dom zu Unserer

Lieben Frau in M .unchen, Munich, 1994, 8, 22–4.

125 E. Bourassin, ‘La herauderie au XXVe siecle: Rois

et herauts d’armes’, in Jeanne d’Arc: Une epoque,

un rayonnement, Colloque d’histoire medievale,

Orleans, Octobre 1979, Paris, 1982, 107–11; P.

Pasatoureau, ‘Aux origins de l’embleme’, in

L’hermine et le sinople: Etudes d’heraudique medie-

vale, Paris, 1982, 327–33; Jacques Lemaire, ‘L’in-

teret pour l’heraldique dans les prologues des

chroniques Bourguignonnes’, in Sources de l’

heraldique en Europe occidentale: actes du 4e Colloque

international d’heraldique, Brussels, 1985, 78–80;

M. Pastoureau, ‘Aux origins de l’embleme: la

crise de l’heraldique europeenne aus XIVe et

XVIe siecles’, in Emblemes et devises au temps de la

Renaissance, ed. M.T. Jones-Davies, Paris, 1981,

129–39. The development of devises and badges

seems to begin in the late fourteenth century.

See W. Paravicini, ‘Gruppe und Person: Re-

pr.asentation durch Wappen im sp.ateren Mitte-

lalter’, in Die Repr.asentation der Gruppen: Texte –

Bilder – Objekte, eds Otto Gerhard Oexle and An-

drea von H .ulsen-Esch, Gottingen, 1998, 366–8.

126 E. Eisenstein, The Printing Press as an Agent of

Change, Cambridge and New York, 1979, vol. 1,

33, 88.

127 See W. J. Ong, Ramus, Method and the Decay of

Dialogue, 1958, Cambridge, Mass. and London,

1983, 92–101, 112–14.

128 Roger Chartier, The Order of Books: Readers, Au-

thors and Libraries in Europe between the Fourteenth

and Eighteenth Centuries, trans. L. Cochrane,

Stanford, 1994, 1–3. Chartier begins by citing

Michel de Certeau on the distinct realms of

writing and reading. See Michel de Certeau, The

Practice of Everyday Life, trans. Steven Randall,

Berkeley, 1984, 174.

129 If the presentation of all compartments is a

common feature of open retables, the vertical

orientation is somewhat unusual. The absence

of wings emphasizes the upward ascent as the

three storeys of paired episodes relate the tale

from bottom to top.

130 E. Dhanens, ‘Jan van Roome alias van Brussel,

Schilder’, Gentse Bijdragen tot de Kunstgeschiede-

nis, 11, 1945–48, 96–100. Dhanens attributes the

altarpiece in design to Jan van Roome, which is

not at all certain.



renaissance gothic: pictures of geometry and narratives of ornament

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