PRÉCIS OF A RENAISSANCE APPROACH TO CLASSICAL
GEOMETRY, PROPORTION & COMPOSITION

PART I

David Mayernik, FAAR, RSA
Assoc. Prof., University of Notre Dame

6 November 2006

CONTENTS

INTROIT

A PRIORI
The Renaissance and Antiquity
Process and Proportion: Building types, precedents, and stories
The Canon and Principles: Inductive vs. Deductive reasoning

RHETORIC & POETICS
The Importance of Alberti, Bramante, and Serlio
The Idea of the Orders
The Orders, the Body, and the Canon: “Male and female He made them”
Vignola and the Judicious Ideal

MUSIC
A Priori: Seeing Numbers, Watching Music
A Fixed Ideal and Composition: Polyphony and the Fugue
Bays, Rhythm, and the Colossal Order

BRIEF BIBLIOGRAPHY: Part I


Go to PART II
 


INTROIT

It is a fact of history that the Renaissance marked a new approach to the classical architecture of antiquity that was rooted in both a rigorous recovery of the past and a new inventiveness; it gave the great European cities much of their form that we admire today, and its approach to classicism was important even for the succeeding era of Neo-classicism, if only in reaction against it. The very word “renaissance” has entered our vocabulary with overridingly positive connotations of genius, renewal, and cultural flowering. Strangely enough, the Renaissance is perhaps the least loved epoch of the whole classical tradition among leading contemporary classical architects; whether it is those who locate the beginning of modernism there, or rather those who long for a more literal rebirth of antiquity and see the Renaissance as a misguided attempt at the same, or even those of a simply anti-Italian bias, much misinformation circulates about the Renaissance approach to design principles (often fueled by outdated historiography). This précis is an attempt to correct at least some of the misinformation, in order to rehabilitate our understanding of what is certainly Western culture’s most fertile period (whose legacy is still a living context for modern life). The period here defined as the Renaissance extends from Brunelleschi through the middle of the eighteenth century (acknowledging that the seeds of the Enlightenment that would undermine it were already planted in France in the seventeenth century). I will limit myself to formal issues of geometry, proportion, and composition, but it should be always borne in mind that formalism in pre-Modern culture was always in the service of poetics.


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       One simple Renaissance approach to geometry, proportion, and composition may be impossible to define; however, a fairly consistent, albeit complex, intellectual trajectory can be mapped across the fifteenth, sixteenth, and seventeenth centuries whose principles evolved but didn’t fundamentally change. This path (with some deviations but no real detours) runs through architects as diverse as Brunelleschi, Bramante, and Bernini. It is this trajectory that the following précis (of an inevitably larger argument) attempts to map out.

       This discussion is based on the belief that the Renaissance represents a pinnacle (perhaps the pinnacle?) of the classical tradition in painting, sculpture, architecture, and urbanism. It seeks to elucidate the core principles operating behind Renaissance works in order to regain the capacity to operate that way again, so that we might equal or exceed their achievements. It is also based on some a priori assumptions, which are described below.


A PRIORI

The Renaissance and Antiquity
       If the Renaissance was an attempt to recreate antique architecture, it failed. Neoclassical critiques of the Renaissance tradition to this day have presumed this straw man argument, but in fact Renaissance architects were quite aware that what they were doing was something new, and they believed their unique historical position (not to mention their understanding of God) afforded them a new, critical outlook on the classical language that placed them in a privileged position to exceed the ancients. Antiquity for the Renaissance may have provided a standard of judgment (of sophistication, magnificence, scale), but Alberti for one believed his humanist training afforded him a more systematic and comprehensive intellectual approach to design than the one offered by Vitruvius. When Raphael first discussed the Orders, therefore, or Vignola laid out a canon of the ideal for them, they were each consciously establishing a new, more rigorous approach to issues of composition than any known before. The measure of their success is determined both by the intrinsic merits of what they built and the new criteria they established for the design process.

Process and Proportion: Building types, precedents, and stories
      Renaissance architects began the inventive process from a mental library of great buildings. New buildings were generated out of old, new building types were defined by analogy to other extant types, and new approaches to the classical repertoire of forms emerged metamorphically from the presumed principles of old forms. Precedents didn’t justify forms, as they would much later for Postmodernists, but rather formed a culture of building, a pantheon of forebears, and a challenge to emulation. In some cases the buildings, like lost ancient paintings, were known only from descriptions by Roman and Greek writers; as more new work that emulated the ancients came into being, these new buildings (like Bramante’s Tempietto) enriched the canon and provided new models for emulation. Like an oral narrative tradition, the stories of buildings were reiterated and transformed in each generation’s telling.

The Canon and Principles: Inductive vs. Deductive reasoning
      One cannot arrive at the forms of the classical language of architecture directly from the principles of geometry. These forms (ionic capitals, triglyphs, acanthus leaves) are the result of cultural narratives, tectonics, and mimesis. Of course, Alberti discusses geometric principles—points, lines, planes—in the course of both his treatise on perspective (Della Pittura, or On Painting) and his treatise on architecture (De Re Aedificatoria, or the ), but he presumes that one is already familiar with some sense of illusionistic space in the first case and architectural elements like columns, walls, etc. in the second. His geometric discussion is a corrective to sloppy thinking about the nature of these elements, but he never presumes that the elements can be generated directly from abstract geometry.
      In the same way as one can not arrive at classical forms from classical geometry, one can not arrive at a canon nor a set of principles from purely abstract reasoning (or, in other words, by deductive reasoning). A canon presumes noble exemplars, and the principles of the canon are induced from the evident principles operating in those exemplars. Given the implicitly trial and error nature of this process, and the changing nature of those doing the canonizing, the canon is per force evolutionary—it is working toward an ideal, but it does not (indeed, cannot) perfectly represent it. At the same time, singular moments of achievement can be recognized as being—in some sense—“perfected,” or as close to perfection as is humanly possible.


RHETORIC & POETICS

The Importance of Alberti, Bramante, and Serlio
      The first Renaissance treatise on architecture, and the perhaps first ever treatise on painting, were both by the humanist Leon Battista Alberti. It is significant that Alberti’s The Art of Building in ten books simultaneously matches Vitruvius’ number of books and serves substantially as a critique of the Roman author’s methodology. Given Alberti’s admiration for Brunelleschi (to whom he dedicates the Italian edition of his On Painting), who searched in the remains of ancient Rome and Florence rather than in Vitruvius for the principles of the good, old way of building (and then corrected them with the most systematic approach to proportion and rhythm yet available), it becomes obvious that the early Renaissance was not prepared to take Vitruvius’ words as gospel. Implicitly they sought to articulate, at its inception, a rebirth that would be something new and improved.
      Donato Bramante never wrote a treatise, but his work served as built theory of a full-blooded classicism for his and subsequent generations. His contemporaries, and his intellectual apprentices like Raphael, recognized in his Roman work an ancient grandeur reborn that trumped the past. No more salient argument for this exists than Bramante’s famous idea for St. Peter’s as placing the rotunda of Sancta Maria ad Martyres (the Pantheon) atop the Temple of Peace (the Basilica of Maxentius and Constantine): by doubling the value of Rome’s two best ancient survivors he squared their achievements. Indeed, the idea that the whole was greater than the sum of its parts is the essence of Bramante’s Roman achievement: he coordinated plan, section, and elevation at St. Peter’s as no one had in the past. Michelangelo would famously say, when he took up the completion of the basilica, that those who had deviated from Bramante’s plan had “deviated from the truth.”
      Sebastiano Serlio notably apprenticed with the painter-architect Peruzzi. From him he absorbed a fascination with perspectival space; but he also imbibed the painter’s concern for the representation of the emotions, or the affetti, and one of his two great contributions to the classical tradition was in assigning to the Orders the affective qualities a painter would bring to his figures. His other great contribution was his clear-headed parallel of the Orders, for the first time ever shown in one image side by side in ascending order. And, indeed, these two achievements are intimately related: because without codifying or standardizing the proportions and details of the Orders, one can not precisely codify what they mean—and without an accepted set of meanings and a grammar one can not have proper language. We are accustomed to calling classical architecture a language, but it is arguably only with Serlio that that language becomes mature and capable of a coherent rhetoric.
      Arguably it is these three architects who best summarized and directed the Italian Renaissance approach to architecture. The achievements of a Michelangelo enriched the architecture of his age, but did not substantially define its premises as these three had. Palladio’s effect was enormous later and abroad, but in his own day was confined to the Veneto.

The Idea of the Orders
      Raphael, a painter, first uses the term “Orders” in his famous letter to Pope Leo X to describe the column types which Vitruvius had called genera (until then an “order” might most likely have referred to a monastic order; it also recalled God’s ordering of creation in weight, number, and measure). In this he was probably influenced (as Ingrid Rowland has shown, in The Culture of the High Renaissance, Cambridge, p.230ff) by a parallel argument of the humanist Pietro Bembo, who wanted to “order” an ideal, Ciceronian style of writing prose. Raphael’s search for perfection in painting—his constant absorption of influences seemingly guided by a clear teleological vision—led inevitably to a similar desire in architecture. Guided in its early phases by his distant relative and mentor Bramante, his architectural projects (painted in the Vatican Stanze, built at the Villa Madama) aspire to be both complex and integrated. Integrating a facade’s stories at the Villa Madama led to perhaps the first use of colossal order, for which Michelangelo would provide the public paradigm on the Campidoglio. If there is anything which condenses the value of this “ordered” way of thinking of columns and pilasters, it is the colossal order: for the first time, multistory buildings could be seen as coherent entities, not made simply of stacked floors. The web of horizontal and vertical elements that Bramante, Raphael, and Giulio Romano disposed on their Roman palazzi facades found their most sophisticated compositions in church facades from Michelangelo’s San Lorenzo in Florence, Palladio’s San Giorgio and the Redentore in Venice, and Giacomo della Porta’s Gesù and Carlo Maderno’s S. Susanna in Rome (see below).

The Orders, the Body, and the Canon
            masculum et feminam creavit eos (“male and female He created them”)
            --Genesis 1:27
      It is telling that, while antiquity long operated in sculpture with the paradigm of Polyclitus’ famous Canon (articulated in both a sculpture — the Doryphoros — and a text; see http://www.mlahanas.de/Greeks/Arts/Doryphoros.htm), the classical orders were not so fixedly prescribed. Whether the Renaissance was incorrect in believing the ancients had a precise body-column analogy in mind, or whether they recognized that they were articulating something wholly new, their efforts toward defining a limited range of proportions for each of the Orders (and associating each with a specific body type) brought the narrow bandwidth of the figurative canon to classical architecture. Liberated thus from reinventing the column types for each building and site (as Vitruvius and the disparate antique survivors seemed to suggest), they could move onto more complex systems of composition (see Music, below). Moreover, they were also thus capable of making their buildings “speak” more precisely as rhetorical and poetic “texts,” since they now had a more precise repertoire of moods, allegories, and heroes available.

Vignola and the Judicious Ideal

I shall only say that if someone would dismiss this labor by saying that it is impossible to formulate a Canon with certainty since, in everyone’s opinion, and especially Vitruvius,’ it is often necessary to enlarge or reproduce the proportions of the parts of ornaments in order to compensate artificially for the imperfections of our eyesight, my response in this case would be that it is always necessary to know what we want [my emphasis] our eyes to see, and this will always be a firm rule regarding what is intended to be perceived.
Giacomo Barozzi da Vignola, trans. Branko Mitrovic, Canon of the Five Orders of Architecture, Acanthus Press, 1999 (“To the Readers”)

That the ideal is what we want to perceive is the root of the classical outlook. It is telling that Vignola uses the word Canon for the title of his small, but wildly influential, treatise on the Five Orders of Architecture. Like Polyclitus, his aspiration was to define a fairly fixed ideal for both the whole and the parts; the column as a body, with feet, torso, and head, supporting the weight of the entablature above, could now have a kind of consensus about its ideal, and thus its employment could be more exacting, subtle, and meaningful. Moreover, as he says, it will establish an ideal by which all specific adjustments can be measured. Vignola’s own work illustrates just how nuanced this new dispensation could be: razor-thin layers of pilasters, robust rustication, and graceful brackets make his facades (like Villas Lante and Giulia) sophisticated exercises analogous to contemporary madrigals by the likes of Palestrina, Lassus, or Gabrieli.


MUSIC

A Priori: Seeing Numbers, Watching Music
      Numbers are, of course, abstractions if divorced from quantities. Numbers in architecture, in practical terms, can only really be seen as quantities: a number of columns, a number of bays, a number of floors. In order for numbers to be seen, in other words, they have to be assigned to countable things. Therefore, an architecture that depends on number must establish quantities. Conversely, ratios cannot be seen precisely qua ratios: we cannot readily perceive the difference between a 2:3 proportion rectangle and a 1.95:3.05 proportion rectangle, for example. However, we can count things that are disposed proportionally: the number of gridded squares in a floor pattern or in ceiling coffering, the number of columnar bays on a long elevation vs. another number of equally sized bays on a corresponding short elevation, etc. One thinks of Brunelleschi at San Lorenzo or Sto. Spirito. The ratios beloved of aficionados of proportion are only credible, then, if they can be assigned to recognizably modular elements that can be easily counted (or, effectively, measured by the eye in the real world). Along the same lines, the magical “Golden Section” rectangle is only available to those who can measure it—it does not in any practical sense exist if it cannot be measured and therefore known; and, being composed of an irrational ratio, can not be made up of any modular elements, which means it is of limited value in real world architectural proportioning. It is doubtful we perceive a rectangle of 1:1.618..., even more so when it is part of a classical facade subdivided into smaller bays by pilasters, etc.


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      If Goethe’s memorable expression that “architecture is frozen music” rings a bit hollow after too many refrains, there is still value in seeking out ways to articulate the very real rapport between the architectural and the aural. After all, one certainly can speak about the “structure” of a piece of music, the “architecture” of a Bach fugue; in the same way, musical analogies come readily to mind when describing complex architectural systems (Wittkower spoke of Palladio’s “fugal system of proportions”). While architectural space is inherently static and music dynamic, architecture is less often statically “seen” (as an orthographic image, for example) than dynamically experienced; or, could not one speak of “watching” architecture as one moves dynamically through it? If so, then elegant spaces and forms do unfold musically, but are not at all “frozen.” Rhythm, rest, stress, accent, tempo, etc. all can find their visual counterparts in the progress down a church nave, and these, rather than simple chords played out in orthographic ratios, are the compellingly musical parts of architecture. Even the moldings of the classical syntax can be understood this way.
      This dynamic approach helps explain a facade like Palladio’s Palazzo Valmarana, whose unstressed ends make sense as part of a gradual building toward the center, something that makes sense on the narrow street in which it is experienced rather than in an orthographic elevation. It is perhaps not surprising that the two architects most associated with Renaissance proportion, Brunelleschi and Palladio, favored two-toned materials for order and wall in their churches. The graphic clarity of this approach facilitated the reading of their compositional rhythms.

A Fixed Ideal and Composition: Polyphony and the Fugue
      If the Renaissance tendency toward standardization of the classical orders with more or less fixed proportions and forms gave up something as regards flexibility within the types, it gained much in facilitating complex compositions with the orders: especially major and minor orders, but also rational systems of stacking one order over another, a precise calibration of order hierarchies, a tighter analogy with musical modes (relative gravitas vs. lightness, etc.), and more predictable horizontal rhythms across a facade or interior. Just as standardized musical notation facilitated ever increasingly sophisticated compositions, so too did arabic numbers and a common canon of the orders allow the rich harmonies of Renaissance facades.


 

What makes the comparisons of Brunelleschi and DuFay, or Borromini and Biber, fruitful is the way in which one can count and compare visual elements the way one unconsciously counts notes (in other words, seeing pilasters or aedicules, and understanding the number of each per bay, is not dissimilar to hearing whether a syllable gets one or more notes). Just as Elizabethan England frowned on papist polyphony, neoclassicists eschewed precisely this polyphonic and melismatic (more than one note per syllable) approach to the Orders and composition. And just as, for Bach, the fugue was the ne plus ultra of composition, so too were the complex overlays of a Baroque church facade or interior the pinnacle of what Renaissance architecture could do (see della Porta’s facade of the Gesù).

Bays, Rhythm, and the Colossal Order
      Seeing that, more than the form of a particular Order, it was the distribution of the Orders according to bays that characterized Renaissance priorities, it is rhythm rather than numeric ratios which must have counted most to those architects’ minds. And with the overlapping melodic lines of polyphony defining Renaissance high style music, it is inevitable that the same overlapping constructs in architecture (the Colossal order, broken entablatures that link vertically stacked Orders, etc.) would typify later Renaissance aspirations (and would generally distinguish Italian from French and English exteriors in the seventeenth century). The idea of the Colossal order, and the concomitant understanding of major and minor Orders, is then the greatest contribution of sixteenth century architects to the classical tradition, in that it allowed architecture to keep pace with the extraordinary developments of music throughout the Baroque era.

Strategies of disposition of the Orders
      Combining columns and walls in the Renaissance was a rational exercise that led to systematic strategies for the disposition of the Orders according to requirements of decorum, rhetoric, and poetics. Again, these strategies are not ends in themselves, but speak metaphorically of larger, non-architectonic issues. From the simplest to the most complex they can be described as:

I.   Implied: the Order is not expressly present, but its character and proportions are implied by, or generate, the building’s elements of cornice, base, window rhythm, etc. of a facade; Roman palazzi are paradigmatic examples

II.   Emblematic: the columns and entablatures retain their integrity and reference to the temple type precisely by not establishing a system across a facade, but rather remaining discrete or autonomous; the points of contact between the Order and the wall (assuming the former is projected some distance in front of the wall) are as simply resolved as is feasible (if resolved at all); the Palladian temple front is paradigmatic in this regard

III.   En Ressault: a detached column’s entablature breaks away from the face of the wall, creating autonomously articulated columnar units often crowned by a finial or figure

IV.   Embedded: the pilaster or engaged columns are treated as if they are piers or columns, respectively, whose complete presence is contained within the thickness of the wall; coincident with the wall, therefore, they are assumed to be essentially continuous with it, their presence either explicit or implied wherever the wall exists (unless an overt element breaks their continuity); an extreme but telling case is the stairway of the Laurentian Library

V.   Overlaid: the Orders exist as a thin “skin” grafted onto the wall surface; the thinness of the skin is relative, however, and can include robust elements like rustication; the entablature either responds solely to the plane of the Order, or breaks out from the plane of the wall over each Order or Order cluster; Vignola’s facades often partake of this strategy

VI.   Overlap: the Orders, especially employing the colossal order, overlap each other in often complex rhythms; this strategy can also describe the combination of arcuated and trabeated systems (Vatican Belvedere), the progressive stepping out from the wall of the same order (Roman church facades), or the interposition of a “stripped down” order between a full column/pilaster and the wall

VII.   Superposition: in the tradition of the Colosseum, the Orders are stacked one atop the other is sequences that run from the most rustic/simple at the base to the most refined at the top; in combination with wall articulation like rustication, the superposition can either stress the continuity from one floor to another (e.g. by broken entablatures) or the distinction of floors; in general, Roman church facades of the sixteenth and seventeenth centuries tend toward the former strategies, French of the same period the latter

VIII.   Fugal: more than one (or all) of these strategies are employed on a single facade or building; a sophisticated example is Borromini’s interior of S. Ivo or Le Vau’s Enveloppe facade for Versailles

 
BRIEF BIBLIOGRAPHY: Part I
These ideas have rarely been treated comprehensively either by treatise writers or historians, but they have been discussed in a fragmentary way in disparate places. Some of those are listed below:

Arnaldo Bruschi, Bramante
John Onians, Bearers of Meaning
Ingrid Rowland, The Culture of the High Renaissance


Go to PART II
 



 

 
 

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