In the introduction we examined, and tentatively rejected, the idea that Palladio’s plans are based on his canonical rectangles or on ratios derived from musical intervals. Let us look further at two aspects of this subject.
The first point regards the proportions of individual rooms. Planmaker has shown that Palladio’s own list of canonical room proportions does not control his plan style. As to Planmaker itself, never in its splitting process does it check or adjust the proportions of a room except to ensure that it is less than two squares. It lets final room proportions lie where they fall, whether 1:1, 32:17, or 29:43. Yet, as we are about to see, Planmaker can nonetheless produce plans that an expert would not distinguish from Palladio’s originals. Of course one might try to argue that our truly Palladian Planmaker designs are that way precisely because, by chance, they consist mostly or entirely of canonically shaped rooms. If Palladio had deployed his canon of shapes in a consistent way this would be a cogent argument. But in fact he does so haphazardly—just as Planmaker does, in fact.
Let us illustrate. In figure 4.1 are two plans, one the Villa Ragona from the Quattro Libri (minus doors, windows, and stairs, which allows us to focus solely on proportions), the other a plan we drew by hand. Can you tell which is the original? Actually, it’s not possible: since Palladio uses his canon inconsistently, and since the only difference between the two plans lies in the shapes of the rooms, you cannot distinguish the actual from the imitation. To be truly “un-Palladian” means to break one of the rules we discovered in chapter 2, and neither of these plans does that.
Let’s make the game easier. It has been said that Palladio labels dimensions in the Quattro Libri not simply to tell us the sizes of the rooms but to signal their proportions.1 Palladio’s dimensions, supposedly, serve a higher pedagogical purpose. Accordingly, in figure 4.2 we add the dimensions. We label them on the actual Villa Ragona exactly as Palladio does in the Quattro Libri, and we label our imitation similarly.
But now that we have incorporated Palladio’s proportional signals into the plan we have to note that plan b, which has no canonically shaped rooms, is the real Villa Ragona, and plan a, which has eight canonically shaped rooms out of nine, is the fake. So not only is the Villa Ragona completely noncanonical, Palladio has emphatically let us know this by inscribing the room dimensions on it. Our fake, furthermore, is only one of many simple ways he could have “perfected” his plan had he so desired. (One might argue that the 5:4 proportion found in each of Palladio’s corner rooms is “harmonic” because 5:4 is a major third. But if Palladio considered 5:4 ideal, why didn’t he include it in his canon?)
Another example. Figure 4.3a is the Villa Zeno, Donegal di Cessalto, from the Quattro Libri, and figure 4.3b is our “corrected” version. If Palladio were indeed intent on using canonical proportions, it is puzzling that he did not make the two minor adjustments we show, to wit: at point 1 we extend the plan’s length by two feet, which makes the two 14 × 12 rooms into perfect squares; at points 2 and 3 we remove half a foot in width, which makes the ungainly 21½ × 14 rooms each a canonical 21 × 14, or 3:2, while the top center room becomes a canonical 28 × 14, or 2:1. So our slight changes lead to a total of six newly canonical rooms. They also create a symphony of fourteens and multiples of fourteen that one supposes would appeal to Palladio. Why didn’t he do something like this? One answer is variety—two adjacent rooms of the same size (14 × 14 in this case) are extremely rare in his work. But another answer is that he is much less doctrinaire than is commonly thought.
The second aspect of proportion that we want to discuss regards sequences of dimensions among rooms. These are what Wittkower refers to as Palladio’s “fugal system of proportion. “2 One could assert that by having Planmaker use split ratios like 1:2 (an octave) and 3:2:3 (two perfect fifths) to create room sequences, we are in fact implementing a fugal system of proportions between neighboring rooms, and that that is why Planmaker works in the first place. However, Planmaker uses many nonmusical split ratios, like 3:1 and 4:1:4, and produces Palladian plans anyway. Also, even when using a musical ratio such as 3:2:3 there is only a slight chance that Planmaker will be able to split the room into a musical sequence. For example, if it splits a 50-foot-wide space using a 3:2:3 ratio, the resulting rooms will be a nonmusical sequence of 18, 14, and 18 feet wide, because 3:2:3 does not divide evenly into 50 but only into multiples of 8. One could also bring in our earlier argument: truly Palladian Planmaker plans are that way because, purely by chance, they incorporate musical sequences.
Many of Palladio’s own plans contain dimensions that can never be massaged into a progression. The dimensions from the Villa Ragona (fig. 4.2b)—which has rooms that are 12, 15, 17, 18, and 21¼—and those from the Villa Zeno (fig. 4.3a)—with 12, 14, 21½, and 29—fall into no known musical, harmonic, fugal, arithmetic, geometric, exponential, Fibonacci, or other sequence we know of. The conclusion is the same as for musical proportions within rooms: Palladio uses musical sequences but does so inconsistently. One therefore cannot formulate a theory of his style based on sequences.
It may be significant that Planmaker is equally averse to laying out consistent musical sequences. Early in our work we tried to teach it to do so, but the task proved impossible. First, we could not assemble a usable set of them. For example, Wittkower relates the dimensions from the Villa Pisani—16, 18, 24, and 32—using five different ratios, some musical, some canonical. But he gives no indication as to which type of ratio to use where, nor as to the order in which they are to occur. Secondly, sequences only cover some of the dimensions in any plan. What do we do about the others? Similar rogue dimensions are the 7 and 46½ in Malcontenta (fig. 4.34). And thirdly, of course, there are the innumerable dimensions Palladio does not label. The order in which Planmaker could or should pick these stepchildren would have had a dramatic effect on any plan. Yet Wittkower’s theory gives us no guidance as to how to do so. What we need, instead, are the rules painstakingly discovered above in chapter 2.
Finally, a reply to those who have argued that one should use a shape grammar to generate plans consisting only of square rooms, and that one can worry about proportion later. This would mean that we would learn nothing about the actual role of proportion in Palladio—which, as we have just seen, is, despite its inconsistent occurrence, an all-important subject. By empowering Planmaker to generate proportions at random we have discovered the exact limits of that role. A shape grammar would not have taught us that Palladio’s proportional system is much less rigid, much less central, than previously thought, that musical and other ideal ratios don’t hurt but don’t by themselves determine Palladian qualities.
Palladio’s facades make the same point. Aside from remaining within certain bounds, they too conform to no rigid proportional rules. To show this, we have calculated the width/height ratio for all the villa facades in the Quattro Libri and plotted them on the bar graph in figure 4.4. What the chart shows us is that Palladio preferred facade width-to-height ratios of about 2:1 but used others as he saw fit. Reflecting this fact, our system accordingly has no fixed proportional link between plan width and facade height except for the constraints imposed by a few pieces of data that Planmaker passes to Facademaker (see chapter 3). This insouciance exactly matches the master’s.
Using a noncomputerized version of this method, furthermore, Palladio would have been able to design a building fairly rapidly. The method’s flexibility, indeed, was probably one thing that made it possible for him to design large numbers of unique buildings—in other words, to be “paradigmatic.” We should therefore not be surprised that he was prolific. Between 1531 and 1580 he was responsible for no less than 143 projects and buildings, not to mention scores of drawings, illustrations for Barbaro’s Vitruvius, and the Quattro Libri. This comes out to an average of three built buildings a year.3 Given the technology of the time, the remoteness of many of the sites, and the complexity of some of his large urban projects, Palladio’s output is considerable. We believe that this productivity is in part, at least, the result of his efficient system of laying out plans and facades.
To buttress the point we turned to the Macmillan Dictionary of Architects, which lists a total of eight Italian architects more or less contemporary with Palladio who each produced 20 buildings or more (fig. 4.5). (The Dictionary credits Palladio with only 95 structures rather than the 143 in Puppi’s catalogue; it does not count small jobs, altars, doorways, and the like.) The difference among the architects is striking: Palladio’s productivity is more than double that of his next most productive rival, Michele Sanmicheli, and triple or quadruple that of everyone else.
The method we have described works well for most types of Palladian villa, but there are other designs by Palladio that it could never produce. Let us look at a few of them: the experience may help whoever wants to continue with our project. More important, it will give us further insights into Palladio’s mind.
First of all, Planmaker cannot produce circular rooms as in the Rotonda (fig. 4.6b). To correct this failing, we could of course tell the program to inscribe a circle every so often in one of the square rooms it so frequently produces. We could then get circular rotundas with four identical residual rooms as in figure 4.6a, as in the Rotonda itself, or as in the Villa Trissino (fig. 4.6c). But unfortunately there is more to it. Figures 4.6b and c illustrate the only two circular rooms in all Palladio’s published domestic plans. In both schemes the rotundas must sit precisely in the center of the whole. To extrapolate a rule from these two examples, we would have to allow Planmaker to inscribe a circle in a square only when the square is central and the plan symmetrical on both the x and y axes. Theoretically Planmaker can produce such plans, but statistically the chances of its doing so are nearly zero. Anyway, this type of plan, we have just seen, is a rarity in Palladio’s own domestic oeuvre. We can set it down as a “sport,” an interpolation from public and urban architecture.
Similarly, Planmaker is at present unable to design T, I, and Greek cross–shaped rooms; and these shapes are not rarities in Palladio. Given our present technique, the only way to create them is to erase some of the walls in an all-rectangle plan. All of Palladio’s nonrectangular rooms are in fact just such derivations from rectangular spaces; he himself erases walls, so to speak. The Villa Pisani at Montagnana (fig. 3.18b) and a study for the Villa Gazzotti (fig. 4.26) are typical. (The facade we generated for this latter building, by the way, is extremely close to what was built.)
But, again, there is more to it. Look at two of Palladio’s most memorable nonrectangular spaces, the Greek crosses of the villas Barbaro and Malcontenta (figs. 4.22, 4.34). Carving out crosses like these from completed plans is difficult and would require a Planmaker much cleverer than ours. Furthermore, Palladio seems to have developed his plans from the crosses, while Planmaker always does the reverse and starts with the building’s envelope. It would therefore have to carve its crosses out of whatever central set of symmetrical rectangles it ended up with. This is no minor computational task. On the other hand a new or alternative Planmaker, specifically for central-plan houses, is certainly a possibility.
Palladio’s facades are also less tersely defined than we have implied. Some do not conform to our horizontal structure of a center zone and two outer ones. Others conform horizontally but cannot be modeled vertically as stacks of discrete blocks.
Figure 4.7a, a drawing in the Royal Institute of British Architects, London, thought to be either for the Villa Valmarana at Vigardolo or for that of Taddeo Gazoto at Bertesina, is what in our system we have called a simple base + center composition + roof facade. (If, as is thought, the villa was designed for two families, Palladio would purposely have replaced the normal single center focus with this pair of flanking foci.) To accommodate such a design to our system, we could easily divide the facade into our standard center zone plus two outer ones. But our current rules would still force the main emphasis onto the center rather than the two ends as in the drawing. The “center composition block,” a prime part of Facademaker’s procedure, is simply not present in Palladio’s scheme. Facademaker, furthermore, draws only rectangular windows in the outer zones, and here the outer zones have serlianas. The roof block, meanwhile, unlike those created by Facademaker, has not one pediment but three.4
On the other hand, in the Villa Thiene, Cicogna (fig. 4.7b), Palladio does not redefine the zones but does append a second pair of outer zones. The facade area between the towers is perfectly producible by our system. And our system could also produce two pairs of outer zones. However, whatever outermost pairs it produced could never consist of separate horizontal groupings each with distinct rooflines yet without entablatures, as here.
The project for the Villa Poiana (fig. 4.8) also defies our method—not horizontally this time but vertically. It cannot be analyzed into blocks because the entrance arch has deeply invaded the attic block. Our system has to separate facades into discrete, consistently horizontal bands, and we note that nearly all of Palladio’s other villa facades are treated in just this way. In this sense Poiana is the exception that proves the rule.
Other facades go beyond our present possibilities in other ways. The Villa Sarego (fig. 4.9a) is zoneless, according to our system, because its U-shaped portico has no defined center aside from the front door. Figure 4.9b, a drawing for the Villa Pisani at Bagnolo, is also unusual. Horizontal and vertical elements overlap on several layers. Palladio even has a colonnade side by side with flanking arches, which is common enough in the work of his contemporaries but unique among the villas we are considering.
The anomalies analyzed above involve one-of-a-kind specimens, so our failure to encompass them is not crucial. But our system does have a number of other foibles that are thoroughly generic to it. A more complicated program (taking up a huge amount of memory) could eliminate most of these generic foibles. For now we will content ourselves with simply pointing them out; we will hold the virtues of simplicity superior to those of completeness. (One problem with a too-perfect program, aside from its inordinate length, is that it would soon begin to narrow the options down to Palladio’s actual schemes. Its idea of what Palladio would do would turn quickly into what he did do, and nothing more.)
We will illustrate Planmaker’s foibles in decreasing degrees of “un-Palladianness.” The first few, indeed, are blatantly un-Palladian and could and should eventually be programmed out of existence. The later foibles imitate what Palladio himself did when, as happened, he broke his own rules. We should reemphasize that what follows applies only to villa planning, not palazzo planning. Most of the following “flaws”—for example, having a large number of room layers—are perfectly acceptable in city palaces.
First, the plans in figure 4.10 suffer from varying degrees of what we call checkerboarding. These are plans with too many rooms, especially too many interior rooms. None of Palladio’s own villas has more than twenty rooms or more than four interior rooms, including staircases. Some of our plans exceed these limits. Obviously this is the result of too much splitting and aligning. Although some of Palladio’s own plans do approach checkerboarding, he never designs unadulterated grids like those in figure 4.11. There is always at least one internal break or variation. The plans in figure 4.12, on the other hand, while they exceed Palladio’s limit as to the number of internal rooms and the number of rooms in general, are not checkerboards and so are relatively inoffensive. An obvious though somewhat clumsy solution would have Planmaker count the number of rooms as it went along. Then, when it came to the limit, it would simply stop splitting and draw out whatever it had done up to that point.
Another problem is Planmaker’s penchant for creating narrow rooms along the vertical center string. The largest room in every Palladian villa is not necessarily right in the middle of the plan, but it does always lie on this vertical axis. Therefore in the two plans in figure 4.13 the central vertical string is too narrow. As a result, even if Planmaker had not split the center rooms at all there would still be no room for a large central hall. In a related foible, the plans in figure 4.14 have center vertical strings wide enough to accommodate a large central hall, yet the largest rooms in both plans are on the flanks. This is a clear violation.
A third problem is that Planmaker can make plans with too many layers of rooms. We will define the number of horizontal or vertical layers in a plan as the greatest number of rooms intersected by any line drawn perpendicularly through the plan. For example, figure 4.15a has nine vertical layers and figure 4.15b seven. Palladio’s villa plans never have more than four. Given Planmaker’s proclivities, a plan with more than seven such layers would probably also have too many rooms. There are exceptions: figure 4.15c has an acceptable seventeen rooms but nine horizontal layers.
There is also the problem of extra interior rooms. As stated earlier, Palladio’s villas never have more than four, even counting staircases. Overall, the plans in figure 4.16 do not have too many rooms. Nor do they have far too many interior rooms, as the checkerboard plans usually do; but they do have a few too many—seven in figure 4.16a and five in figure 4.16b.
Another foible might be called disparate room scale. Palladio tells us explicitly that center halls are supposed to be the largest rooms in the plan. The plans themselves tell us that the disparity between the largest and the smallest rooms should not be too great. Even if we consider small staircase halls as rooms, Palladio’s most extreme ratio is 9:1. To our eyes, both plans in figure 4.17 seem misproportioned because they have largest-to-smallest room ratios of about 14:1.
We have seen that, despite its several foibles and occasional outright failures, Planmaker is nonetheless capable of true Palladianism. Let us now look further at some of these triumphs.
A first group of designs consists of what we will call doughnut plans. These follow the basic form of figure 4.18a, consisting of a single layer of rooms around a central hall (figs. 4.18b–d). Palladio uses this simple doughnut arrangement occasionally, most notably in the Villa Rotonda (fig. 4.6b). The Villa Cornaro (fig. 3.20b) is another such. A second basic Palladian type is the upside-down U shown in figure 4.19a. Figures 4.19b and c have the same configuration, as do built villas like Angarano (fig. 3.20c). Most often, however, Palladio’s plans are neither pure doughnut nor pure U but variations on these shapes. The Villa Valmarana at Lisiera (fig. 2.3a) and figures 4.20a and b are thus quasi doughnuts, since the outer layer is not always one room deep. Similarly the plans in figures 4.20c and d, as well as the Villa Zeno (fig. 2.16a), are what we might call partially multilayered U’s.
The designs shown so far have no close counterparts in Palladio’s oeuvre. In other cases, with no prompting on our part and purely by virtue of their own internal rules, Planmaker and Facademaker created close approximations of actual villas by Palladio. In the following pages we will set designs by Planmaker and Facademaker next to their closest Palladian cousins. (We have felt free to remove walls manually from some of our plans in order to create nonrectangular spaces, e.g., Greek crosses. Where we have made these manual alterations we illustrate the computer’s original in the center and the altered version on the right.)
In the Villa Angarano, to take one example (fig. 4.21), the five small rooms surrounding the top of the center hall are all an “imperfect” 18 × 13 feet. In Planmaker’s version they are perfect squares. Unlike Palladio’s center hall, Planmaker’s is not a perfect 2:1 rectangle, but you can’t see the difference without measuring. The facades of the two villas also teach an interesting lesson. The Villa Angarano has four columns and the computer’s facade six. In this case Facademaker is being more “Palladian” than Palladio. Palladio tells us that his columns are 4 feet in diameter, and from the plan we know they are 18 feet apart. So the intercolumniation ratio is 18:4, or 4.5:1. This is considerably greater than Palladio’s own prescribed 2:1 ratio for the Corinthian order. But, by using only four columns, Palladio was able to locate the outer zone windows on the facade so that in plan they line up on axis. Facademaker on the other hand played by the rules: it used a ratio of 2.5:1, and so had to insert two more columns. Consequently, its windows are off-axis. In short, Palladio knew when to break his own rules.
The Palladian villa, especially as published in the Quattro Libri, was an essential model for later Venetian architects, chief among them Vincenzo Scamozzi. Farther afield, Palladio’s ideas deeply influenced the work of Lord Burlington, William Kent, and James Gibbs in England and that of Thomas Jefferson in America. Palladian ideas have marched on down to the present. Colin Rowe has shown that striking parallels exist, for example, between the plans of Palladio’s Villa Malcontenta and Le Corbusier’s Villa Stein.5
One virtue of our rules is that, in a more systematic and convincing way than hitherto, they can be used to separate Palladio’s own work from that of his host of imitators. Let us begin with Palladio’s closest follower, Scamozzi. In his plan for the Pisani villa at Rocca Pisana presso Lonigo (fig. 4.37), the building is contained in roughly a 60-foot square. A central dome is set into a square base exactly one quarter the size of the outer square. So far the building is strongly reminiscent of Palladio’s Rotonda (fig. 4.36). But instead of rotating an L of rooms at 90° intervals around the dome core, as Palladio does in both his domed villas, Scamozzi’s scheme makes use of Palladio’s own more characteristic system: he has a central vertical string of spaces with symmetrical flanking sides. Here is a triple vertical split with a ratio of 1:2:1, which establishes the two outer sections, and then a central string containing the dome. The horizontal split meanwhile is 2:1:1:3. In short Scamozzi here puts together two Palladian systems, strings on the one hand, rotated L’s on the other, that Palladio himself kept distinct. Nevertheless the result is close to being in accord with our rules. And the facade, except for the octagonal drum, is also something that our software might easily produce.
Yet Scamozzi did not always remain so tightly tethered to his master’s rules. His plan for the Villa Molini, near Padua (fig. 4.38), is a standard Palladian doughnut but has an asymmetrical stair. In the facade there is what we would call a perfect half entablature block, plus a column with dado block that is on top of a center composition block. But Palladio never seems to have designed a belvedere of the type we see here. Scamozzi also departs from Palladio in his project for a villa on the Brenta (fig. 4.39). The plan follows Palladio’s rules to the letter except that the central hall is about thirteen times larger than the small rooms adjacent to the stairs. This un-Palladian disparity is even greater if we consider the whole central string as a single room of Greek cross shape. On the facade, meanwhile, the third-story windows bleed down into the column block. Though there are a few Palladio facades that, similarly, are not composed of truly discrete sections, none of them uses the arrangement Scamozzi has chosen here.
Indeed for Scamozzi even such a basic Palladian necessity as the rectangular perimeter was not particularly normative. He has many T-shaped plans. And, though he often worked on a larger scale than Palladio, he preferred not to use the colossal orders Palladio loved. Instead, he favored individual superimposed colonnades or pilastrades for each floor. In fact only a small proportion of the designs in Palladio’s repertory fully overlap, in terms of our rules, with Scamozzi’s most characteristic work.
The most important center of Palladianism outside Italy was probably Great Britain. During the seventeenth and eighteenth centuries a whole series of classical country houses was erected, most of them, then and now, described as “Palladian.” One of the earliest is by Inigo Jones’s assistant John Webb. A glance at Webb’s design for the famous south front of Wilton House, near Salisbury (c. 1649; fig. 4.40),6 however, shows that the whole shape by our standards is far too long and low. The Baroque central stair with its four differently oriented flights is equally anomalous. Palladio’s only remotely comparable design is that for the Villa Pisani at Bagnolo (Quattro Libri, 2.47), which has lateral towers and an arched frontispiece. Other examples could be mentioned. But Palladio does not integrate towers with pedimented tops into the facade plane, as happens at Wilton, and he certainly never starts a story, as at either end of Webb’s facade, and then fails to continue that story across. Finally, he never designs a frontispiece that is so small by comparison with the facade as a whole.
Another instructive design is Colen Campbell’s 1715 plan for Wanstead I (fig. 4.41a). Here, first of all, there is an un-Palladian disparity between the largest and the smallest room (about 15:1). Another, more obvious departure is in the areas of the plan indicated by the arrows (added by us). This arrangement of rooms we call a spiral cluster (fig. 4.41b). Why might such a device interest an architect? For one thing, spiral clusters are the only way to divide a given rectangle into smaller ones without splitting. (Notice that no wall in fig. 4.41b runs all the way through from perimeter to perimeter.) Spiral clusters are frequently found among devotees of the golden section. Such an arrangement is not found anywhere in Palladio, for it cannot coexist with the technique of splitting.
Figure 4.42 reproduces one of the most Palladian designs from James Gibbs’s influential Book of Architecture (1728). The facade is fully in one of our sixteen styles—a center composition block plus attic—though the quoins, corbels, and window frames (treated with “Gibbs surrounds”) give it a heavily British look. And the plan is definitely quirky. The staircases are not symmetrically sized and the windows do not line up with the interior doors. Other Gibbs houses are much more obviously non-Palladian. Many of his plans do not have rectangular perimeters but jog in and out in a resolutely post-Palladian fashion (fig. 4.43), or else they have interior corridors (fig. 4.44), a feature never found in Palladio.
The most exalted and sedulously imitative Palladian in Great Britain was of course Lord Burlington. Yet consciously or unconsciously he was as loose in his interpretations of his master’s rules as any of the other architects we have discussed—indeed more so. Both in plan and facade, Burlington’s famous villa at Chiswick (fig. 4.45) utterly abandons Palladianism as we define it. The octagonal drum for the dome is heterodox—borrowed, it is often pointed out, from Scamozzi’s Villa Pisani (fig. 4.37). Equally un-Palladian are the various elaborate multiaxial arrangements for front steps that were built or planned.7 Much more non-Palladian, not to say anti-Palladian, is the basic conception, in plan, of the wall-to-volume structure. Palladio designed buildings composed of uniformly thick walls surrounding rectangular (and, very occasionally, cylindrical) rooms. Chiswick, in contrast, goes back to the tradition of Bramante and Michelangelo, as revived in the age of the Baroque: it is essentially a set of volumes carved out of a solid mass, as in a cave or rock-cut temple. Indeed, if we take account of the thick window embrasures and other ways of funneling light into the rooms, we have in Chiswick an essentially seventeenth-century arrangement of heterogeneous geometrical shapes: octagons, a cylinder, a double-apsed rectangle, plain rectangles, and squares (fig. 4.46). Burlington also includes a circulation space that verges on being that supremely un-Palladian feature, an interior corridor.
America’s own great Palladian architect, Thomas Jefferson, was no doubt inspired by the Quattro Libri as well as by some of the many books it spawned.8 The earliest versions of the design for Monticello date from 1771. The plan, however, which underwent changes over time, is less indebted to Palladio than it is to the anti-Palladian Chiswick.9 Indeed one can recreate the plan of Monticello, at least in the 1796 version (fig. 4.47), by reshuffling Chiswick’s component room shapes into Monticello’s distributions (fig. 4.48). Allowing for overlaps, the proportions and number of the shapes remain unchanged. Chiswick’s central octagon establishes the thrust half-octagon portico in the center of Jefferson’s house. Chiswick’s two larger square rooms turn into Monticello’s two front chambers. Burlington’s two smaller square rooms, at the rear, then become Jefferson’s two rear chambers. The Chiswick cylinder and small octagon melt into Monticello’s front rooms to make the larger polygonal bays on the forward sides of Monticello. And the apses of Chiswick’s rectangular hall do the same for Monticello’s rear chambers.10 The two lateral rectangles at Chiswick, finally, are rotated and placed one on top of the other to become the central spaces of Jefferson’s house.
The discussion could be continued, but by now our point is made. By distinguishing between the certain, the possible, and the impossible, by showing how Palladio salted his firmest rules with statistically measurable doses of preference, we claim to have defined the layout and facade of the Palladian villa better than has been done so far. To us, in fact, these ideas comprise something that can be developed further. We believe we have found a new way of analyzing architectural design, a way not based solely on an architect’s numerically limited accomplishments, however brilliant, but on the far greater realm of possibilities that may be rigorously extrapolated from those accomplishments.