Cohen, M.A.
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Cohen, M. A. (2011, November 15). Beyond beauty : reexamining architectural proportion in the Basilicas of San Lorenzo and Santo Spirito in Florence. Retrieved from
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experience of architecture. I call this belief Proportional Aesthetic Mysticism (P.A.M.), and it is problematic because, as noted in Chapter 1, it directs scholarly attention towards the perceptions and aesthetic opinions of present-day observers rather than the thoughts and intentions of the architects in history who incorporated sets of proportions into the designs of the monuments of architectural history. It thus distracts architectural historians from the study of architectural history, and leads them into the areas of criticism and aesthetics. As I will argue below, furthermore, P.A.M. is illogical. Considering its wide influence, therefore, it calls into question the rigor of architectural history as a scholarly discipline.
Claude Perrault formally challenged the notion that architectural proportions (proportion-1) contribute to architectural beauty in the “Preface” to his Ordonnance des cinq espèces de colonnes selon la méthode des anciens of 1683 by arguing that “…in architecture there are, strictly speaking, no proportions that are true [veritables] in themselves….”
1Thus, he argues, architectural proportions cannot be examples of what he terms “positive” beauty, or, that which is “bound to please everyone”
due to its easily apprehended “value and quality.”
2Examples of positive beauty in architecture that he provides include richness of materials, size and magnificence, and precision and cleanness of execution.
3Conversly, perceived beauty in architectural proportions, he argues, is always determined by “custom” and therefore constitutes a form of “arbitrary” beauty.
4“For to be offended or pleased by architectural proportions…” he contends, “…requires the discipline of long familiarity with rules that are established by usage [i.e., custom] alone….”
5Perrault’s argument against any possible aesthetic benefits of particular architectural proportions (proportion-1) may be summarized in the following two points: 1) certain abstract proportions cannot contain a priori beauty while others do not; and 2) for a proportion to contribute to beauty in architecture it must be associated with favorable architectural forms, and therefore taste, and therefore custom.
Perrault’s concept of positive beauty is confusingly similar to the proportional aesthetic belief
system that he opposes, for one could use his notion of arbitrary beauty to argue that no positive
beauty exists at all, but rather, that all beauty is arbitrary (i.e., determined by custom). Nevertheless,
the second part of Perrault’s argument, his notion of arbitrary beauty, remains a fundamental point of
reference for consideration of this controversial topic today. Perrault provides insights into the
widespread beliefs of his day pertaining to beauty and proportion, which were similar to widespread
beliefs about this subject today, when he laments:
“…most architects…would have us believe that what creates beauty in the
Pantheon…is the proportion of that temple’s wall thickness to its interior void, its width to its height, and a hundred other things that are imperceptible unless they are measured and that, even when they are perceptible, fail to assure us that any deviation from these proportions would have displeased us.”
6Thus, he argues, that which creates beauty in the Pantheon cannot be merely a series of dimensional proportions. Perrault expresses his frustration with his fellow architects by noting that he would not even bother to address the issue of beauty in proportion had widespread opinion of his day not compelled him to. The preceding passage continues:
“I would not linger unduly over this question…were it not for the fact that most architects hold the opposite opinion. This shows that we must not consider the problem unworthy of examination…even though reason appears to be on one side….”
7The purpose of Perrault’s preface was to enable his primary readers, architects, to set aside their preconceptions regarding customary rules of proportion for the orders, and to consider
receptively his proposed set of refinements to those rules. The purpose of the present epilogue, which elaborates upon Perrault’s argument that only arbitrary beauty can guide perceived beauty in
architectural proportions, is similar. By asking scholars to confront their preconceptions pertaining to assumed relationships between architectural proportions (proportion-1) and architectural aesthetics, I hope to facilitate new ways of exploring the uses of proportion (proportion-1 and proportion-3) in the history of architecture.
Why Sets of Proportions Cannot Contribute to Architectural Beauty
I have derived the following five contentions from my research into the sets of proportions of the
basilicas of San Lorenzo and Santo Spirito, which included several months spent inside each of these
buildings, looking at them from many different heights and locations. These contentions frequently
overlap, and thus should be considered areas of emphasis rather than firm categories. Sets of
proportions cannot logically contribute to beauty in architecture because:
1. Sets of Proportions are mental, not visual, constructs.
Sets of proportions can consist of intentional geometrical, numerical and arithmetical relationships.
8The last two of these types of relationships are always invisible, and thus can only be described verbally. We cannot see, for example, how many units of measure (such as Florentine braccia) separate two columns, nor how many modules (such as column diameters) that distance is equivalent to, nor the arithmetical relationships that may link any group of dimensions (such as lengths of 9, 12 and 18 having a common divisor of 3). Thus Wittkower’s claim: “I think it is not going too far to regard commensurability of measure as the nodal point of Renaissance aesthetics” has no visual relevance because commensurability of measure is not perceptible.
9Numbers provide ways of talking and thinking about certain kinds of architectural proportions, but have no impact on architectural appearances.
Intentional geometrical proportional relationships influence the visible characteristics of architecture, as in, for example, an unadorned, rectangular opening in a wall, but the relationships themselves are not visible. Like numerical and arithmetical relationships, intentional geometrical proportions can only be precisely identified mentally, not visually. The façade of the basilica of Santa Maria Novella in Florence, for example, looks like it is composed of a series of squares and various 1:2 relationships as Wittkower claims it is (see Chapter 1). Careful measurement of the façade, however, is more likely to demonstrate that it consists of, depending on the points of measurement, a series of variously lopsided and distorted shapes, not quite squares and perhaps not quite even rectangles. We could choose to ignore such data and say “close enough,” and describe these various shapes within the façade as named geometrical figures anyway, such as squares and whole-number-ratio rectangles, but such descriptions would be mental constructs, not visual
observations. The very requirement that we need measurements in order to confirm or refute what we think we are seeing proves that geometrical proportional relationships are not visible in architecture.
Furthermore, the absence in the architectural literature of any claims that the geometrical proportions of famous buildings consist of obscure geometrical proportions for which we have no names, such as, to take two random and obscure examples, a 3 : 3 12 17 rectangle, or a 5 x 6 x 6 1 3 x 7 trapezoid (and let us not even consider non-rectilinear buildings), proves that most observers are only interested in familiar, named geometrical figures. Since named figures cannot be distinguished from nameless ones with the unaided eye, their precise proportional characteristics must not be visible. These
characteristics can only be apprehended mentally, just like numerical and arithmetical characteristics.
2. Architectural proportions do not exist in isolation of architecture.
Architectural proportions describe architectural forms, and thus cannot be isolated from the physical materials in which they are expressed. In architecture you can have a square window, but not a square. Thus, no one could ever prove that perceived beauty in a particular architectural composition were attributable to a particular proportional relationship rather than other aspects of an architectural design such as style and color, the effects of environmental phenomena such as light and shadow, optical illusions created by non-parallel or irregularly-intersecting lines, or the psychological and cultural predispositions of the observer.
103. Proportions have no intrinsic beauty.
Even if architectural proportions could be isolated from architecture, as discussed in #2 above, no proportion or group of proportions could ever be proven to contain intrisic beauty, universally recognized by all people everywhere, always.
11Tests of proportional aesthetic preferences that superficially emulate scientific research methods are inherently flawed because such preferences are subjective and thus resist quantitative analysis. For example, the very act of asking individuals in a test group to select the rectangles that they find most beautiful from an array of provided rectangular cutouts taints the results from the outset because it suggests to the individuals being tested that a rectangular cutout can be beautiful; and furthermore, because it assumes that the individuals’
selections will indeed be determined by proportional assessments rather than other aesthetic considerations or associations, consciously or not.
124. Sets of proportions rarely correspond precisely to built form.
Sets of proportions usually describe regular, symmetrical proportions based on straight lines and ninety-degree angles. Since complexity and irregularity are the normal conditions of architecture, however, the ideal relationships described by sets of proportions are rarely found in built works. The space between two columns may appear to be rectangular, for example, but since the sides of
columns gently curve in entasis, and the profiles of capitals are usually much more complex, the shape of that space is in fact not rectangular but highly complex. In addition to such inherent design complexities, inherent irregularity caused by construction error, settlement, damage, intentional architectural refinements, and dimensional compromises that the architect may have been forced to accept for a great variety of reasons all make buildings unreliable platforms for the precise
expression of sets of proportions. Furthermore, architectural proportions must be tied to specific
points of measurement in the built fabric that do not necessarily correspond to visible edges of
proportional figures. For example, if the distance between two columns were determined by a square
proportion based on the column height (vertical dimension) and the on center distance (horizontal dimension), due to the thicknesses of the columns the eye would perceive a squarish, approximately rectangular space (it would not be truly rectangular, for the reasons noted above) between the column shafts, since the sides of the square proportional figure would be embedded in the centers of the columns.
Beauty-in-proportion believers typically dismiss such concerns by claiming that a close approximation of a particular proportion in built form can be as beautiful as an exact manifestation, a response that reveals the futility of attempting to apply logical reasoning to a discussion of the subjective and therefore inherently illogical topic of architectural aesthetics. Indeed, the preceding typical response (which I have heard numerous times in my conversations with beauty-in-proportion believers) raises the questions of how far a building can stray from some set of proportions that a believer has judged to be beautiful before the building ceases to be beautiful, and what kinds of deviations are allowable, and according to what criteria, and documented by what means; and for all of these questions, according to whose judgment? Believers, however, tend to shun such specifics as well, seeking shelter within the fog of ambiguous clichés such as “timeless architecture,”
“harmonious proportions” and the most common one, “nevertheless, maybe there is something to it.”
5. Proportions are fixed, while aesthetic judgment is capricious.
Sets of proportions incorporated into the dimensions of a building are quantitative and essentially unchangable (some slight movement due to structural degredation nothwithstanding). Aesthetic judgements, by contrast, are qualitative, rarely unanimous among all people and always subject to change. Thus, the two are conceptually incompatible, cannot be studied using the same research tools, and cannot influence each other. While the presence or absence of certain proportions in a building can be established based on verifiable, scientific methods, the claim that sets of proportions contribute to architectural beauty can never be scientifically proven. Indeed, if it could be so proven, surely someone would have done so during the more than three centuries of debate over this belief since Perrault published the first serious challenge to it in 1683. The beauty-in-proportion belief system could never be definitively disproven either, however, since no problem involving the qualitative issue of aesthetic preferences could ever be defined in scientifically precise terms.
Since sets of proportions can be neither visually perceived nor visually isolated from
architecture (except through the use of separate, drawn diagrams, which are thus isolated from
architecture), have no intrinsic beauty, hardly ever correspond precisely to built form; and consist of
fixed and measurable relationships of geometry, number and arithmetic, they cannot be the causes of
subjective and potentially changeable assessments of visual beauty in architecture. If one
nevertheless wanted to determine whether indeed they could be, a scientifically rigorous test for this purpose would be impossible to devise because sets ofproportions must be described in quantitative units, while opinions as to what is beautiful can only be described using the qualitative tools of verbal expression. One could argue that, aesthetic judgment being personal and subjective, the mere knowledge of the presence of certain proportions in a building causes some people to think of the building as beautiful. Such an effect, however, would be the result of psychological rather than physical causes. Furthermore, it would not occur in all people in all times, and thus could not be considered causal in the scientific sense of being repeatable and predictable.
It follows, therefore, that we cannot attribute dimensional qualities to an idea, except metaphorically; and likewise, that we cannot attribute the dimensional properties of a set of
proportions to an assessment of beauty. Since a belief that is illogical, unprovable, and impossible to
support with quantitative evidence cannot be based on reason, it must be based on faith. Since the
beauty-in-proportion belief system lacks the institutionalized doctrines and customs of organized
religion, I have labeled it as a type of mysticism: Proportional Aesthetic Mysticism.
1
“…& que par consequent il n’y a point, à proprement parler, dans l’Architecture de proportions veritables en elles-mesmes [mêmes]…” Claude Perrault, Ordonnance des cinq espèces de colonnes selon la méthode des anciens (Paris: Jean Baptiste Coignard, 1683), xiv. Claude Perrault,
Ordonnance for the Five Kinds of Columns after the Method of the Ancients, Julia Bloomfield, Kurt W. Forster and Thomas F. Reese, eds. and trans. (Santa Monica: Getty Center for the History of Art and the Humanities, 1993), 54. Veritable here refers to the possession of inherent, measurable qualities, independent of an observer; what Descartes and the British Epiricists would call primary qualities. I thank Caroline van Eck for clarification of this translation.
2
“…j’appelle des beautez fondées sur des raisons convaincantes, celles par lesquelles les ouvrages doivent plaire à tout le monde, parce qu’il est aisé d’en connoistre [connaître] le merite & la valeur….” Perrault, Ordonnance, 1993, 50; and Perrault, Ordonnance, 1683, vi.
3
Perrault, Ordonnance, 1683, v-vi.
4
“Or j’oppose à ces sortes de beautez que j’appelle Positives & convaincantes, celles que jappelle Arbitraires, parce qu’elles dependent de la volonté qu’on a eu de donner une certaine proportion, une forme & une figure certaine aux choses qui pourroient en avoir une autre sans estre [être] difformes,
& qui ne sont point renduës agreables par les raisons dont tout le monde est capable, mais seulement par l’accoûtumance….” Ibid., vii
5
“…car pour estre [être] choqué, ou pour recevoir du plaisir des proportions de l’Architecture, il faut estre [être] instruit par une longue habitude des regles que le seul usage a établies….” Ibid., xiii.
6
“C’est là pourtant ce que disent la plûpart des Architectes qui veulent qu’on croye que ce qui fait la beauté par exemple du Pantheon, est la proportion que l’épaisseur de ses murs a avec le vuide du Temple, celle que sa largeur a avec sa hauteur, & cent autres choses, dont on ne s’apperçoit point, si on ne les mesure; & par lesquelles, quand on s’en appercevroit, on ne seroit point asseuré qu’elles ne pussent estre [être] autrement sans déplaire.” Ibid., v; and Perrault, Ordonnance, 1993, 49-50.
7
“Je ne m’arresterois pas tant sur cette question…n’estoit que la plûpart des Architectes tiennent l’opinion contraire: Car cela fait voir qu’on ne doit point considerer ce Problême comme ne meritant pas d’estre [être] examiné…si la raison paroist estre [être] d’un costé [côté]….” Perrault,
Ordonnance, 1683, v-vi; and Perrault, Ordonnance, 1993, 50.
8
In this study numerical relationships are those that highlight the quantitative qualities of integers,
such as number progressions; and arithmetical relationships are those that highlight calculations with
numbers, such as a pair of numbers (whether whole or fractional) that approximate the ratio 1:√2,
and that can only be recognized as arithmetical by carrying out calculations. These definitions
sometimes overlap, such as, for example, when numbers that approximate the ratio 1:√2 occur in progressions (Figure 3-49). Since sets of proportions are interpreted in this study as modes of communication, the determination of whether a relationship is numerical or arithmetical depends upon the historian’s interpretation of the architect’s intention in selecting the relationship.
9
Rudolf Wittkower, “Systems of Proportion,” Architect’s Yearbook 5 (1953), 16.
10
Regarding the effects of optical illusions on the perception of architectural proportions see: Eugene Emmanuel Viollet-le-Duc, Entretiens sur l’Architecture, Paris, 1863, 2 vols., 1, “Septième
entretien,” 249-251; A. Thiersch, Optisch Täuschungen auf dem Gebiete der Architektur, Berlin, 1873, illustration sheet “Beispiele von Linientäuschungen.” Geoffrey Scott, The Architecture of Humanism, London, New York and London, 1974 (rpt.1914), 170.
11
This is, of course, Perrault’s central argument. See note 2 above.
12
Studies that attempt to determine, using scientific methodology, whether the golden section has universal aesthetic value, see: Gustav Theodor Fechner, Zür experimentalen Aesthetik (Leipzig: S.
Hirzel), 1971; Idem, Vorschule der Aesthetik (Leipzig: Breitkopf & Härtel), 1876; C. Lalo, L’esthétique experimentale contemporaine (Paris: Alcan), 1908; Frank C. Davis, “Aesthetic Proportion,” American Journal of Psychology 45 (April 1933), 298-302; LeRoy A. Stone, “The Golden Section Revisited: A Perimetric Explanation,” American Journal of Psychology 78 (1965), 503-506; D.E. Berlyne, “The Golden Section and Hedonic Judgements of Rectangles: A Cross- Cultural Study,” Sciences de l'Art - Scientific Aesthetics 7 (1970), 1-6; Michael Godkewitsch, “The
‘Golden Section’: An Artifact of Stimulus Range and Measure of Preference,” American Journal of Psychology 87 (1974), 269-277; and John Benjafield, “The ‘golden rectangle’: Some new data,”
American Journal of Psychology 89, (1976), 737-743.
Spirito, recorded by the author for this study, are the first comprehensive surveys of these structures ever published, and perhaps ever recorded.
1The surveys are based on points of measurement that correspond to the edges of clearly articulated components of the classical orders and their
subdivisions (points that usually correspond to the locations of masonry joints), those points being likely to indicate the dimensions that the various capomaestri and masons responsible for these buildings considered important. As a rule, these surveys include the mortar joint height with the element above it.
In order to minimize measurement error, the author worked alone whenever possible, using the simplest possible measuring techniques (Figure 36). Basic equipment consisted of steel tape measures manufactured by S.E.B., 80 cm levels, and a plumb line. For most vertical measurements, the zero end of the tape measure was secured to the floor at the edge of the column or pilaster plinth with a heavy weight. The measurement was then recorded from the scaffolding by projecting the desired point horizontally from the masonry surface to the tape measure, kept vertical with the plumb line. For upper entablature measurements, from the scaffolding the zero end of the tape measure was raised to the desired points with a specially adapted extendable pole, while an assistant recorded the measurements at the floor. The ceiling heights were measured in July 2005 with a Leica Disto A5 laser measuring device.
The surveys are organized into a system of key diagrams and spread sheets rather than
traditional measured drawings, in order to make them easily retrievable and conducive to statistical
analysis. The organization of each survey follows the compositional structure of the building it
documents. The compositional structure of San Lorenzo is rather complex and requires some
introduction. The basilica contains five types of vertical point supports (some of which are actually
structural, and others merely expressions of structure). The minor order contains the nave columns
and two types of pilasters, which I will term “floor pilasters” and “step pilasters.” The tops of all of
these minor order members align with the lower entablature circumscribing the basilica (see Figure
25). The positions of the bottoms of these members vary, however. While the bases and plinths of the
columns and floor pilasters stand on the nave floor, those of the step pilasters stand atop three steps
(see Figures 1 and 25). Thus, the shafts of the step pilasters are approximately 1 br. shorter than
those of the columns and floor pilasters. The major order contains the tall crossing pilasters, half of
which are “floor crossing pilasters,” and the rest “step crossing pilasters.” The nave arcades contain
only columns and floor pilasters. The nave arcade survey excerpted in Appendix 2 contains three sets
of measurements: 1) San Lorenzo Nave Arcade Bay Horizontal Measurements (Intercolumniations),
2) San Lorenzo Column and Floor Pilaster Vertical Measurements, and 3) San Lorenzo Column and
Floor Pilaster Horizontal Measurements. Key diagrams corresponding to these categories identify the
various measurements recorded, and spread sheets contain the actual measurements.
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