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In "Palladio's Villa Emo:The Golden Proportion Hypothesis Rebutted" [March 2001], Lionel March argues that the Golden Section, or extreme and mean ratio, is nowhere to be found in the Villa Emo as described in I quattro libri dell'archittetura. Palladio, he says, "has given the actual measurements" and they simply do not add to a scheme of Golden proportions. He is absolutely right. The extreme and mean ratio is not observed in the Emo plan as it was published. But the villa Palladio described in that publication is not the villa he built and that survives today.
The discrepancy between the two versions was known as early as the 1770s. That was when Bertotti Scamozzi published Le fabbriche e i disegni di Andrea Palladio, in which he struggled to reconcile numerous inconsistencies between built and published versions of Palladio's works [Scamozzi 1976: 75-76]. Alas, Scamozzi's measurements were not as accurate as we would have liked. Fortunately, a more definitive survey was performed in 1967 by the architects Mario Zocconi and Andrzej Pereswiet Soltan for the Centro Internazionale di Studi di Architettura "Andrea Palladio" (C.I.S.A.) [Rilievi 1972; Favero 1972: 29-32 and scale drawings a-m].
Many believe Palladio's published plans present idealized versions of his buildings, permitting him to make adjustments for the special conditions of specific sites. But perhaps, in some instances, different versions provided options for design and proportional schemes. For example, the published plan for the Villa Emo presents a conventional set of stairs that leads to a south-facing portico. In fact, a unique, elongated ramp was built. Members of the Emo family today believe it served as both an entryway and a threshing floor to meet the villa's agricultural needs. Does it correct the building's proportions to substitute the ramp with shorter conventional stairs? The Emo family thinks not, and perhaps Palladio did not think so, either, for a corrected set of measurements is not indicated.
Different measures are specified, however, for the plan of rooms on the main floor of the central block, and these are the stuff of musical and mathematical harmonies, as Lionel March so brilliantly demonstrates. The discrepancy is subtle, perhaps too subtle to reflect real versus ideal conditions, but sufficient to suggest a different mathematical interpretation.
BUILT AND PUBLISHED MEASURED COMPARED
Overall length and width of the main floor plan
Lionel March calculates total length by adding individual measures along a north-south axis of length, including the lengths of three individual rooms and the thickness of four walls. For the moment, the thickness of any given wall is called x.
Total width is calculated in similar fashion:
Taking x = 1 as an initial choice for the wall thickness, following March, results in the ratio of total length to total width of 59:63, or 1:1.067.
How does this compare with the ratio of overall length to width in the villa's plan, as it was built (Figure 2)? According to the C.I.S.A. survey, total length and total width are 20.56 meters and 22.35 meters, respectively. Therefore, the ratio of length to width is 20.56:22.35, or 1:1.087. A subtle difference from the 1:1.067 ratio of the published plan, but one that may be viewed at a glance.
Since the published plan does not provide a measure for the thickness of walls, we cannot assume it is equal to 1. But applying a variation of Lionel March's method, we can determine what the thickness must be for the published plan to match the built plan's 1:1.087 ratio of length to width. In other words: (55 + 4x) : (59 + 4x) :: 1:1.087. To satisfy the proportion, the thickness of a wall x must be approximately equal to -2.2557 feet. Not quite as impossible as the negative wall thickness of over five feet required for a Golden Mean scheme to match the plan's published measures, but impossible nevertheless.
Overall length and width of the geometric scheme
Length and width of individual rooms
This does not mean that the inside measurements of the rooms as built convey extreme and mean ratios, either within themselves or in relation to others. But when the thickness of walls is factored to one side or another, a scheme emerges in which the overall rectangle divides continuously in Golden proportion.
Given the evidence of the plan as it was built, perhaps Lionel March will reconsider whether "the visually gratifying result is so very wrong when tested by the numbers."
Lionel March further cites the ancient theatres, which are based, Vitruvius tells us, on arrangements of squares and triangles and their inherent and proportions. Pentagons, however, are nowhere to be found. Never mind that the two sections of Epidaurus's theatron contain 21 and 34 rows and merely approximate a true extreme and mean division. I wouldn't consider it, either, were it not for a study by German scholars Gerkan and Müller-Wiener [1961: Pl. 3] that relates the theatre's skene, orchestra and theatron through a regular pentagon and its inscribed and circumscribing circles.
Let's face it. From as early as Euclid through the Renaissance and beyond, the extreme and mean ratio was not unknown. Beside the examples already cited, as early as 1726, well before the nineteenth century, mathematicians, builders and architects published exact geometric constructions based on the Golden ratio. Peter Nicholson, Batty Langley and others illustrated its use for architects and builders [Nicholson 1827: Pl. 13 and problem XXII; Langley 1726: Pl. I, fig. XXVII and p. 41]. Mathematicians such as Sébastien Le Clerc demonstrated numerous constructions in elementary texts [Le Clerc 1742: 112-113, 180-181]. In at least one instance, Ephriam Chambers linked the extreme and mean ratio to the pentagon's exact construction [Chambers 1738: opp. 142].
None of this proves that Palladio favored the extreme and mean ratio. He did not publish an exact construction, but neither did he produce a book on geometry comparable to Serlio's Book I. Had he written such a book, might it contain an extreme and mean construction? Unfortunately, we probably will never know.
It is true that the extreme and mean division does not rank among Palladio's ratios for shapes for rooms. All but one, in fact, are comprised of ratios in whole numbers. But these address individual rooms, not the plan as a whole, nor the rooms as they relate to one another. The beauty of the Golden ratio, as it adorns the Villa Emo, is that it distinguishes the plan as a whole and persists through every level of subdivision. "Proportion" is defined conventionally as the relationship of parts to one another and to the greater whole. One would be hard pressed to find a better example.
Finally, Lionel March's most compelling argument is the practical one. "Buildings" he says, "have to be set out," and triangulation has been the method of choice "since time immemorial". Certainly, the Pythagorean 3:4:5 triangle is well suited to achieving the right angle, but surveyors may use triangles for many purposes. Consider the simple right triangle of sides one and one-half: it does not ensure the right angle, but its hypotenuse leads directly to the Golden Section.
We base our understanding of the past on precious little evidence and so it is prudent, from time to time, to revisit what we know with a new and open mind. Without doubt, the Golden proportion hypothesis is filled with speculation, for we cannot prove that Palladio applied it with deliberate intent. And yet, given its persistence throughout the plan of Villa Emo, it may be time to consider if all the relevant evidence is in.
Lionel March is to be thanked for illuminating the many rich and wonderful mathematical techniques that grace the Villa Emo, from its 3:4:5 triangles to elaborate musical harmonies. Is it so hard to imagine that extreme and mean ratios occupied the Renaissance mind as well?
 To be precise, the tolerance throughout is within 1 cm., with the exception of a single 9 cm. deviation. return to text
 The circumscribing circle traces the inside face
of the theatron, or auditorium; the inscribed circle traces
the inside edge of the orchestra perimeter; and the base of the
pentagon locates the front edges of the paraskenia, or
the skene's projected wings [Gerkan and W. Müller-Wiener
1961: Pl. 3].
 The one exception is a room in the ratio of 1: root-2 [Palladio 1997: 59]. return to text
 A simple whole number ratio may suffice for an individual room to express grace and harmony. But Jay Hambidge  explains that incommensurable ratios such as the Golden Section permit a "dynamic symmetry" in which the same ratio persists through endless levels of subdivision. return to text
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Copyright ©2001 Kim Williams