Branko MitrovicSchool of Architecture UNITEC Institute of Technology Carrington Rd. Auckland NEW ZEALAND
The villa was designed in the winter of 1551-1552 and its
main block with the exception of the side wings was inhabited
by 1554 [Lewis 1972; 1975]. The side wings were completed only
in 1596 by Vincenzo Scamozzi, although they appear in Palladio's
presentation of the villa in his treatise,
In his treatise, Palladio listed his preferred room types:
circular, square or rectangular with length-to-width ratios 2/1,
3/2, 4/3, 5/3 or Ö2/1 [Palladio
1997, 1.52]. This list is commonly referred to as the list of
Palladio's preferred room length/width ratios. Its interpretation
and implications have been in the center of debates within Palladian
scholarship for the past 50 years.[3] In the second book of his treatise Palladio
presented plans of forty-four buildings he designed; in these
plans, room length-to-width ratios have been indicated for 153
rooms.[4]
Eighty-nine of these 153 ratios -- or 55% -- indeed correspond
to the ratios from Palladio's list. An analysis of the remaining
45% shows that some other proportional systems were used by the
architect as well. The ratio Ö3/1
appears in a number of plans -- most prominently in the plan
of the Rotonda -- as well as ratios such as and
[Mitrovic 2004,
65-70]. One may be tempted to speculate, but it would be impossible
to prove, whether there could have existed some background theory
which would have motivated the architect's choice of individual
ratios, both those stated in the list and those not mentioned
explicitly, but implicitly indicated in the plans of Palladio's
buildings presented in the treatise. Could such a theory account
for the remaining 45% of ratios which cannot be explained by
Palladio's list? For instance, all three ratios I have just mentioned,
Ö3/1, and
, as well as one
ratio from the list of preferred ratios, Ö2/1,
can be seen as cube-derived. Ö2/1
is the diagonal-to-side ratio of a square, Ö3/1
is diagonal-to-side ratio of a cube. and
are the solutions
to the Delian problem of doubling the cube: if Half a century ago, this kind of speculative search for the
comprehensive interpretation of Palladio's proportional system
received great impetus from Rudolf Wittkower's It is, however, important to differentiate between the derivation
of certain proportional rules and their explanation. In the case
of Palladio and Barbaro, their statements did not refer to musical
proportions in order to deduce which proportions should be used,
but only in order to explain an already existing practice. When
Wittkower emphasized the importance of the narrative about harmonic
proportions for Palladio's architectural theory, he adopted the
case-study method. In his book he analyzed only eight out of
forty-four Palladio's buildings presented in the Wittkower's was also an ideological position -- something we must never forget: by emphasizing the importance of the proportional relationships between room lengths and widths, he actually asserted that the use of ornamentation -- and especially the orders -- did not matter in Palladio's design process. This interpretation of Palladio supported the Modernist approach to design precisely in the years when the Modernist movement needed it the most, and, as I have argued elsewhere, it coincided with the commercial interests of architectural profession in the 1950s, which substantially contributed to the popularity of Wittkower's book. At the same time, even if Wittkower's interpretation were true, it really explains only Palladio's design procedures when it comes to the proportioning of individual rooms. In other words, the question of whether Wittkower was right
or wrong is ultimately an ephemeral one. Even if he was right,
his approach accounts only for a minor segment of the design
problems Palladio had to resolve in his work. A comprehensive
proportional analysis of a Palladian villa must take much more
into account. In his design work, Palladio had many other design
problems to resolve besides the length-to-width ratios of individual
rooms. Wittkower's theory did not even attempt to explain the
totality of proportional relationships between room dimensions,
such as the determination of room heights and mutual proportional
correlation of individual rooms. Palladio said that the heights
of rooms should be the arithmetical, geometrical, or harmonic
means of the height and width, if the room is vaulted. If the
room is square, its height should be 4/3 of the width, and if
the ceiling is flat, the height should equal the width of the
room. In Palladio's time, ground-floor rooms -- the level at
which a villa or a palazzo is entered -- would typically have
vaulted ceilings, whereas upper storeys would be covered with
wooden beams and have flat ceilings. Palladio's plans usually
consist of rows of rooms surrounding a sala (in the case of a
villa) or a central courtyard (in the case of a palazzo). If
we look at the plans presented in the An analysis of Palladio's works based on the proportions of rooms, is particularly applicable to his villas of the 1540s. These villas do not have orders applied to the façade. In this group belong Villa Godi in Lonedo, Villa Poiana in Poiana Maggore, Villa Saraceno in Finale, Villa Caldogno in Caldogno, and so on. But from the late 1540s and early 1550s Palladio started systematically using the orders in his designs and -- together with Palazzo Chiericati, Villa Pisani in Montagnana and the Basilica -- Villa Cornaro was one of first major works in which this new approach was manifested. It was in the decades of the 1550s and 1560s that Palladio and Vignola introduced a revolution in the Renaissance use of the classical orders. The standard use of the orders through the Renaissance before Palladio and Vignola implied that columns or pilasters were placed at regular distances and in those positions where internal walls cut the façade. Through the Renaissance it was common to disregard Vitruvius's advice that intercolumniations should not exceed three lower column diameters. In his treatise Vitruvius listed different intercolumniation types: 3 diameters for diastilos, 2.25 diameters for eustilos, 2 diameters for eustylos and 1.25 diameters for picnostylos. Typically, the Renaissance use of the orders before the 1550s relied on the placement of columns in the corners and at places where the internal walls cut the façade. Additional columns or pilasters would be added in order to ensure equal intercolumniations. The approach was regularly combined with disregard of Vitruvius's precepts for intercolumniations. The columns, pilasters and entablatures would completely frame the facade, but the wide intercolumniations result in a visually unpleasant span between columns or pilasters. The intercolumniations on the contemporary works the young Palladio could have seen near Vicenza by far exceeded Vitruvius's recommendations. Intercolumniation-to-diameter ratio on Giovanni Maria Falconetto's Porta Savonarola in Padua is 4.9; on Porta San Giovanni in the same city 5.8; on Michele Sanmicheli's Palazzo Canossa in Verona this ratio is 4.4; on the Villa Trissino it is 5.7 on the ground floor and 7.9 on the facade of the upper floor. Even on those Renaissance buildings which combine freestanding columns with entablatures, for instance on Brunelleschi's Pazzi Chapel, the ratio is 3.5; on Pirro Ligorio's Casino of Pius IV it is 3.7. This approach normally results in large empty wall surfaces and ultimately unsuccessful attempts to establish a visual rhythm on the facade. Before the 1550s, Palladio's use of the orders conformed to this Renaissance practice, in those cases when he used the orders -- e.g., Palazzo Civena, Palazzo Iseppo Porto, Palazzo Thiene or Villa Gazzotti in Bertesina. The placement of columns on the façade was thus an
important unresolved problem which Renaissance architecture faced
in the mid-cinquecento. The question was whether columns on the
facade should be placed in relation to the walls behind (to "express
the interior" as we would say today) or should they be placed
according to certain rules for intercolumniations, similar to
those Vitruvius stipulated. In his But Palladio, in the early 1550, formulated a very different approach to the use of the orders. A survey of the way his use of intercolumniations changed through his career shows that in the early 1550s he started systematically using intercolumniations of less than 3 diameters, as Vitruvius had suggested [Mitrovic 2004, 203-204]. Intercolumniation-to-diameter ratios are 2.75 on the palazzo Chiericati (1550), 2.7 on the villa Pisani in Montagnana (1552), 2.25 on the villa Cornaro, 2.4 on the villa Chiericati in Vancimuglio (1554), 2.3 on the palazzo Antonini (1556) and so on. With the exception of Villa Sarego, after the year 1550 intercolumniations of more than 3 lower column diameters appear only on those buildings where Palladio's involvement is considered debatable by Palladian scholarship. (Obviously, one must take into account that intercolumniations had to be increased over 3 diameters when it comes to the main entrances, and that upper storeys are likely to have larger intercolumniations, because columns in upper storeys have thinner diameters.) Palladio's approach differs from Vignola's in that the position of columns for Palladio had to correspond to the position of walls in the interior of the building. At the same time, the position of interior walls was determined by the proportional rules for length/width ratios, and proportional relationships between individual rooms had to satisfy the CCH rule. Consequently, the two sets of requirements for internal and external proportions had to be mutually coordinated. The proportional coordination of internal and external elements is further complicated by the fact that the internal height ("floor to floor") must equal the sum of column height plus entablature thickness on the façade. The introduction of these complex mathematical requirements
appears for the first time in Palladio's work in the Palazzo
Chiericati, at the very beginning of the 1550s ( It is in this context that the proportional system of the
villa Cornaro needs to be analyzed; it was for this reason that
we undertook a new surveying campaign. Together with Villa Pisani
in Montagnana, Villa Cornaro was designed within two years from
Palazzo Chiericati. In this case, the portico has only six columns
and it cannot be taken to determine the position of all internal
walls orthogonal on the façade (as is the case on the
Chiericati), but only of those behind the portico. The size and
proportions of the large sala, with its four columns, correspond
to the position of the columns in the portico. The sala in this
case is a typical Palladian four-column sala with a flat ceiling
-- a motif Palladio often used. The general morphology of the
villa and its volumetrics relates to other Palladian villas of
the same period, in whose plans we can similarly read the architect's
efforts to align internal bearing elements with the orders on
the façade -- e.g., Villa Pisani in Montagnana ( Analyzing the proportional system of an executed building is not the same thing as working with a set of an architect's drawing.[6] Precision in the execution of a built work can never be great. In the case of Palladio, we can safely rely on considerable precision in stonecutting. Those elements of the orders which were executed in stone show a high level of precision in execution. But when it comes to built walls and masonry work, the level of precision is not nearly so great. One can hardly expect precision greater than 5 cm. The building has also changed in the meantime; some of its parts have been changed and dimensions of rooms have been slightly altered by the addition of new layers to the walls. The heights of rooms are particularly susceptible to even greater imprecision because the floors have been changed in some rooms and because the ornamentation of the ceilings makes it difficult to estimate what Palladio would have considered to be the actual height of individual rooms. It is also recommended that the proportional analysis of side wings added by Scamozzi is left aside -- it is not only uncertain in how far these parts of the building correspond to Palladio's intention, but they were also substantially changed in later centuries, unlike the main block of the villa. The precision in stonecutting allows one to conclude with great certainty that the lower column diameter of ground floor columns was meant to be about 70.3 cm and plinths are regularly 930 mm. But intercolumniations vary between 152.5 and 157 cm, which gives an intercolumniation-to-diameter ratio between 2.17 and 2.23. Because the columns are Ionic, one is tempted to interpret these ratios as an almost accurate eustylos, which would mean that the architect originally intended intercolumniations to be 2.25D. In that case the optimal intercolumniation would be about 157.5 cm. (The largest measured intercolumniation is 157cm.) The central intercolumniations of the portico are larger -- this is typical of Palladio's work and we shall soon see how it was calculated. The measurements of the rooms on the sides indicate length/width
ratios of about 1.7 which is a reasonable approximation of Ö3 in built work. The height of these
rooms is 717 cm and can be read as the geometric mean of the
length and width. The height/width ratio is about 1.3. In the
The square rooms show how difficult it is to analyze proportionally a survey of an executed building. These rooms were obviously meant to be square -- but the difference between their longest and shortest side is 12.5 cm. Quite appropriately for square rooms, the height-to-width ratio is about 1.3. This is a rough approximation of Palladio's rule that the height-to-width ratio of square vaulted rooms should be 4/3. As mentioned before, rooms within the same row in Palladio's designs tend to have one dimension in common. In the case of Villa Cornaro, the width of the larger rooms is the same as the side measurement of the square rooms. Since the ceilings have equal heights and since the height/width ratios of both rooms are equal, one can conclude that the CCH rule has been successfully applied in Villa Cornaro. The smallest rooms are the hardest to analyze. Their length/width ratios are between 1.8 and 1.9. Those who have worked with Palladio's proportional system know that he rarely used ratios between 2/1 and Ö3/1. But it would be difficult to interpret the length/width ratios of these two rooms as one of these two ratios. To do so, one would have to assume inaccuracy in execution of about 30 cm, which is unlikely to happen on both sides of the same building. These smallest rooms have mezzanines above and their ceilings are lower than in other rooms. One should note that the height/width ratio is about 3/2. The ratios of the large sala also differ from the ratios which
Palladio listed in his list of preferred ratios ( Fig. 8. Villa Cornaro: ground floor sala. (photo/author) They are not easy to interpret, but it is remarkable that
the length/width ratio of the sala is 1.23 whereas width/height
ratio is 1.22. (In this case one should talk about the width/height
ratio and not vice versa because the width is greater than the
height.) However, if we consider internal length/width ratio
-- by "internal" I mean here the lengths and widths
of the space between the columns -- we can see that this ratio
is 1.5 or 3/2, one of Palladio's preferred room length/width
ratios. The larger distance between the columns equals their
height -- a point Palladio made himself in the As one would expect, the horizontal proportions of the upper
storey closely follow the proportions of rooms at the lower level.
The rooms at the upper storey have flat ceilings and, in accordance
with Palladio's rules, the ceiling height is (more or less) the
same as the width of the rooms. Palladio's tendency to keep one
dimension the same for all rooms in a row shows perfect sense
in this case -- otherwise, walking down a row of rooms on either
side, one would note unpleasant changes in ceiling heights. But,
when it comes to entering the large sala, the change of ceiling
height contributes to the impression of the dignity of space.
A remarkable aspect of the large sala on the upper storey is
Palladio's dogmatic application of the rule that the height should
be equal to its width. As a result, the sala is more than nine
meters high -- an impressive and somewhat daunting space ( Fig. 9. Upper storey sala. (photo/author) Palladio's approach to design in the villa Cornaro thus combines
the principle of preferred room proportions and the use of a
columnar system to determine the placement of walls. The proportions
of the main sala and porticos are derived on the basis of the
proportional rules for the order used; the proportions of the
side rooms on the basis of preferred ratios (or their equivalents,
such as Ö3) as well as the CCH
rule. In the case of Villa Cornaro, these two separate systems
were combined but not intertwined, except in the case of the
central space between the columns of the sala. It would be fruitless
to attempt to deduce the proportions of the rooms in the side
rows from the system of intercolumniations. The distance between
the final column of the portico and the end wall of the central
block cannot be expressed as the sum of column diameters and
intercolumniations. In this sense, Villa Cornaro differs from
Palazzo Chiericati. Chiericati has columns across the whole façade
and all walls orthogonal to the façade were aligned with
these columns. Something similar seems to have been suggested
by Palladio on the façade of Villa Pisani in Montagnana.
This villa was designed at about the same time as Cornaro and
the two villas have very similar morphology. The interesting
feature of this villa is the entablature which extends around
the villa, even along those walls which have no columns ( Fig. 10. Villa Pisani in Montagnana. (photo/author) Ultimately, the result is that the mathematics of the orders became decisive for Palladio's design principles and the use of proportions from the early 1550s. It was combined with preferences for certain proportional relationships in the sense of ratios of lengths, widths and heights of rooms. But the thesis of the Modernist historiography, that when it comes to Palladio it is only the relationships between bare walls that matters, has to be rejected.
[2]
[Beltramini and Guidolotti 2001] is particularly useful when
it comes to providing the information necessary to separate original
Palladio's works from later additions. [3]
See [Mitrovic 2004, 64-73 and 83-95] for a summary of these debates
and further bibliography. [4]
For statistical analyses of the second book of Palladio's treatise
see [Howard and Longair 1982] and [Mitrovic 2004, 64-65 and 190-198].
[5]
For the impact of Wittkower's book, see [Millon 1972] and [Payne
1994]. [6]
For a discussion of precision in Palladio's built work see [Robison
1998-1999].
L'architettura.
Ed. and Italian trans. Giovanni Orlandi. Milan: Edizioni Il Polifilo.
(Parallel Latin/Italian version of De re aedificatoria).______. 1988. Barbaro, Daniele. 1987. Beltramini, Guido and Pino Guidolotti. 2001.
Bertotti-Scamozzi, Ottavio. 1968. ______. 1998. Howard, Deborah and Malcolm Longair. 1982.
Harmonic Proportion and Palladio's Lewis, Douglas. 1972. La datazione della villa
Corner a Piombino Dese. ______. 1975. Girolamo II Corner's Completion
of Piombino with an inrecognized building of 1596 by Vincenzo
Scamozzi. Millon, Henry. 1972. Rudolf Wittkower, Mitrovic, Branko. 2001. A Palladian Palinode:
Reassessing Rudolf Wittkower's ______. 2002. Palladio's Canonical Corinthian
Entablature and the Archaeological Surveys in the Fourth Book
of ______. 2004. Mitrovic, Branko and Steve Wassell, eds. 2005.
Palladio, Andrea. 1990. ______. 1997. ______. 1988. Payne, Alina. 1994. Rudolf Wittkower and Robison, Elwin. 1998-1999. Structural Implications
in Palladio's Use of Harmonic Proportions. Wittkower, Rudolf. 1962.
Learning
from Palladio (Norton, New York 2004), the translation
of and commentary on Vignola's Canon
of the Five Orders (Acanthus, New York 1999) and a number
of scholarly articles about Renaissance architectural theory.
He has been awarded fellowships from Harvard University, Canadian
Centre for Architecture and the Humboldt Foundation.
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