1
Francesco Benelli
Columbia University
"Rudolph Wittkower and the Theory of Proportion: Premises and Practice"
This paper focuses on the origin of Rudolph Wittkower's theory of proportion and
the way in which Wittkower uses this theory in analyzing Leon Battista Alberti's and
Palladio's architecture in his essays of the 1940s, which eventually formed the body of
Architectural Principles in the Age of Humanism. The paper will examine a number of
Wittkower's previously unpublished sketches of plans, sections and elevations. The paper
will explore these themes in relation to a newly discovered box of documents in the
Wittkower Archive of Avery Library pertaining to the preparation for the 1951 Milan
conference on proportion.
2
Franco Barbieri
Mentre ci si è variamente occupati del problema delle proporzioni in Palladio, sia
riguardo agli ‘Ordini’ di architettura che alle forme e dimensioni degli ambienti, quasi
nullo l’interesse sul tema per quanto concerne Scamozzi. Specialmente Wittkower,
intento a “far giustizia una volta per tutte”, come ebbe a scrivere Sir Kenneth Clark,
“della concezione edonistica, o meramente estetica, dell’architettura rinascimentale”, gli
dedica, nei ‘Principi architettonici nell’età dell’Umanesimo’, qualche puntuale
attenzione. Ne trae convinzione che Scamozzi abbia, in fondo, rispetto ai predecessori e
specie all’Alberti, semplificato, ancor più dello stesso Palladio, misure e rapporti
proporzionali: sul che può genericamente convenirsi, osservando che, ad esempio, nei tipi
di ambienti da lui ritenuti perfetti, l’altezza risulta, in ogni caso, il medio aritmetico tra
larghezza e a lunghezza. Va tuttavia tenuto presente come Scamozzi, convinto assertore,
da un lato, del “carattere antropomorfico” dell’architettura, dall’altro strenuo cultore delle
‘mathematiche’ e delle “meccaniche’ tramite soprattutto le lezioni del Clavio e la lettura
di Pappo, dedichi al sistema degli ‘Ordini’ l’intero Libro VI della parte II del suo
Trattato, 174 pagine contro le 37 riserbategli da Palladio nel primo dei ‘Quattro Libri’. E
ciò viene proprio dalla specifica volontà di Scamozzi, convinto razionalista non
indifferente al metodo ‘scientifico’ galileiano, di sottoporre a rassegna critica le diverse
opinioni in merito, da Vitruvio ai contemporanei: arrivando alla ‘verità’ per coerente
imperterrita via deduttiva.
3
Robert Bork
The University of Iowa
“Dynamic Proportioning Strategies in Gothic Architecture”
Historians of Gothic architecture working over the past century and a half have
generated a wide range of theories about Gothic proportioning systems. One important
strain of this research has argued for the importance of geometrical design methods based
on the use of the compass, while another strain has emphasized modularity and
arithmetical measure. In the German-speaking world, where the survival of hundreds of
original design drawings should facilitate the analysis of Gothic proportioning strategies,
the polemically anti-geometrical writings of Konrad Hecht continue to inhibit scholarship
four decades after their publication. Careful proportional analysis of such drawings
reveals, however, that Gothic draftsmen developed both their ground plans and their
elevations using a fairly small set of basic geometrical operations, which could be
combined in unfolding sequences to create final forms of great complexity and
sophistication. This inherently dynamic design strategy placed more emphasis on the
rules of form generation than on the proportions of the final product. In this respect it
differed markedly from the more static module-based approach that Rudolf Wittkower
saw as characteristic of Renaissance design, although recent research has demonstrated
that the boundary between these two architectural cultures was by no means clear-cut in
the fifteenth and early sixteenth centuries. Since this procedural logic could be translated
only with difficulty into written form, the rise of architectural treatises in the Renaissance
contributed significantly to the eclipse of Gothic design in the decades after 1500.
4
Lex Bosman
University of Amsterdam
“Proportion and Building Material, or Theory Versus Practice”
The emergence of the Renaissance and a concept of theory seem to point in the
direction of a kind of break with the Middle Ages. Yet in the daily practice of building
this break is difficult to find. Gradually it is becoming more clear how many elements of
routine, such as methods of dressing stone, methods of designing buildings and the use of
these methods on the building site, continued to influence both the design of architecture
as well as the way architectural designs were realized throughout both the Middle Ages
and the Renaissance. Architectural theory did not move in suddenly and obviously could
not take the place of otherwise necessary ways of transporting the stone from the quarry
or ways to connect the process of design with the process of building.
A fascinating element in this respect might be the way a module was chosen.
While most other aspects of architectural theory concerning proportional systems are
discussed in scholarly debate, the question of the origin and the choice of a module is
rather obscure. I will try to connect the module with the practice of delivering building
material (specifically column shafts) from the quarry to the building site. A related item
will be discussed as well, which is the use of three-dimensional (usually wooden) models
as intermediaries between design and building practice.
5
Jean-Louis Cohen
New York University
“Le Corbusier’s Modulor and the French Debate on Proportion”
Finally codified in 1945, after several years of research, Le Corbusier¹s Modulor
is probably the most comprehensive proportional system imagined during the 20th
century. Developed through contacts with consultants such as art historian Elisa Maillard,
and referred to the statistical measurements of the human body, the Modulor concluded
decades of discourse on proportions, a theme that preoccupied Le Corbusier ever since
his sojourn in Germany in 1910.
Matila Ghyka¹s work on the Golden section was one of the sources for the
Modulor, but was also used by other architects, such as Le Corbusier¹s rival André
Lurçat, who proposed his own range of proportions, related to the work of the builders as
much as to that of the designer. Proportions thus became a central issue in the postwar
French reconstruction, as architects struggled to keep their status in a changing building
production.
6
Matthew A. Cohen
Washington State University-Spokane
“Simultaneity: A Distinguishing Characteristic of Medieval and Early Renaissance
Architectural Proportional Systems”
Architectural proportional systems of the medieval and early Renaissance periods
appear to have served three main purposes in the minds of their designers: to help ensure
structural stability, to impose overall diagrammatic logic on their designs and,
encompassing the previous two, to imbue their designs with a comprehensive notion of
architectural correctness that is commonly referred to in Italian documents with the term
ordine. My recent studies of several buildings in Florence suggest that architects of these
periods often strove to reinforce the quality of ordine in their designs by weaving
together multiple layers of proportional relationships within a single composition—a
condition that I will term “simultaneity.” In this study I will identify two ways in which
the identification of simultaneity in architectural proportional systems can advance the
study of architectural history.
First, simultaneity can help to distinguish intentional proportional systems from
those coincidental proportional relationships that inevitably occur in any architectural
composition. Second, the identification of distinct categories of simultaneity can suggest
possible lineages among various groups of proportional systems, and perhaps even the
proportional signatures of individual designers. Such categories can thus provide a new,
non-visual basis for architectural comparison that holds the promise of illuminating
previously unknown historical relationships.
Based on new surveys, in this paper I will identify simultaneity in the proportional
systems of the Basilicas of San Lorenzo (including the Old Sacristy), Santo Spirito, Santa
Maria del Fiore and Santi Apostoli; and of the Ospedale degli Innocenti. I will then
propose lineages of influence within two groupings of these buildings. Ultimately I will
argue that Matteo Dolfini designed the proportional system of the Basilica of San
Lorenzo, that Filippo Brunelleschi modified it for use in the Basilica of Santo Spirito, and
that both architects referred extensively to precedents as they developed distinctive
proportional systems.
As a preface to these case-study explorations I will provide an historiographical
overview of the study of architectural proportional systems over the past sixty years,
focusing in particular on 1) the widespread belief, which continues today, that
proportional systems contribute to the aesthetic experience of architecture—a
phenomenon that I will term “proportional aesthetic mysticism”—and 2) Wittkower’s
fundamentally aesthetic framework for the study of architectural proportional systems,
which I will term the “Wittkower Paradigm.”
7
Mario Curti
“Canons of Proportion and Laws of Nature: A Permanent and Unresolved Conflict”
(Note: This paper will be presented in English.)
Tutti i canoni proporzionali, a partire da quelli antropomorfici espressi dal pensiero
greco antico, dei quali ci rende testimonianza Vitruvio, fino ad arrivare al Modulor di Le
Corbusier, basato sulla Sezione Aurea, intendono, come è noto, introdurre nei processi
della produzione artistica leggi compositive universali e perciò tendenzialmente fisse e
immutabili.
Ma nella redazione del progetto, in cui si rende manifesto l’impatto con la
complessa e imprevedibile realtà fenomenica, i canoni proporzionali nella quasi totalità
dei casi si trovano a dover essere confrontati con altre leggi, quelle cioè che regolano
ogni aspetto della natura sensibile, anch’esse, per loro stessa definizione, universali e
immutabili.
Tali sono, solo per accennare alle più evidenti, le leggi fisiologiche della percezione
visiva (sia statica che dinamica), quelle relative alle caratteristiche fisiche di resistenza
alle sollecitazioni, proprie dei materiali costruttivi impiegati, e quelle che, più in generale,
sovrintendono alla statica dell’edificio. Accanto a queste vi sono anche altre leggi, di
altra natura, che confliggono con alcuni canoni proporzionali. Si prendano come esempio
le leggi della matematica euclidea, le quali, tradotte in disegno geometrico, tendono quasi
naturalmente a confliggere con quei rapporti proporzionali esprimibili unicamente in
numeri irrazionali, ai quali, nel corso della storia, sono stati attribuiti valori esoterici o
simbolici. È il caso ben noto del rapporto cosiddetto “aureo”, o di quelle figure modulari
elementari, o anche di alcuni “tracciati regolatori” (che al rapporto aureo fanno
generalmente riferimento), difficilmente traducibili in elaborati di progetto.
Tra canoni proporzionali e leggi di natura nascono cosi’ conflitti che talvolta
comportano inevitabili aggiustamenti, emendamenti, rimedi dei canoni stessi, in
considerazione delle varie situazioni che condizionano il processo creativo, come già
sostenuto da Vitruvio e più tardi dai suoi esegeti. Altre volte invece, come avviene con
Claude Perrault, il conflitto, interpretato in modo perentorio, viene considerato come del
tutto insanabile; di conseguenza l’idea di proporzione si trova ad avere un’importanza
ridotta.
In ogni caso tale conflitto provoca nelle coscienze più avvertite profondi
turbamenti. Ciò ha imposto talora agli architetti scelte radicali o soluzioni di
compromesso, capaci anche di influire in modo determinante sui modi più generali e
complessi nei quali si materializza l’espressione artistica.
8
Krista De Jonge
Catholic University of Leuven
“’…de questien der Simmetrien met redene der Geometrien.‘ Early Modern
Netherlandish Artists on Proportion in Architecture”
Sixty years after Rudolf Wittkower’s book Architectural Principles in the Age of
Humanism (1949), the question of geometrical and/or/versus arithmetical proportions
remains unresolved insofar as Netherlandish Early Modern architectural production is
concerned. At first glance, sources offer a contradictory image. In his preface to the 1528
Antwerp edition of Gauricus’ De Sculptura, Cornelis Grapheus expressed the hope that
the passages on symmetria or proportioning would be useful to sculptors, painters, and
architects, since it “feeds all arts.” However, Pieter Coecke van Aelst, author of the first
Netherlandish text on modern architecture (Antwerp, 1539), lamented at the close of his
life that “most of our craftsmen… hardly pay any attention to the right [antique]
proportion in their works, which is very confusing to see”. And in the very last years of
the century, the Bruges master mason Charles De Beste borrowed over a hundred Gothic
geometrical patterns to explain properly what the art of geometry and proportioning was
in his manuscript treatise Architectura (1596-1599). A newly discovered manuscript
book on the orders that can be attributed to a Netherlandish artist active in the 1530s
confirms the need for a less antithetical interpretation of Renaissance proportional
systems in northern European architecture. From the 1530s a geometrical way of
expressing both geometrical and arithmetical proportions developed, connecting both
masters of the “antique” and of the “modern” through one notation system
understandable by all. This paper will trace its offshoots till the seventeenth century.
9
Sigrid de Jong
Leiden University
“The Secret of Primitive Proportions Unveiled: Paestum as an Eighteenth-Century
Laboratory”
‘à en juger par le pesant et le massif de ses proportions, il est indubitable que ces
Monumens ont été construits par les Grecs dans l’origine de l’Architecture, et
qu’ils sont de la première antiquité, étant très certain que tout ce qui reste en Italie
de Temples et de Monumens construits par les Romains est d’une architecture
bien plus légère, et de proportion et de forme toute différente.’ (Saint-Non on
Paestum, 1760)
When seeing the Doric temples of Paestum in Southern Italy with their own eyes,
eighteenth-century travellers were provided for the first time with true examples of the
proportions of archaic Greek architecture. Contrary to the Roman proportional systems,
the Greek ones were until then largely unavailable to architects. With the rediscovery of
Paestum, conveniently located south of Naples and not in far-away Greece, the secret of
Greek proportions was no more. Architects were able to measure the temples precisely
and wrote many accounts about their primitive forms and proportions.
But what did they mean exactly when describing the proportions as primitive?
How do they define these proportions, what kinds of reflections do they provoke, and
which elements are of importance therein? With the reactions to Paestum primitive
proportions were to play a significant role in architectural discourse, while
simultaneously opening up the more general debate on proportions. As I aim to show in
my paper, the discourse on proportions changed in this period, giving more room to the
cultural and historical meaning of proportional systems. The writings by architects such
as Soane, Wilkins and Labrouste demonstrate how Paestum functioned as a laboratory to
unveil the secret of primitive proportions, and how, with the different meanings architects
attached to them, it enlarged and renewed the debate on proportions.
10
Elizabeth den Hartog
Leiden University
“1, 2, 3, 6: Medieval Church Architecture and Perfect Numbers”
“Knowledge of numbers should not be despised. We are instructed in number to
avoid confusion. Take away number in all things, and they all perish. Take away
computation from the world, and all things are encompassed by blind ignorance; people
who are ignorant of the knowledge of reckoning cannot be distinguished from the other
animals.” Thus wrote Isidore of Sevilla in the 7th century (Book III, 4). Numbers clearly
mattered. Indeed, the medieval world seems to have taken to heart the words expressed in
the Book of Wisdom (11.21): “Omnia in mensura et numero et pondere fecisti.” In such a
number-obsessed world, one would expect number to have played a significant role in the
design of medieval architecture; and indeed, many medieval descriptions of buildings
display a great concern for numerical values.
After a short introduction into the issues involved, this paper will concentrate on
the use of perfect numbers as a design principle in several select examples; i.e. the choir
of St. Rémi in Reims, the transepts of Noyon Cathedral and the Canterbury Cathedral
corona. These examples will show that numbers were sometimes used as a design
principle, but not in the way that has been commonly thought.
11
Francesco P. Di Teodoro
Politecnico di Torino
“Leonardo: The Architectural Drawings and Their Proportions”
In The Notebooks of Leonardo da Vinci, the first anthology of Leonardo’s
writings, compiled by Jean Paul Richter from the original manuscripts and published in
London in 1883, only in the seventh chapter do we find the word “proportion” in relation
to the human body (“On the proportions and on the movements of the human figure”). In
this chapter, the drawings and related notes by Leonardo specifically treat of the
proportions of the head, face, foot, hand, legs, arms and of the whole body. Richter also
incorporates Leonardo’s famous drawing of the Vitruvian man, preserved in the Gallerie
dell’Accademia in Venice, into this chapter.
Subsequent studies of proportion in Leonardo’s work have evolved within the
thematic groupings of Jean Paul Richter. Thus they have focused on the drawings of
human anatomy and horses, and on the Sforza and Trivulzio equestrian monuments.
Rarely has the interest of scholars concentrated on architectural proportions (Pedretti,
1978; Schofield, 1991); more frequently scholars have tried to “ridurre in proportione”
the plans or to arrange the sketches by Leonardo into real dimensions (see for example
Guillaume and Kübacher, 1987).
The purpose of this paper is to understand what proportional schemes form the
basis of Leonardo’s architectural drawings and how the plans, elevations and
architectural members are proportionally related.
12
Sara Galletti
Duke University
“Philibert Delorme’s ‘Divine Proportions’”
Judging by his claims in the Premier tome de l’architecture (1567), Philibert
Delorme believed that proportional systems were of paramount importance in the
conception of architectural projects. Not only did Delorme mention proportional systems
in numerous instances throughout his text, but he also repeatedly reminded his readers
that the second volume of his oeuvre, suitably titled Des divines proportions, was entirely
dedicated to this specific aspect of architectural planning. This much publicized Second
tome was never published however, nor is there any indication that it was ever written.
Moreover, as the vast majority of buildings designed by Delorme have been destroyed,
hardly any data is available on the architect’s use of proportional systems in practice.
Historians have generally assumed that Delorme, who died in 1570, simply lacked the
time to approach the Divines proportions. They also have taken his statements about
proportional systems (and, generally, his text) at face value – mostly because of the
importance accorded to proportional systems in Renaissance architecture and its history,
but in disregard of the fact that Delorme has been arguably described as “nonconformist,”
“ironic,” and “disrespectful of authority” (by Anthony Blunt, Manfredo Tafuri, and Jean
Guillaume). My paper will try to offer a reassessment of the importance accorded to
proportional systems in the Premier tome.
13
Anthony Gerbino
University of Manchester
“Were Early Modern Architects Neoplatonists? The Case of François Blondel”
What was the status of Neoplatonism among early modern architects? What
relationship did they see between their designs and the “design” of nature? What, if
anything, guaranteed the aesthetic claims for specific numerical ratios or geometrical
forms? Did early modern architects even require such a guarantee?
We have little direct evidence to answer these questions. It has generally been
assumed, since the publication of Wittkower’s Architectural Principles, that practitioners
held to stronger or weaker versions of Renaissance Platonism. Music, bodies, and
buildings, according to this notion, shared a structural affinity with the order of the
heavens, because they depended on the same basic numerical ratios. It is worth pointing
out, however, that Wittkower himself adduces only circumstantial evidence for such
beliefs. Alberti and Palladio, while suggestive, are both very terse on this point, obliging
Wittkower to supplement his case with further evidence drawn from philosophers and
mathematicians, in particular Luca Pacioli, Francesco Giorgi, and Nicolas of Cusa.
It is this set of circumstances that makes François Blondel’s extensive response to
Claude Perrault in their famous debate over the efficacy of proportion so important. The
twenty chapters that Blondel devoted to this issue in the final volume of the Cours
d’architecture (1675-1683) represent a rare historical testimony: an explicit, selfconscious, and theoretically elaborate justification of proportion by a Renaissance
practitioner. Blondel’s interpretation of this tradition, too, is noteworthy. What these
pages show is not an orthodox expression of Platonic doctrine, but rather an attempt to
adapt the age-old principle of cosmic symmetria to a new, modern context.
14
Jeroen Goudeau
Radboud University Nijmegen (NL)
“The Matrix Regained: Reflections on the Meaningful Scheme”
From the Renaissance onward the column dominated architectural theory, at least
in the written treatises. The system of the orders superimposed a second design layer
upon the geometrical composition principles, which had existed since ancient times and
had flowered throughout the Middle Ages right into the Early Modern period. Perhaps it
was where these two systems met that arose new thoughts about proportion. Column
proportions led to immediate questions, such as how geometry, which generated
irrational measures, related to elementary, discrete ratios. One of the ways to cope with
this sort of question was the design grid, which linked the orders to a larger threedimensional composition.
This contribution will try to illustrate how the design grid or matrix could provide
new solutions to endow the architecture of the orders with proportions. First, the focus
will be on the Dutch-German architectural theorist Nicolaus Goldmann (1611-1665). His
architectural theory of 1665 contained a system by which every building had its
meaningful place and was dimensioned within the hierarchy of the city quarter. Each
quarter again was related to the network of the city as a whole. At the same time the gridbased architecture of all the building types was dimensioned by the orders. In the end,
this system was based on the biblical measurements of the Temple of Solomon.
The analysis of Goldmann's detailed and unusual theory will be followed by some
reflections on the use of the grid structure in relation to the question of proportion. To
what extent can the grid be seen as a meaningful design tool? As soon as the principle of
the grid had taken root in the design of buildings, the ways of applying and interpreting it
began to vary.
15
Gerd Grasshoff
Institut für Philosophie der Universität Bern
“The Bern Digital Pantheon Project”
The subject of the presentation will be the Bern Digital Pantheon Project which,
after the conclusion of the second development phase, will now be continued in the
context of the Excellence Cluster TOPOI in Berlin. TOPOI is a joint research cluster by
Berlin universities, Stiftung Preussischer Kulturbesitz, Deutsche Archäologische Institut,
Berlin-Brandenburgische Akademie and the Max Planck Institute for History of Science.
In the first part of my talk I will present the result of the digitalization campaign of the
Pantheon in Rome. The content and organisation of the digital data repository will be
presented. The second part of my talk will outline further studies carried out on the basis
of this digital data; furthermore, a workflow for the development of the data will be
presented. The digital data of the studies on the Pantheon will be made accessible via
open access. All results and publications based on these data will be collected and
provided to the scholarly community. I will present a pilot study of our findings on the
entasis of the columns of the Pantheon portico, and develop a thesis about the
geometrical construction of the entasis. This pilot study will exemplify methods of how
the proportions of parts of buildings can be determined and how, by way of mathematical
modelling, the digitized data can be used toward this end. In addition, I will demonstrate
which Roman measuring units were used for the construction of the Pantheon.
16
Volker Hoffmann
Institut für Kunstgeschichte
“The Geometrical Design of the Palatine Chapel in Aachen”
Aachen Cathedral, also known as the Royal Church of St. Mary at Aachen, has a
centrally planned building at its core, which is recorded as having been built as a
“Palatine Chapel” by order of Charlemagne around 800 (which appears to have been
confirmed by recent dendrochronological investigations). The interior two floors, open on
the ambulatory through arcades, as well as the tambour and the cupola, rise above an
octagonal ground plan to a height of 30.60 m. The ambulatories are enclosed by a
sixteen-sided wall with an external diameter of 32.76 m.
This extraordinary and at the same time puzzling construction has not been fully
explained by researchers—as demonstrated in detail by Siebigs (1). This uncertainty also
applies to the question of the design geometry. After numerous attempts at deciphering its
structure, the ground plan has revealed a good, but not complete approximation to the
respective geometric patterns of the building; however, all attempts break down in
respect to the frontal perspective.
My suggestion is based on the architectural survey by Albrecht Haupt (2) and on
my own laser-supported measurements, which, however, do not record the entire
building. The result of the analysis: the entire geometric design is based on two squares
106 and 100 Byzantine feet in size (1 bF = 30.89 - 31.0 cm). Such a double square was
already an element of the fundamental design figure of the Hagia Sophia in Istanbul (532537) (3); arithmetically, the number 106 is yielded if you divide the number 150 by the
square root of 2 (actually 106.066). Geometrically, the 100 square can be easily
transformed into a 106 square and vice versa. The ground plan as well as the elevation
can be represented completely by the double square with the aid of a compass and ruler;
yes, you can even say that the design figure of the 100 square suffices as a basis.
1. Hans-Karl Siebigs, Der Zentralbau des Domes zu Aachen. Unerforschtes und
Ungewisses. Worms 2004.
2. Albrecht Haupt, Die Pfalzkapelle Kaiser Karls des Grossen zu Aachen. Leipzig
1913.
3. Volker Hoffmann mit Nikolaos Theocharis, Der geometrische Entwurf der Hagia
Sophia in Istanbul. Erster Teil. In: Istanbuler Mitteilungen 52, 2002, 393-428.
17
Frédérique Lemerle
Centre national de la recherche scientifique, Tours, Centre d’études supérieures de la
Renaissance
“Orders and Proportions from Serlio to Perrault”
The treatises of the Renaissance resumed and further developed the typological
and modular studies of the orders addressed by Vitruvius in Books III and IV of the De
architectura. This talk will show how theoreticians of the cinquecento (Alberti, Serlio,
Philandrier) revisited the modular and fractional system of Vitruvius, invented another
type of proportional system (Vignola), and adopted “composite” solutions (Palladio,
Scamozzi); and how the French in the seventeenth century (Roland Fréart of Chambray,
Abraham Bump and Claude Perrault) personalized this inheritance.
18
Emanuele Lugli
Kunsthistorisches Institut, Florence
“Thinking in Measurements or Thinking in Proportions?
Different Approaches to Space Between Italy’s Middle Ages and Renaissance”
There is an equivalence between measurements and proportions, or so
architectural studies seem to imply. In order to discover the proportional correspondences
within a building, most scholars automatically reconfigure the building’s dimensions into
modules oblivious to their historical specifications. This paper argues, however, that
dividing space into modules became embedded in architectural thinking only beginning
in the Renaissance, with Alberti openly championing this practice. Most medieval
builders may not have envisioned proportionality as their ultimate goal, even if their
buildings can today be seen this way. Rather, proportionality may have been obtained by
the consistent use of locally standardized units of measurement, such as the pertica or the
foot, not modules. By reconstructing the importance measurements had for medieval
communities and looking at the way some twelfth-century Italian churches may have
been planned, this paper attempts to re-frame our historical discourses about
proportionality in medieval architecture and highlights that medieval proportionality was
less the result of modular thinking than the natural consequence of medieval
communities' conceptualization of space sustained by local measurement systems.
19
Stephen Murray
Columbia University
“Metrological Investigation of Gothic Buildings: A Paradox”
The study of the systematic application of systems of mensuration and proportion
in Gothic architecture leads us to a paradox. Richard Krautheimer concluded more than a
half century ago that medieval buildings convey meaning partly through the numbers that
they embody. Although few scholars would disagree with this in principle, attempts to
survey the question more fully or to pursue the way an individual building was plotted
have generally not been well received by scholarly audiences. Thus, for example, Otto
von Simson’s broad overview of the relationship between musical harmony and
architectural proportion in The Gothic Cathedral, while popular with the general public,
was widely condemned by scholars.
The application of laser surveying techniques has, in the past decade, provided a
tool that allows us to generate three-dimensional animations of buildings to galvanize the
lay audience, but may also provide the means to conduct new metrological studies or to
verify the results of traditional surveys. Using recently-completed scans of Beauvais and
Amiens Cathedrals I will return to reconsider the conclusions that I reached twenty years
ago using the old tools and methods—steel tapes, calipers, plumb bob, theodolite and
strings nailed to the pavement. Will digital technology finally lend authority to a
troubled arena of architectural research?
20
Mauro Mussolin
Scuola Normale Superiore di Pisa
“’Sì come il naso... non è obrigato né all'uno né a l'altro ochio’: The System of
Proportion in the Architecture of Michelangelo”
(Note: This paper will be presented in English.)
È ben noto come il sistema proporzionale utilizzato in architettura da
Michelangelo appaia differente da quello elaborato dagli architetti a lui contemporanei. I
motivi sono svariati, tra cui la sua formazione di scultore, l’interesse per gli studi
anatomici sul corpo umano, l’insofferenza verso ogni accademismo teorico e verso gli
studi vitruviani, l’attenzione agli aspetti funzionali dell’architettura. Per tutta la carriera,
l’artista sembra essersi lasciato guidare più da un sistema proporzionale basato sulla
complessità organica di tipo anatomico che su una astrazione estetica basata su aritmetica
o geometria, come già magistralmente riconosciuto nella monografia di James Ackerman
del 1961. Inoltre, avendo avuto la possibilità di avviare pochissimi progetti architettonici
ex novo, Michelangelo si trovò più spesso a progettare, costruire e portare a termine opere
architettoniche già iniziate da altri o in contesti edilizi fortemente condizionanti. In
questo modo, attraverso il ricorso a un sistema proporzionale sui generis, di volta in volta
modellato sul contesto, realizzò capolavori architettonici di grandissimo impatto, studiati
per risolvere i vincoli ambientali imposti, le limitazioni spaziali e tecniche, la scarsità di
mezzi economici.
Partendo da una riflessione storiografica sulla celebre cosiddetta “lettera
vitruviana”, questo contributo prenderà in considerazione alcuni progetti architettonici,
realizzati e non, utili a comprendere i principi guida del complesso sistema proporzionale
michelangiolesco e di valutarne scarti e continuità rispetto alla tradizione del tempo.
21
Werner Oechslin
ETH Zürich
“(Modern) VICTORY Over Empiricism; and its Consequences in Architectural Theory
and Practice”
PROPORTIONS, in endless proposals of spontaneous ad-hoc “theories,” have
constituted a dominating issue in modern “theoretical” discourse in architecture. Such
theories claim universal validity. Architects such as Le Corbusier have defended
proportional systems against "mystique" and "mystère". Naturally, the (declared) aim is
to find a solid ground for a “deduced,” systematic method—against the fortuitous
character and contingencies of history. However, the historian, as ever, “tends” to
establish “continuous” discourses which too often try to imply causalities. But
discontinuous situations are more frequent, and correspond better with reality. The
historian might describe the 1951 proportion conference in Milan as a successful
encounter among architects, historians and theorists but it was instead a juxtaposition of
diverse approaches reflecting diverse interests rather than offering mutual exchange. The
architect still hopes for universal laws giving him security and comfort, whereas the
philosopher is aware of the insurmountable difficulties of the 'Leib/Seele' problem, the
sensuous and cognitive approaches. On the other hand this dichotomy has always been
reflected within architectural texts.
Daniele Barbaro, in his commentary on Vitruvius (1556) formulates: “La ragione
non opera, cioè non discorre senza l'occasione del senso, perche non fa giudicio di cose,
che prima non siano conosciute. E' adunque necesssario congiungnere una parte, & l'altra
in modo, che il senso prima s'adoperi, dopo segue la ragione." Conversely Vignola, less
patient, declares his wish to find a rule whose advantages are to be short, easy and
speedy. What in music is evident ("come ben provano li Musici nella lor scienza") should
be equally valid and evident, and accompanied by "sicurezza," in architecture. Such are
the circumstances of method-making in architecture, when the (expected) result “urges”
and imposes priority over any logical, and more complex, analysis; and this explains
many “results”—and errors!
22
Konrad Ottenheym
Utrecht University
“Drawing Harmony: Proofs of Dutch Seventeenth Century Proportional Systems
Dutch seventeenth century classical architecture was strongly embedded in the
legacy of sixteenth century Italian architects and their theoretical works, such as those of
Andrea Palladio and, above all, Vincenzo Scamozzi. Not only were architectural details
and the use of the orders based on these works, but occasionally even the ground plans
and façade schemes from these treatises were used as sources of inspiration for
contemporary Dutch buildings. There is even written evidence in Dutch sources that the
theoretical framework of these Italian scholarly architects was well received by a small
group of erudite patrons and a limited number of architects. They were well aware of the
fundamental notion as proclaimed by Alberti, and further enforced by Palladio and
Scamozzi, that beauty in architecture is based on the harmony of its proportions.
In this paper I will focus on some architectural drawings that contain indications
of authentic proportional systems from the “inner circle” of Dutch seventeenth-century
classical architecture. Some of these drawings are already well known, while others have
been only recently discovered. Taken together these drawings provide various examples
of how these architects actually used arithmetical grid systems as well as geometrical
constructions in order to achieve their classical ideal of beauty and harmony. In light of
these authentic proportional systems we may propose a method for analysing other
drawings from this period that do not have any proportional systems inscribed.
23
Andrew Tallon
Vassar College
“Divining Proportions in the Information Age”
To know the proportional systems of historic buildings has ever been to divine
them through a cloud of imprecision. Error is introduced on three levels: acquisition of
the data necessary to represent the building, using the inherently imprecise means of steel
tape and plumb bob; rendering of this data in graphical form, with the rectification that is
invariably required by the inaccuracies of the acquisition techniques and the
impracticality of surveying the building in its entirety; and finally, reproduction, a term
which can stand both for the problems associated with using plans created by others for
which the conditions of the previous two terms are unknown, and for the relatively small
scale of “found” plans printed, with generational loss, in a book—plans which must then
be scanned or photocopied, with further generational loss or morphological distortion, in
order to iterate, in (relatively thick) pencil or ink lines, the proposed proportioning
schemes.
In the last few years it has become possible, thanks to modern laser surveying
techniques, to speak with confidence of an historic building as it actually is, to speak not
of divining but rather of determining its geometry. Because the entire operation, from
acquisition to reproduction, occurs in the digital domain, error can be virtually
eliminated. Using recent scans of the cathedrals of Paris and Bourges I will demonstrate
how the laser-based acquisition of building geometry and its subsequent processing in the
digital realm profoundly transforms—and legitimizes—the venerable but vexing process
of “reverse engineering” proportional systems.
24
Marvin Trachtenberg
New York University
“To Build Proportions in Time, or Tie Knots in Space?”
Since Alberti, and most critically since Wittkower’s Architectural Principles,
architectural theory has tended to construe “proportions” in plenary, static terms. As with
most aspects of modern architecture culture, the dimension of time and change that
relentlessly affects all human endeavor is not accommodated by the celebrated Albertian
ideal of immutable design perfection, so perfect in all respects that once attained
“nothing can be added, taken away, or altered, but for the worse.” This paper, drawing
on the author’s recent book, Building-in-Time from Giotto to Alberti and Modern
Oblivion (Yale, 2010), outlines the antithetical, dynamic proportional methodology of the
pre-Albertian architectural regime, which in practice continued alongside and long after
Alberti’s treatise. Its point of departure was the author’s concept of durational
aesthetics: in place of the postmodern notion that “form is not perfected act but process
and incessant revision” (George Steiner), in durational aesthetics, perfected architectural
form is produced by a process of incessant revision. In this regime, aesthetic totality is
always provisional, and means are provided to accommodate time and change, even—
indeed, especially—in the proportional dimension of planning. Whereas Alberti
advocated a proportional method that sought to bind dimensional relationships into
unbreakable knots, pre-Albertian proportional methodology employed what the author
terms concatenation, in which all elements are proportionally linked to all other elements,
forming a chain or net that, critically, is open to change at any time at all compositional
levels. In effect, concatenation was a dynamic version of the Vitruvian principle of
symmetria (I.2.4 and III.1), that every part be related to every other part, and the parts to
the whole, which was later reflected in a rigidified, static mode not only in Alberti but
Palladio and others, as studied by Wittkower. What distinguished concatenation from
related ancient or neo-antique doctrines was above all its dynamic modality and
participation in the fluid orientation and processes of Building-in-Time.
25
Caroline van Eck
Leiden University
“The Rhetoric of Proportion: Nature or Nurture?”
Proportion in building can be studied from two perspectives: the architect’s and
the viewer’s. Usually the former is the starting point for proportion studies, but here I
want to take the beholder’s part. Doing so raises two issues: is the viewer capable of
recognizing proportion, and what is its visual impact? The first issue is usually discussed
in terms of its rational character and the recognizability that entails, and mainly in the
context of Neo-Platonic theories on the mathematical nature of the universe, and the
relation between the microcosm and the macrocosm, even though it is hard to substantiate
that architects indeed explicitly defined proportion in such metaphysical terms before the
late sixteenth century. As for the visual impact of proportion, the absence of comments
by viewers on it has often been noted. When viewers do note proportion, they do it in
very general terms, and often seem to refer to symmetry and an impression of regularity,
solidity and organization rather than to grasp concrete geometrical or numerical relations
between parts and the whole of a building. The rhetoric of proportion seems to be not so
much to convey an awareness of numbers or ratios, but of more general impressive
qualities.
It is only with Claude Perrault’s arguments against the natural or even
metaphysical foundations of proportion that the visual rhetoric of proportion becomes an
explicit issue in architectural discourse. His arguments against these foundations also
refuted traditional Neo-Platonic claims for proportion’s recognizability. At the same time
his brother Charles would open much wider horizons for that argument by asking in the
Querelle des anciens et des modernes whether proportion, like the orders and indeed
rhetoric itself is universal and innate or acquired and contingent on local circumstances.
In my paper I will reconstruct the rhetorical view on the visual impact of
proportion from Cicero to the Perraults, and argue that the visual rhetoric of proportion
does not aim to facilitate the recognition of the actual mathematic proportions used, but
instead uses proportion to point to the social and cultural qualities of a building, and by
doing so raises the issue whether the use and visual effect of proportion is a matter of
nature or nurture.
26
Mark Wilson Jones
University of Bath
“Ancient Approaches to Proportion and the Case of the ‘Poor old Parthenon’”
Proportional studies have been regarded with relative indifference over recent
decades in large part, it seems to me, because the subject has too often been treated in a
hermetic fashion, as if it were divorced from the rest of architecture. But the
mathematical qualities of a building only make sense as part of the design process as a
whole, interacting with its other facets. This is particularly true of antiquity, where there
was an abiding practical dimension to the way the goal of mathematical harmony was
achieved. (Select examples will be illustrated.)
While this assertion can be demonstrated with ease for the Roman period, the
finer manifestations of the Classical age such as the Parthenon might be thought to be
exempt. But, after reviewing some of the over-optimistic interpretations to which ‘the
poor old Parthenon’ has been subjected, I aim here to look at the building afresh as in
some ways just another case of Doric design, albeit more complex. I hope to gain traction
with an approach that finds support in three key areas: a) a metrological foundation
firmly based on archaeological evidence; b) comparative analysis of general Doric design
procedures used for other buildings of the period; c) detailed consideration of the specific
constraints imposed on the Parthenon by the recycling of material from the ‘PreParthenon.’
Doric design can best be understood via a theory of ‘modulated proportions,’ by
which arithmetical proportions and modules go hand in hand in Doric colonnades.
Contrary to most authorities, who privilege the column diameter, I see the triglyph width
as the lynchpin of the system. Significantly, this tallies with Vitruvius, our sole ancient
authority. Not only did he describe Doric design in modular terms, his module matches
the triglyph width. Since the triglyph is the nux of the thorny ‘corner problem,’ couching
design in this way brought tangible advantages for laying out temples.
I contend that the octastyle facade of the Parthenon conforms to the same
principles as hexastyle ones. The proposed design scheme helps explain the famously
pronounced ‘corner contraction’ (the narrowing of the corner bays) of the Parthenon, the
aesthetic merits of which have often been celebrated. This can perhaps now be seen as a
mathematical response to a design problem, or vice versa, as a design response to a
mathematical problem.