Beauty and Proportionality in Architecture
The highest honor a traditional building can receive is to be called beautiful. Traditional architects, and occasionally modernist architects, support their judgment with the claim that it is well-proportioned. When pressed, they invariably fall into statements that depend on ratios between whole numbers, geometric constructions that yield the golden section, diagrams showing parallel lines falling on important parts of its composition, and other numerical and geometric propositions. Their devotion to the classical columnar orders is often founded on their capacity of the dimensioning of the many parts and the whole with traditional numerical ratios. These are found in a long and illustrious series of books beginning with Jacopo Barozzi da Vignola’s from 1562 and Palladio’s 1570 Quattro libri d’architettura down to William Ware’s American Vignola and George Gromort’s recently translated book, which served as a textbook at the École des Beaux-Arts.1
Proportions have been fundamental to architecture’s claims on the beautiful ever since it emerged from the art of building with a content that theory could explain.2 Pythagoras (c. 570–490 BC), identified proportion as the instrument for establishing the mean between extremes and blending opposites into a relationship. This role became a pervasive element in the thought of the Western tradition.3 Without proportion, there is mere random chaos. Proportion is evidence of order and the congruence between two things of different kinds that have and share proportions, such as a well-formed human figure and a building. Proportions allowed reasoned speech to address the perception of beauty, which otherwise lay outside speech. Polyclitus embodied proportions in his canon figure, and it brought justice into the good city in Plato’s "City of Pigs" passage in The Republic (370c–372d). In classical thought, proportion provides the conjunction between the good and the beautiful.
Conjoining the good and the beautiful is no longer central in discussions of architecture, cities, justice or beauty. The conjunction was framed in antiquity, when the moral and the natural sciences were interpreted within the same framework of reason and were bound to the same cosmic order. That orderly cosmos was closed but infinite. Creation was complete, and all created things were arranged within the Great Chain of Being.4 In that Great Chain, man alone was endowed with reason and free will. These burdened him with the charge "Know thyself!" and planted in his human nature the quest to know the true, do the good and make the beautiful, and he developed the doctrine of imitation for doing so.
In architecture, imitation’s principal instrument is proportion. Its role is described in the conditions and criteria architecture must satisfy. First come what Sir Henry Wooton called the three conditions of "well-building," commodity, firmness and delight.5 Building then confronts the six criteria for architecture that come in two groups, the formal criteria (symmetry, eurythmy and decorum) and those at work on the building site (ordering, configuration and allocation).6 Proportion does heavy lifting in both groups.
Among the formal criteria, symmetry occupies pride of place in Vitruvius’ discussion in books III and IV. It becomes the agent for carrying out the comprehensive design for temples. His first lines in Book III come right to the point:
The composition of a temple is based on symmetry, whose principles architects should take the greatest care to master. Symmetry derives from proportion, which is called analogia in Greek. Proportion is the mutual calibration of each element of the work and of the whole, from which the proportional system is achieved. No temple can have any system of composition without symmetry and proportion, unless, as it were, its elements have precisely calculated relationships like those of a well-proportioned man.7
Here is the familiar Vitruvian man fitted into his square and circle, the first source Vitruvius mentions for proportions. Next come the various numerical ratios derived from him and then numbers supplied by philosophers. These ratios, or proportions, are congruent with the order, harmony and proportionality of the cosmos, that is, nature. Man, and the building based on his proportions, is a microcosm that embodies the beautiful order of nature.
Ordering works on the building site involves translating proportions into the actual dimensions of the building’s various physical elements and locking them into relationships by using a common dimension deriving from the lower diameter of the column. Rowland’s translation puts it this way: "Ordering is the proportion to scale of the work’s individual components taken separately, as well as their correspondence to an overall proportional scheme of the symmetry."8
Vitruvius’ word symmetry is a short-hand notation for the ratios, numbers and geometric shapes of the formal qualities that the architect transfers from nature, the microcosm of the human figure and philosophy to the building.
Imitation finds the properties of the symmetry, and ordering receives them on the building site and embeds them in the building.
A millennium and a half later, Leon Battista Alberti rewrote Vitruvius. Alberti retained Vitruvius’ delight, venustas, but when a building with delight approached architecture, he used a different word, pulcher, which has a Christian lineage. Pulcher appears in classical literature but not in Vitruvius, and it gains this meaning in the medieval period. Architecture possesses the beauty that makes God accessible, through perception of beauty in creation and man’s imitation. This shifts the objective content that is perceptible in a building up a notch from delight. Pulchritude suggests that, when beauty is the content, so is aspiration for the good.
All this disappears from the dominant narrative of architectural history produced after the seventeenth century. Proportions remained attached to beauty, and beauty retained an objective presence in the building until Claude Perrault broke that alliance in the late seventeenth century.9 Finding nothing universal in beauty, he shifted it from the building to the viewer, from the object to the subject. He claimed that custom, not imitation of nature’s beauty, determines the qualities we find beautiful. Producing something people recognize as beautiful requires only a cultivated taste. The proportions that we find pleasurable are the ones we are accustomed to. They have nothing to do with the order, harmony and proportion of nature, or of the human body, or the musings of philosophers. Symmetry is mere formal similarity on opposite sides of an axis.10 There is no role for imitation in producing things that give us pleasure. If there were, the closer the imitation is to its original, the greater our pleasure would be. Beauty is found in a judgment based on individual taste and, therefore, is not open to discussion.
This diminishing role for proportions and beauty occurred alongside the increasing status of empirically verifiable experience. Galileo showed us previously unseen things in the cosmos, and Antonie Philips van Leeuwenhoek (1632–1723) revealed tiny living things in a water drop’s microcosm. According to Leibnitz and Newton, the new mathematics of number and geometry dealt with the observable, measurable, objective facts, unmolested by subjective belief. Science, or knowledge, had been a unified body that included interpretations about how things ought to be. From those interpretations, people construed laws of nature that held in both the moral and the physical world. Now science was transformed into something different, and so were the interpretations the empirical data yielded. As Daniel Robinson has explained, those earlier interpretations "were rationalist inventions, as is the belief that such laws exist. Nature itself, however, is for the [empirical] scientist a perceptual affair. The laws of [natural] science must describe nature as it is experienced, not the way it ‘ought’ to be." On the Continent, the leading spokesman for the new era was René Descartes.11 Proportion would lose its two-millennia-long relationship with reasonable conjectures and judgments as well as its role of controlling the chaos of unbridled extremes and disproportionate grotesqueries. The solid certainties of the classical unified body of knowledge imbedded in reason would degenerate into relativism, and architecture would decline into mere building undertaken as self-absorbed narcissistic self-expression.
When beauty, imitation, symmetry and proportions were major players in architecture so were reason, judgment and eurythmy. Proportions were not fixed ratios but guides for proportionality. More important, proportionality governed perceptible relationships in shapeliness. Vitruvius wrote: "Shapeliness (eurythmy) is an attractive appearance and a coherent aspect in the composition of the elements."12 Indra Kagis McEwen’s comment is incisive. "The built analogue for a man’s well-shapedness," she writes, "the appearance of symmetry, is what Vitruvius called eurythmy, ‘the beautiful appearance and fitting aspect of the parts once they have been put together’ (I, iv, 5); the utterly convincing visible coherence of form that an architect must strive for by adjusting or ‘tempering’ proportions so as to flatter the eye of the beholder."13 Vitruvius and Alberti stressed the adjustments made to the dimensions needed to produce the eurythmy that made the canonic proportions perceptible. (Figures 1, 2) To achieve eurythmy required judgment based on experience, talent and reason, which Perrault rejected. He wrote that eurythmy and proportion are the same thing, explained that symmetry (bilateral similarity) is a property of proportion and concluded that the three words could be used interchangeably.14 Untempered proportions left unadjusted in the composition would serve quite well, as long as symmetry was honored. (Figure 3) The proportions might be found in an architect’s cultivated taste, Vignola or any other source, and they came unaccompanied by reasoned explanations that connected canonic ratios to things outside architecture. Reasoned judgment in theory, criticism and practice—the union that Vitruvius referred to as ratiocination and fabrica, and Alberti called lineaments and structura—would wither and die. The role for proportions that Alberti had elevated to a force of nature called concinnity, which the architect was to imitate, would be replaced by some ill-defined role for proportions in the theory, criticism and practice of architecture and in marginalized beauty.
Events unfolded differently in Britain, where the new empiricism, ballasted by the English civil order, led to fresh inquiries into nature, including the nature of man. Men were endowed by nature with a moral sense and an aesthetic sense. The qualities perceived in good acts and beautiful things were congruent with qualities found in the unity that nature made from its great variety. Nature was law abiding, and proportionality was one of her laws. Proportionality was not measurable in terms of Newtonian mathematics but was perceptible in its analogue, the natural law that was the foundation of the constitutional order in the United States.
In the Federalist Papers No. 51, James Madison writes: "What is government itself but the greatest of all reflections on human nature? If men were angels, no government would be necessary." In the beginning of Federalist No. 31, Alexander Hamilton writes: "In disquisitions of every kind there are certain primary truths, or first principles, upon which all subsequent reasonings must depend." He offers four examples from geometry, including "all right angles are equal." The American civil order, with its foundation on natural law and human nature, assured that its proportionality imitated nature’s order, to assure the liberty of each individual. A government based on majority rule, with natural law protecting minority rights, balanced the claims of duties and rights with liberty and pluralism, the proportional mean between the extremes of license and conformity.
Thomas Jefferson translated that proportionality into American architecture, imported principally from England and from England’s classical mentor, Palladio. (Figure 4) Classical architecture has always sought proportionality between what tradition transmits and the modifications it needs. The principle is at work in the art of governing, the art of building, and the art of renewing and improving the cities and rural countryside that any new building necessarily affects. The chief rule and guide is always the proportionality that is required to bring unity to the diverse elements. An institution seeks proportionality between its ends and its means, and with other institutions of the civil order, between purposive institutions and the functional arrangements serving them, and between the civil order and the people. Buildings require proportionality as it serves and expresses the purposes of the institution that builds or uses it, and in the place it occupies among other buildings in the rural and urban order.
Vitruvius and his successors always distinguish between well-built buildings (based on commodity, firmness and delight) and beautiful architecture. Beauty resides in perception and reason, not in mere ocular sensation. We can think of architecture as being supported on three legs: the tectonic that builds a material thing, the formal that allows judgment of its visual qualities, and the urban that serves the civil order by contributing to the setting. Each of these begins in the art of building and joins with the others to provide the unity required for beauty in architecture.
In the tectonic leg, the perception of beauty requires that the building honor the laws of nature concerning stability and deterioration. But to contribute to the beauty of the building’s architecture, more is required. It must use imitation to distance itself from building as "the product of necessity" and be visible as "the product of artistic intention."15 And it must possess the proportionality that makes its stability convincingly perceptible as it imitates the proportionality in nature.
Proportionality reins in monstrous oversizing or anorexic insubstantiality. Individual supporting elements must appear robust enough to support their loads. Hard or rough materials are not placed above less hard or smooth materials, unless there is a convincing visible support for them, especially for anything above a void or something transparent. Tradition provides guidance. Judgment provides the fitting result.
The ancients were right when they identified seven kinds of movement: up and down, back and forth, left and right, and around. Therefore we expect to perceive perfectly vertical walls and columns, perhaps buttressed for additional apparent support. We know loads travel over a void to find a support, which calls for a right-sized lintel or arch. The arch that is nominally a segment of a circle and perhaps stilted or stunted, with lintel, arch and support ornamented with a conventional array of bases, moldings, capitals, cornices, mortar courses (actual or fictive), etc., will reinforce the perception of stability. There should be an adequate purchase on its support, perhaps a wall, perhaps jambs, perhaps free-standing supports.
Where loads change direction, for example, at the junction of post and lintel or support and arch, there must be a perceptible intermediary that both eases and declares the transition. Because it is expected, when it is missing, as in many Gothic examples where the departure from the arch’s normative circle segment is also found, its absence assists in perceiving some other aspect of the building’s character. All supports—whether walls, columns, piers or arches—also require an intermediary before planting themselves on the earth with pedestals, bases, platforms either stepped or not, podiums and watercourses.
Vernacular construction always provides the model for artifice to imitate. Scoring horizontal lines in the mortar courses of a wall made with irregular bricks, or scoring stucco on a rubble wall to represent regular ashlar, elevates building by investing it with geometric clarity. At the University of Virginia, Jefferson’s columns, which are architecture’s most important ornament, have brick cores that do the work and a sheathing of stucco finished with sand painting to present them as if they are stone and worthy of their task. In modern construction, convincingly robust columns are often shells around steel stanchions. Pilasters add no actual strength to a wall, but their scansion evinces regularity and thereby a more convincing perception of stability. The first to condemn their use was the abbé Marc-Antoine Laugier, a revered anticipator of modernism.16 Building uses fact, architecture uses fiction to portray truth. To claim "truth to materials" is to reduce architecture to construction, and to claim that ornament is crime is risible.
Beauty in architecture is perceived in a building’s visual qualities. The aesthetic sense assesses the beautiful, while its counterpart, the moral sense, assesses the good. There is a strong tendency today to conflate judgments about the one with the other, especially in condemning classical architecture because it has been the favored architecture of tyrants, dictators and others antithetical to liberty. This calls for two observations. First, in the Western tradition, until the rise of modernism in the twentieth century, there was no other architecture available. Second, when an alternative did become available, the classical was the architecture of choice for any government that wanted to exercise what Hamilton, in Federalist No. 1, referred to as the vigor of government. For him, as for President Franklin Delano Roosevelt, that vigor was to protect liberty; for Roosevelt’s contemporaries, Hitler and Stalin, it was to exercise evil tyranny. The judgment about the very different purposes of the governments has nothing to do with the judgments about the buildings as architecture. The beautiful pertains to buildings, the good to acts of those who use them.
Within architecture, proportionality is required between a building’s use and its appearance, which addresses the urban leg of architecture’s tripod. A bicycle shed that pretends to be a cathedral can no more be beautiful than can a cathedral that looks like a bicycle shed. They are disproportionate to one another, not only in size but also in the formal tradition of architecture each is expected to evoke. Proportionality is the rightness or aptness of the building, relative to the role that the institution that built or uses it serves in the civil order. This is not a judgment about the good of the institution’s purpose, but the fittingness of the building to the city or rural countryside it inhabits. The aptness, or decorum, has several components, including size, quality of materials and workmanship, relationship to the traditional form that allows its purpose to be identified, and its location in the urban or rural realms. Proportionality guards against falling into chaos or kitsch, at one extreme, and banality or triviality, at the other, into either bombast or meanness. It will also assure that the means of serving and expressing its builder’s or user’s purpose is proportionate with that purpose. Justice administered in a bar is barroom justice; a courthouse that seems little better than a bar demeans justice.
Proportionality in the well-tuned city makes perceptible the proportionality between means and ends in the civil order and in the urban order. It displays the congruence between the order, harmony and proportions of the parts that are united to make the civil order, the parts that are united to make the building, and the buildings that are united to make the city or rural countryside.
The loss of proportionality in architecture coincided with the abandonment of beauty as the content of architecture. Heirs of Perrault, Julien Guadet and others at the École des Beaux Arts were perhaps not off the mark when they dismissed proportions as "Pures chimères," lacking validity even when they were rendered in numbers sanctioned by science, or "cabalistic combinations with mysterious properties," or analogy with music, or an inviolable antiquity.17 After proportions became detached from the metaphysical cosmos, they could quickly become quackery, or absurd, idiosyncratic discoveries, such as Le Corbusier’s in The Modulor.18 In general, proportions became meaningless.
In the American civil order and its architecture, proportionality can retain its role and, with it, the potential for making things that are beautiful. Proportionality—not as numerical relationships, but as the perceptible "nature and the reason of the thing," to use Hamilton’s language from Federalist No. 78—allows the beauty of architecture to maintain its liaison with the good. Under natural law, proportionality has retained its fundamental role of guiding judgment in separating fabrication from fact, hearsay from knowledge, copying from invention, and opinion from truth. It fends off chaos and disorder in governing and in building. And it marshals diversity into unity.
When a building can be explicated in reasonable speech, it can also make visible the invisible analogy between the good and the beautiful. That analogy is sanctioned by the traditions of architecture as a civil art and the sources of the good and the beautiful in nature, as classicism understands it. Such a building becomes the symbol of the good. Buildings that are well and aptly designed as civic art will be recognized by those who have the eyes to see and perceive it. And those who have the talent and training to imitate nature, as they make new buildings, will be able to restore the città felice, the good city that fulfills the needs of men.
1. Georges Gromort, Choix d’élements empruntés à l’architecture classique (Paris: A. Vincent, 1904), with later editions in 1907, 1920, 1927, 1949, 1954, 1960 and 1964; translated as the Elements of Classical Architecture by Henry Hope Reed and Steven W. Semes with Professor J. François Gabriel (New York and London: W. W. Norton, 2001); William R. Ware, The American Vignola (Scranton, Pennsylvania: International Textbook Company, 1902 and 1906); reprinted, Part I based on 4th ed., 1906, part II of 1st ed.,1906, by John Barrington Bayley and Henry Hope Reed (New York: W. W. Norton, 1977).
2. Indra Kagis McEwan, Socrates Ancestor: An Essay on Architectural Beginnings (Cambridge, Mass.: MIT, 1993).
3. This point is clearly presented and richly developed in Keith Critchlow, "The Platonic Tradition on the Nature of Proportion," in Homage to Pythagoras: Rediscovering Sacred Science, ed., Christopher Bamford (Hudson, New York: Lindisfarne, 1994), pp. 133–68.
4. Arthur O. Lovejoy, The Great Chain of Being: A Study in the History of an Idea (Cambridge, Mass.: Harvard University Press, 1936).
5. Henry Wooton, The Element of Architecture (London: John Bill, 1624), p. 1.
6. Indra Kagis McEwen, Vitruvius: Writing the Body of Architecture (Cambridge, Mass., and London: MIT, 2003), p. 58, notes the distinction between building and architecture but does not parse the six criteria. Alberti accounts for all nine; the bridge from his interpretation to Palladio’s is in Vitruvius, I Dieci libri dell’architettura, trans. and commentary, Daniele Barbaro (Venice: Francesco Marcolini, 1556). Notable modern commentators are Herman Geertman, "Teoria e attualità della progettistica architettonica di Vitruvio," in Le project de Viturve, Actes du colloque internationale…1993 (Rome: École Française de Rome, Palais Farnèse, 1994), pp. 7–30; Alina A. Payne, The Architectural Treatise in the Italian Renaissance (Cambridge: Cambridge University Press, 1999), pp. 35–41 and passim in chapt. 2, who notes that "despite its remarkable modern fortuna critica, [the triad of the three conditions] holds a modest place in Vitruvius’ text," p. 267, n. 31; and Mark Wilson Jones, Principles of Roman Architecture (New Haven and London: Yale University Press, 2000), pp. 40–43.
7. Vitruvius, Ten Books on Architecture, trans., Ingrid D. Rowland (Cambridge: Cambridge University Press, 1999), Book III, chapter i, line 1; hereafter citations are from this translation, except that "precisely calculated relationships" is the diction in Richard Schofield’s translation (London: Penguin, 2009).; see also Rowland Commentary, pp. 188–89.
8. I, ii, 2.
9. Claude Perrault, Ordonnance des cinq especes des colonnes selon la methode des anciens (Paris: J.B. Coignard, 1683); Ordonnance for the Five Kinds of Columns after the Method of the Ancients, trans., Indra Kagis McEwen (Santa Monica: Getty Center, 1993).
10. Perrault moved the word toward its late eighteenth-century meaning as bilateral, mirror-image identity; see Giora Hon and Bernard R. Goldstein, From Summetria to Symmetry: The Making of a Revolutionary Scientific Concept (n.p., Springer, 2008).
11. Daniel N. Robinson, An Intellectual History of Psychology, revised ed. (New York: Macmillan; London: Collier Macmillan, 1981), p. 258.
12. I, ii, 3. The passage continues directly: "It is achieved when the elements of the project are proportionate in height to width, length to breadth, and every element corresponds in its dimensions to the total measure of the whole."
13. Indra Kagis McEwen, Vitruvius: Writing the Body of Architecture (Cambridge, Mass., and London: MIT, 2003), quoting p. 198 (original emphasis); see also pp. 210–12.
14. Dix livres d’architecture de Vitruve, corrigex et tradvits nouvellement en françois, avec des notes & des figures (Paris: J.B. Coignard, 1673), abridgement, Abregé des dix livres d’architecture de Vitruve (Paris: J.B. Coignard, 1674). An anonymous English translation appeared in 1692. The edition used here is the revised and enlarged second edition of 1684; p. 9, and p. 11, n. 8.
15. Demetri Porphyrios, Classical Architecture (London: Academy Editions, 1991), p. 41.
16. Marc-Antoine Laugier, An Essay on Architecture (1755), trans., Wolfgang and Anni Herrmann (Los Angeles: Hennessey & Ingalls, 1977).
17. Julien Guadet, Éléments et théorie de l’architeture (Paris: Librairie de la construction modern, 1901), vol. I, pp. 137–41.
18. Le Corbusier, The Modulor: A Harmonious Measure to the Human Scale Universally Applicable to Architecture and Mechanics, trans., Peter de Francia and Anna Bostock, 2nd ed. (Cambridge, Mass.: Harvard University Press, 1954); and Modulor 2: 1955 (Let the User Speak Next), trans., Peter de Francia and Anna Bostock (Cambridge, Mass.: Harvard University Press, 1958).