Introduction (Roberta Spallone, Marco Vitali)

The magioni per fare alla villa fuori delle città (country houses), as they are called in the table of contents of Serlio’s Vienna Manuscript, preserved in Vienna’s Österreichische Nationalbibliothek as Codex Cod. Ser. n. 2649 (Serlio n.d. [Vienna Manuscript]), are private country houses, also known as villas. Other Renaissance treatise writers, such as Francesco di Giorgio Martini (Trattato di architettura civile e militare, about 1470), dealt with this kind of domestic architecture, but it was only with Serlio (Book VII on Architecture, published posthumously in 1575) and Palladio (I quattro libri dell’architettura, 1570) that this typology assumed significant importance.

Interest in the design of villas developed in a period permeated by Renaissance research on proportions in architecture, which included Leon Battista Alberti (De re aedificatoria, about 1450) among the initiators. Serlio and Palladio’s villas have plan layouts accurately studied from this point-of-view. The first refers to 24 models of villas of his invention, and the second mainly to buildings designed by him. While Palladio’s drawings (not only from the treatise) and buildings have been the focus of several well-known studies, Serlio’s models have been less studied, particularly the use of proportional ratios as a design criterion. The compositional diagrams of some of the Serlian villas were reconstructed by Rosci and (1966a), who compared them with those of Wittkower (1949) relative to the Palladian villas, identifying convergences and differences.

The object of the present research is to recognize the application of the seven rectangular ratios described by Serlio in Book I on Geometry (1545) in the designs of the 24 villas presented in the Vienna Manuscript preparatory to Book VII on Architecture. These ratios, of which Serlio foresees the use in the proportioning of rooms, correspond in part to the seven room shapes described by Palladio (1570). The Vienna manuscript provides both textual and graphic descriptions of Serlio’s villas, which can form the basis of graphic analyses and examinations regarding criteria for composition and distribution of the Serlian designs, identifying the simple geometries that give shape to the individual room plans and their relationship with the geometric shape that outlines the general plan. Basing ourselves on the work of earlier architectural historians, here we examine the possible links between the works by Serlio and Palladio, considering that the two architects were a generation apart (Serlio being 33 years older than Palladio), and that they could have met in Vicenza before Serlio’s departure for Fontainebleau.

The Vienna Manuscript as a Basis for the Realization of Book VII (Roberta Spallone)

Serlio’s Book VII was published posthumously (Serlio 1575) by Jacopo Strada in Frankfurt. The text of this first edition was in both Italian and a Latin translation. The manuscript of the book, discovered in 1919 by Julius Schlosser in the Kunsthistorishes Museum in Vienna (Dinsmoor 1942: 80), contains original drawings and transcribed texts. It consists of 152 parchment folios. The texts (written on twenty-nine folios) precede the ink drawings (realized on 123 plates). At the front of the book, there is one single autograph sheet by Serlio, which synthesizes the book’s contents.

In the preface to Book IV, first published in 1537, Sebastiano Serlio (1475–1554 or 1555) announced Book VII. However, even if Book VII had been foreseen from the beginning of the draft of the treatise, to reconstruct its elaboration process was rather difficult for the historians. This aspect is relevant for the developments of the present study, as the possible influences that the models of Serlian villas could have had on the designs of Palladian villas depend on when the elaboration of these drawings begins and on the hypothetical encounter between the two masters. Indeed, some scholars consider it likely that a meeting took place in 1539 (Rosci 1966a; Frommel 2008) when Serlio went to Vicenza to build a temporary theatre at Palazzo da Porto. Palladio might have seen the preparatory drawings for the book on this occasion or elsewhere (Frommel 2008: 68). This supports the hypothesis that when Sebastiano Serlio left Venice for France, in the spring of 1541, most of the drawings for Books VI and VII were already prepared (Frommel 1998: 349–369).

Tancredi Carunchio highlights other elements in support of an Italian origin for Book VII, precisely with regard to the drawings of the 24 villas that are featured as “Italian” villas, except the final villa, with attics “in a French way” (Carunchio 1994: 252). Regarding the finishing of the work, Sabine Frommel said that Serlio worked on the manuscript until the end of his stay in Lyon, since the drawing of a portal is dated 9 March 1552. This date perhaps indicates the definitive conclusion of the book. On May 19, 1552, he wrote to his patron François de Dinteville that he had completed the texts (Frommel 1998: 358). Finally, in a letter by Strada, it is written that in 1553 he had the wood tables drawn by Serlio himself for the illustrations of Book VII (which, therefore, represent the final version) (Jansen 1989: 213).

A further issue concerns the existence of a second version drawn up in anticipation of publication, which got lost. Therefore, the Vienna Manuscript should be considered the first version (Dinsmoor 1942; Carunchio 1989: 203).

Lastly, in relation to the decision by Strada to publish the volume in 1575, Dirk Jansen thought that it is probable that Strada was motivated to finally print Book VII because of the publication, in 1570, of the Quattro libri dell’architettura by Andrea Palladio (Jansen 1989: 212). A confirmation of this hypothesis could come indirectly from the way in which the volume, originally designed as a “book of accidents”, was filled by Serlio himself with new materials and, in particular, by the initial addition of 24 inventions of villas that had not found a place in the linear and progressive structure of Book VI. In fact, these are designs that, despite the various shape options (mostly variations on a centralized theme), are impressive because of the homogeneity of clients that they presume (Beltramini 2008: 187).

Drawing Techniques in the Vienna Manuscript (Roberta Spallone)

The Vienna Manuscript was written on parchment sheets measuring 31.4 × 21.3 cm. The scale drawings of the manuscript are in orthographic projections on single plates, according to the plans of the ground floor and the front elevations, except in four cases (Villas IX, XIV, XV, and XVIII), where the model is presented across two plates, including the back elevation and a section. Moreover, Serlio organized some single plates to contain also the rear elevations, or the sections, or portions of them. The projective method is consistent with the recommendations of the 1519 “Letter to Leo X” by Raphael and Baldassare Castiglione (Hart et al. 2006) and is admirably consistent with the variations of the planimetric schemes that allow Serlio to multiply his examples (Fiore 1994: XXV–XXVI).

The layout of the different projections seems to depend on a precise graphic choice by Serlio: to use the entire extension of the sheet, starting from the general shape of the plan (including the garden), and always placed in the lower part of the sheet. The drawings in each plate are in projective correlation and the same scale, except three (Villas X, XI, and XII), where the lateral development of the garden appears only in the plan, leading to an enlargement of the elevation. Given that the unit of measurement is the Vicentine foot, equal to about 35.7 cm, it follows that each model has been drawn at a different scale: ranging from a scale of about 1:100 up to about 1:460, depending on the dimension of the plan. A graphic scale, designed by Serlio generally along the vertical axis of symmetry, allows the transportation of the measurements, with the aid of the compass.

Although historians have observed several differences between the Vienna Manuscript and Book VII as published (Schlosser Magnino 2001; Dinsmoor 1942; Rosenfeld 1974; Carunchio 1976), in the case of the plans of the 24 villas, the differences mainly concern the text, which, as acknowledged, was carefully rewritten (Jansen 1989: 213).

Rectangular Ratios Between Geometry and Architecture (Roberta Spallone)

At the end of the Book I on Geometry, Serlio deals with the seven rectangular ratios that the architect “can use for different things” (Serlio 1545: 20, our trans.). He defines the square as “the most perfect shape” (Serlio 1545: 20, our trans.), in a pragmatic conception of geometry, which uses the simplest shapes as the base of the most complex ones (Lorber 1989: 115). The figures that derive from the square correspond in part to Palladian proportions and harmonic proportions.

In Serlio’s book, a progressive series of rectangles, with ratios between the sides of 4:5, 3:4, 1:√2, 2:3, 3:5, 1:2, follows the square (1:1). Regarding the 1:2 ratio, Serlio establishes links with architecture and, in particular, with the ratios in the plan of the rooms. Thus he specifies that “in the good things of Antiquity there is no shape found that exceeds the double, except the entrance, the lodge… but in vestibules, halls, rooms, and other habitable spaces this ratio is not used by the experts, because it is not suitable” (Serlio 1545: 21, our trans.). Palladio also includes seven “most beautiful and proportionate types of rooms” (Palladio 1570: 52, our trans.), six of which have the same ratios between the sides indicated by Serlio, while the rectangular one (4:5) is absent and is replaced by the circular plan.

The harmonic ratios (1:2, 2:3, and 3:4) characterizes three of the seven figures indicated by Serlio. In light of the results of the analysis presented in this paper, we cannot share the opinion of Lorber who, writing about Serlio’s Book I, affirmed that the issue of musical proportions remained the reference of the theoreticians and certainly not a relevant element in the practices of designing and building (Lorber 1989: 115). The absence of the rectangle obtained with the golden section of the side was also observed; this construction, a canonical in the study of proportions, was considered an idealization of the real design practices (Lorber 1989: 115).

Working Methodology (Roberta Spallone)

The analysis of the villa plans is focused on the geometric proportion and distributive-functional aspect. Working on the plans means also constantly comparing elevation and sections, which reveal and confirm symmetries, rhythm, and layouts of the façades.

Describing the villas, Serlio establishes the measurements of the plans sides for most of the rooms, each of which is identified by a letter, avoiding repetitions through the reference to the symmetries and leaving out the measurements of a few smaller rooms for service and distribution. Serlio’s measurements refer to the clear dimensions of the rooms, while the overall measurements of the villa’s boundary and the thickness of the walls are not defined. The areas considered in the present work are those to which Serlio attributed a value. Only in a few cases do we attribute dimensions to the rooms by reading them directly from the drawings. This was done when there was a lack of one of the two sides measurements or when it was possible to obtain the measurements by observing the alignments of the rooms. The measures integrated in this way are written between parentheses. Moreover, we found that the errors, probably due to the transcription, are very few. We have corrected them by measuring the dimensions from the drawings and writing the exact measurements between square brackets. To justify the lack of a metric definition of some areas, Serlio states that “of many particular measures I do not speak because it would be long to describe everything, but the diligent architect will find what is missing with the compass in hand” (Serlio n.d. [Vienna Manuscript]: fol. 7, our trans.).

The first part of the graphic analysis concerns the definition of the proportional-geometric features of each villa. After having scaled the plans in feet of Vicenza, the analysis turned to the search for the shape and the ratio between the sides of the villa’s boundary, also determining the overall area. Then, symmetries and anti-symmetries, overall and between the rooms, were identified. Finally, areas responding to rectangular ratios according to Serlio’s description in Book I have been identified, indicated by shading in different colours.

Only the exact ratios were considered, which is unlike the procedure of Rosci, who, observing the need for Serlio to insert the wall thickness, proposed approximations, for example, 13 × 20 as 2:3 (Rosci 1966a: 61). Only the ratio 1:√2, which contains an irrational number, has been approximated to the ratios that are closer to it, such as 7 × 10, and 10 × 14, as the canonical approximations during the Renaissance (March 1998: 65–66).

Comparative plates (Figs. 1, 2, 3, 4) have been created as a result of the analysis of all of the villas. The use of the different colours allows us to observe recurrences and relationships between the figures present in the single model, between different models, and in the complex of the 24 villas. These elements, together with the relationship between the figure that outlines the villa’s boundary and the figures that shape the rooms, suggest the compositive criteria used by Serlio.

Fig. 1
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Comparative plate of proportional-geometric features, Villas I–VI. Drawings: Roberta Spallone

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Fig. 2
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Comparative plate of proportional-geometric features, Villas VII–XII. Drawings: Roberta Spallone

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Fig. 3
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Comparative plate of proportional-geometric features, Villas XIII–XVIII. Drawings: Roberta Spallone

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Fig. 4
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Comparative plate of proportional-geometric features, Villas XIX–XXIV. Drawings: Roberta Spallone

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The functional-distributive analysis is complementary to the proportional-geometric analysis, which can be superimposed to it as a layer. This analysis led to the diagrammatic representation of each plan, which was inspired by the study drawings of the Palladian villas made by Wittkower before 1944 (Benelli 2008: 49–53) and by the graphics standards established by Cavallari Murat for the representation of the historical urban fabric (Politecnico di Torino 1968).

For each villa, only those areas intended for residential purposes were considered, thus excluding the gardens, the small pavilions not connected to the body of the residence, and the external staircases, and instead included the entrance lodges and the internal lodges. The wall thicknesses were represented as a wireframe with a medium line, the openings in the façades and the internal passages through their axis, traced with a thick line, having different lengths to distinguish them. The stairs, which constitute the vertical distribution systems, have been drawn in their overall development, and an arrow identifies the main entrance of the villa. This representation allows us to appreciate the distribution paths, as well as the alignments between doors and windows, which can generate enfilade, façade divisions, and rhythms.

The comparative plate, unlike the famous Wittkower plate depicting 11 Palladio villas (Wittkower 1949: 65), presents the diagrams of the villas reproduced at the same scale, thereby facilitating comparison between the models, even from the dimensional point-of-view (Figs. 5, 6, 7, 8).

Fig. 5
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Comparative plate of functional-distributive features, Villas I–VI. Drawings: Marco Vitali

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Fig. 6
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Comparative plate of functional-distributive features, Villas VII–XII. Drawings: Marco Vitali

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Fig. 7
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Comparative plate of functional-distributive features, Villas XIII–XVIII. Drawings: Marco Vitali

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Fig. 8
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Comparative plate of functional-distributive features, Villas XIX–XXIV. Drawings: Marco Vitali

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A synoptic table flanks the two previous graphic analyses, which presents the architectural typology, the shape and size of the plot, the presence of symmetries with respect to the general shape of the building and to the layout of the rooms, the number of rooms on the ground floor and the percentage of which responds to rectangular ratios, the percentage of areas in rectangular ratios with respect to the total area (Wassell 1999), the number of rooms referred to each rectangular ratio, the ratio prevailing in each villa, and the value of the scale reduction (Table 1).

Table 1 Proportional-geometric and functional-distributive features of the 24 villas
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The Designs of 24 Villas from Serlio’s Vienna Manuscript: A Comparative Analysis (Roberta Spallone)

The comparative analysis of the 24 models does not highlight an explicit sequence between them, such as the recurrence and the variation on morphological and compositive themes guided by geometric features (symmetries and antisymmetries, proportional ratios between the sides of the figures that shape the rooms, modular grids). Serlio describes the general shape of the building, but never refers to the figures in which it is inscribed. However, in light of the analysis carried out, it is believed that they are of significant importance in the shape genesis of the plans.

The 24 villas always have an axis of longitudinal symmetry, coinciding with the entrance system to the building, which rules their overall shape. In most cases (14 out of 24), the axis of longitudinal symmetry is orthogonally intersected by an axis of transverse symmetry, giving rise to centralized shapes, on the main hall or the inner courtyard. In one case, that of Villa XIII, in addition to the two main axes, there are two more rotated by 45°, on which there is a diagonal cross plan. The relationship between the exclusively longitudinal axiality and the shape of the building is reflected in the choice of rectangular block plans (Villas I and XI), horseshoe-shaped (Villas VI and XVI), H-shaped with asymmetries (Villas IX and XXII), and C-shaped (Villas XIX, XX, and XXIV). Instead, in the cases of double axiality, the shape of the building ranges between the square block plan (Villa II), cross (Villas III, XVIII, and XXI), X-shaped (Villas IV and VII), courtyard (Villas V, XII, XIV, XV, and XVII), and H-shaped (Villas VIII, X and XXIII).

If the examples of villas are analyzed by grouping them according to the typology to which they belong and following their sequence in the manuscript, they can, in general, be read as an evolution of the shape, from the simple to the complex, and a search for possible solutions to the arising distribution problems. However, we cannot be certain that, with the first example, Serlio wants to propose an archetypal shape for the considered typology and that its variants follow: an example is the development of the courtyard villas, which start from a shape with remarkable peculiarities, and then return to a simpler type. The features of the block-, courtyard-, horseshoe-, C-, H-, cross-, and X-shaped villas can, therefore, be examined, considering all of those characterized by different symmetry relationships.

Recurrences and Variations on the Typologic Theme (Roberta Spallone)

The block villas (I, II, and XI) show a growing dimensional development. Villas I and II, having a large main hall as their central organising element, propose a rectangular and square plan; Villa II, which has a surface of 3.5-times that of Villa I, is divided into several rooms and has two front and rear lodge diaphragms, which interrupt the two façade planes. Villa XI proposes, along the front and back façades, setbacks of the central part, with an entrance lodge. This entails the indentation of the main hall around which the rest is organised. The courtyard villas (V, XII, XIV, XV, XVII, and XXI) are catalogued starting from Villa V. It is outlined by a large square, which presents large breaks in correspondence with the two symmetry axes and an isolated pavilion in the center. Villas XII and XIV develop new internal courtyard shapes, respectively circular and oval. This does not influence the shape of the rooms on the courtyard, which simply appear as residual spaces and perform ancillary functions. Villas XV and XVII seem to refer to the more usual courtyard schemes, having a square boundary and a concentric square courtyard, the main hall placed at the center of one of the sides, and, in Villa XVII, an internal lodge on all four sides. Villa XXI is organized on an octagonal courtyard, surrounded by corridors that distribute the rooms of the individual arms of the cross.

The horseshoe-shaped villas (VI and XVI) show a maturation of the compositive language thanks to which the semicircular curve of the façade, in the second case, is repeated in the rear façade and generates an original and axial main hall.

The C-shaped villas (XIX, XX, and XXIV) have some similarities (both XIX and XX have two short side wings, front and rear, respectively). Villa XIX, exceptionally, has no main hall, and the entrance is through a lodge, whereas Villa XX has a decentralized main hall, like Villa XXIV that presents a remarkable development of the wings that form a real open courtyard, with a sequence of rooms.

The H-shaped villas (VIII, IX, X, XXII, and XXIII) present a series of variations starting from the model of Villa VIII, characterized by a circular, centrally-located main hall, flanked by the two symmetrical wings parallel to the longitudinal axis. In Villa IX, the plan undergoes a 90° rotation: the central body develops along the longitudinal axis that houses the main hall, and the two wings form the front and rear façades. Villa X, which is similar in its size to Villa VIII, also has a centralized square hall, with four expansions along the sides. Villas XXII and XXIII show a loss of centrality of the main hall. In the latter case, the connecting body between the wings is considerably developed and the general contour figure, which in the previous cases was a square, becomes rectangular.

The cross-shaped villas (III, XVIII, and XXI) show a progressive complexity of the compositive theme. Villa III presents a square, centrally-located main hall, from which the rooms are developed in a telescope-like manner. Villa XVIII has the largest central hall, from which the four arms branch off, expanding into the terminal parts. Villa XXI is based on an octagonal centrally-located courtyard that superimposes the radial system on the axial system.

The X-shaped villas (IV and VII) show the need to consider spaces for connecting the different rooms. Villas IV and VII, inscribed in a square, consist of four square corner blocks connected to a central square block, used as the main hall. The connection between the blocks occurs, in the first case, using lodges along the sides of the central block that create alternative passages for the connection between the rooms. In the second, due to the intersection between the corner blocks and the central block, the main hall becomes the distribution center of the building.

Villa XIII, a unique case of the diagonal cross shape, can be considered as the result of shape researches on the cross-shaped villas and the X-shaped villas. The large octagonal courtyard and the two squares rotated by 45° that circumscribe the overall shape drive a radial composition that creates some difficulty in reconciling the general plan with the shapes and sizes of the individual rooms.

Relationships Between the Rooms and Proportional Ratios (Roberta Spallone)

While general symmetry relationships are present in all 24 villas, those among the rooms are less frequent, as these must respond to functional and distributive needs that do not always allow the symmetry of the rooms in relation to an axis. Twelve villas present symmetry relationships between the shapes of the rooms, not necessarily coinciding with those that rule the general shape. In one case (Villa III) Serlio experiments with anti-symmetry of the rooms around the central nucleus that generate a “swirling” effect in the plan. In Villas VII and VIII there are attempts of antisymmetric composition not completely successful.

Most of the rooms (about 57%) to which Serlio attributes dimensions have sides corresponding to one of the rectangular ratios, as documented in Table 1. The 1:1 ratio, which accounts for approximately 61% of the total of rooms in rectangular ratio, is the most applied ratio. The other ratios vary between about 3 and 9% of the total, for rooms in ratio 1:√2 and 3:4 respectively. The 3:5 ratio, which Serlio describes as “a very beautiful ratio” (Villa XVII), is present in about 6% of the cases.

Regarding the proportional ratio prevailing within each villa, it can be observed that despite the clear prevalence of the square rooms, in some villas, Serlio adopts mainly another ratio. In Villa IX, the 4:5 ratio prevails, 3:4 in Villas IV and XXI, 1:√2 in Villa XVIII, 2:3 in Villa VI and XXII (Figs. 1, 2, 3, 4).

As said in the methodological notes, in the present work we have chosen to consider only the exact ratios and the canonical approximations of the ratio 1: √2. Instead, if Rosci’s remarks about Serlio’s Book VI, reasonably applicable to the Vienna Manuscript, had been taken into account, the number of rooms in rectangular ratio would have significantly expanded. Indeed, Rosci believes that it is clear and demonstrable that Serlio proposes his dimensions based on precise proportional ratios. He also explains that the dimensioning in Palladio’s projects conventionally omits the thickness of the walls, so the dimensions of the building are obtained from the exact sum of the dimensions of the rooms, while in Serlio’s projects they refer to the measurements of the internal perimeter of the rooms: the small differences with respect to perfect ratios can be explained precisely with the presence of even small “variables” of wall thicknesses. Therefore, in his analysis Rosci highlights Serlio’s design intentions, beyond the objectively observable metric values.

The survey we carried out concerning the rectangular ratios present in the villas’ rooms cannot deny that there are numerous rooms whose “imperfect” ratios are the result of Serlio’s adjustments due to the need to consider the thickness of the walls. However, the variability and consistency of these thicknesses, often equal to three feet, and more rarely to four feet, would have given a certain degree of uncertainty to our analysis, which in this phase of the research seems to us prudent to avoid.

Geometric Hypotheses on the Compositive Method (Roberta Spallone)

In some cases, Serlio emphasizes the character of the invention of his villas. Thus, describing Villa XIII, which is certainly one of the most original, Serlio states that “this house is very different than those I have ever seen” (Serlio n.d. [Vienna Manuscript]: fol. 4r, our trans.). As stated above, to highlight the underlying compositive criteria, the relationship between the boundary of the villa and the shape of the building can be investigated. In the majority of cases (17 out of 24), the boundary is a square. Moreover, in the case of Villa XXIV, a measure given in the text does not correspond to that in the drawing: this seems to reveal a first thought regarding a square outline. In another case, the outline responds to rectangular ratios, 3:5 for Villa VI.

The recurring reference to the large contour square suggests a compositive method ad quadratum, according to which the overall shape is divided through a modular grid, within which solids and voids of the building are juxtaposed. In the subdivision, a 3 × 3 matrix prevails, which in some cases could be considered regular (Villas III, IV, and XVIII), in others it presents a wider central module, identical on both sides (Villas II, VII, VIII, X, XI, XII, XVII, and XXI), while in others it still diversifies the two central modules (Villas IX and XXII).

The partition of the large square also takes on 4 × 4 and 5 × 5 matrices (Villas XV and V). Also, in the horseshoe-shaped Villa XVI, the outline is a square. In this case, the 3 × 2 grid gives rise to a portion occupied entirely by the hall hemicycle and another by two wings. Finally, the square that surrounds Villa XIII, a diagonal cross rotated by 45° gives rise to the octagon that guides the arrangement of the four arms which, in turn, influence the size of the octagonal internal courtyard.

Villa XIV has a large internal oval court. A 3 × 3 grid, with the central module of greater spans that rule the lengths of the oval axes, defines the entire composition. For the remaining seven cases (Villas I, VI, XIV, XIX, XX, XXIII, and XXIV), in which the regulatory figure is a rectangle, this seems to be valid for both the compositive criteria of a geometric kind and the additive logic underlying the compositive method of Serlio, as highlighted by historians (Carunchio 1989: 206; Kühbacher 1990: 169).

In Villas XIX and XX, the compositive scheme seems to be ruled (with some approximation), in the first case by the partial overlapping of two equal squares which shape the vestibule, and in the second by two equal squares whose distance generates the vestibule’s space. In Villas XXIII and XXIV, the additive-type composition is manifested in the sequential arrangement of the rooms (Figs. 5, 6, 7, 8).

The Main Hall as a Regulating Element of the Composition (Marco Vitali)

Other interesting considerations can be made on the relationships between the position of the main hall and the general structure of the villas. In 13 of the 24 villas, the main hall is on the entrance axis of the complex, assuming in 9 villas a central position, in the other four a position translated in relation to the center. When it assumes a central position it clearly declares its dominant role of distribution: only in the case of Villa I, it assumes a central position even on a rectangular scheme.

In many cases of centrality of the main hall it always assumes a square shape (Villas III, IV, VII, and XVIII), or in rare cases oval (Villa I), octagon (Villa II), circular (Villa VIII), or square with expansion in the four main directions (Villa X). The mail hall, therefore, sets the dimensions of the central field of the compositional grid, of ratio 1:1 and produces symmetrical fields along the two longitudinal and transverse axes of the grid. In just one case, that of the Villa IX, while maintaining a central position, it takes the shape of the double square, generating a compositional grid with modules of different ratios along the two axes.

When the main hall is translated along the entrance axis, it defines the width of the subdivision modules in plan along that axis, and occupies a central position with respect to the back façade of the building (Villas XI, XIV, XV). Only in the case of Villa XVI, the compositional grid of which can be assumed to be 3 × 2, does the main hemicycle-shaped hall occupy the three modules of the back façade. In contrast, it takes a position along the transversal axis in Villas XII, XVII, XXII and XXIII, assuming an elongated shape, and in only one case using rectangular ratios (ratio 2:3 in Villa XXIII). In these villas, the translation of the main hall position can be justified by the presence of an internal courtyard (Villas XII, XVII) or by the H-shaped configuration, in which the center is occupied by a lodge (Villa XXII, where the central body is extremely thin) or by a vestibule (Villa XXIII). A separate mention must be made for Villa XIII, in which the general organization depends on a courtyard and the main hall is placed on one of the arms of the diagonal cross, according to one of the diagonal axes. In the remaining villas (V, VI, XX, and XXIV) the main hall, always elongated, is placed in a corner position (V and VI) or in a decentralized position on the back façade of the building (XX and XXIV).

An anomaly is instead represented by Villa XIX, which does not include a main hall. Serlio himself, in the textual description of the villa, reports: “From the right side there is a little hall C… This villa has no main hall, but as it is designed as a summer villa, the terrace and the lodge will take the place of it, according to the position of the sun” (Serlio n.d. [Vienna Manuscript]: fol. 6v, our trans.).

It is also possible to make an analysis in relation to the rooms of entrance to the main hall following the path of access to the villa. In only four villas (I, VII, VIII, and X) can the main hall be directly reached without going through any other room. In Villa V, the main hall can be reached directly from the internal garden: this is because of the particular shape of the courtyard, that is opened along the longitudinal and transverse axis.

In Villas IV, XI, and XXII, the main hall has direct access from a lodge. In all other cases, the main hall is reached by differently composed and increasingly complex systems: from a simple vestibule (VI, IX, XX, XXIII, and XXIV), which in one case is reduced to a small-sized corridor (XVI), to a system of lodge and vestibule (II, XVIII, and XXI) or vestibule and lodge (XVII), or vestibule and internal courtyard (XII, XIII, and XIV), double lodge and courtyard (XV), and finally a system composed of a vestibule and a little hall (III).

Proportioning Criteria and Dimensions of the Rooms (Marco Vitali)

Another theme of interest is related to the shape and size of the rooms in relation to the intended use. Starting from the entry spaces and those that distribute the main hall, it is easy to notice how normally they are proportioned with recurring criteria. The lodges always present an elongated shape that never assumes rectangular ratio. The vestibules, when present (in 15 villas out of 24), are mainly elongated: in Villas VI, XII, XIV, XVII, XIX, and XX they present the 1:2 ratio, in two cases, doubled along the secondary façade (XII, XVII); in Villa II it has a 2:3 ratio; in Villa XIII it has a 1:√2 ratio; in Villas IX, XIII, and XXIV a square ratio (1:1). In the remaining cases, the vestibules have dimensions that do not follow any of Serlio’s preferred rectangles from Book I on Geometry.

Anterooms and little halls are present in 12 out of 24 villas, and mainly have a prevalent sizing with rectangular ratio of 3:4 (V and XXI) or very close to it (VI and XIII), sometimes with a square ratio (III, XXIII and XXIV).

The bedrooms, present in large numbers in every villa, deserve a more general discourse: in great prevalence they are proportioned on the square shape, which presents, also in relation to the size of the villas, modules of 16 × 16 feet (I), 20 × 20 (XI and XIX), 21 × 21 (II and III), or 22 × 22 (IV and VIII) and, in the vast majority of cases 24 × 24 feet (V, VI, X, XII, XIII, XIV, XVI, XVII, XX, XXII, XXIII, and XXIV); only in exceptional cases do they reach larger dimensions, as in the case of Villa XIV (25 × 25 feet) or in Villa VII, in which the 25 × 25 module is associated with the circular and octagonal shapes, or in the case of the Villa XXIII, with a truly impressive size, reaching up to 30 × 30 feet.

Case Studies (Marco Vitali)

Following the comparative analysis of the 24 villas, a detailed analysis of some case studies, critically selected as representative sample of the whole series, was organized. Villas of different shapes and sizes have been chosen: block-, cross-, horseshoe-, and H-shaped, ranging from the smallest (Villa I, about 2000 square feet) to the largest (Villas XIII and XXIII, about 12,000 square feet).

The selected cases testify to how the rectangular ratios are used differently for the proportioning of the rooms in relation to the logic of composition: the composition of the general figure with modules, as much as possible, respecting rectangular ratios (Villas VI and XXIII), the prevailing use of a certain rectangular ratio for the definition of almost all the rooms (such as the square module in Villas III and X), and a freer proportioning of the rooms in relation to certain difficulties of composition. Losses of the proportional criterion often occur:

  • when, in the presence of general symmetries, parts of the building are organized in sequences of differently shaped rooms, where the wall thickness plays a fundamental role (Villas VI, XIII, XXIII and XXIV);

  • when the subdivision of the plan in rooms it is necessary because of distribution requirements (Villas II and III);

  • when the rooms due to their function assume a particularly elongated configuration, as in the case of lodges or in the expansions of a room (as in Villas II and X);

  • when residual spaces with particular shapes and/or ratios have to be divided (Villas VI and XIII).

Lastly, it should be noted that the choice of cases also considered the analyses carried out by other scholars, which relate the individual villas by Serlio with the subsequent production by the young Palladio. Beyond some similarities related to the general principles of composition, such as the raising of the ground floor of at least five feet, or a clear symmetry in the layout of the façades (Rosci 1966a: 34), there are some precise reverberations of the Serlian models in Palladio’s work:

  • as in Villa II, connected by Frommel with a design for a villa (RIBA VIII, 13r) which is a variation of the Odeon Cornaro of Falconetto in Padua (Frommel 2008: 68), and connected by Rosci with a drawing (RIBA XVII, 1) for Villa Pisani in Bagnolo, which is a prelude to the final version of the Villa Rotonda (Rosci 1966b: 131);

  • as in the case of Villa VI, which Frommel compares to another drawing by Palladio for Villa Pisani (RIBA XVII, 17) in relation to the organization of the entrance with an exedra and a circular stair (Frommel 2008: 68).

In order to facilitate the reading of individual cases, we present Table 2, which provides, for each villa, some information regarding the size of the villa in relation to the area of the lot on which it sits, when possible, and the indication of the dimensions of the rooms, grouped by homogeneity of intended use: vestibules (V) and lodges (L), main halls (H), halls and antechambers (h), bedrooms (R), service rooms (r), and dressing rooms (dr). The intention is to show, through some numerical data, the characteristic aspects of each villa.

Table 2 Dimensional and functional features of the case studies
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Villa I

The reading of the general structure of the building would suggest an additive composition of rooms: they are organized into two mirror-like apartments connected by the central space of the main hall, oval in shape with niches “in which there will be benches to sit on” (Serlio n.d. [Vienna Manuscript]: fol. 1r, our trans.). The composition logic emphasizes the axiality with respect to the entrance direction, also highlighted by the organization of the access stairs. As already highlighted in the general part, the bedrooms follow the most common logic of proportioning: they have a square dimension and stand on a minimum size, given the small overall dimensions of the system (Fig. 9).

Fig. 9
figure 9

reproduced by permission; graphic overlay: Marco Vitali

Sebastiano Serlio, Villa I. Graphic overlay of the proportional-geometric and functional-distributive analyses. Image: Vienna, Österreichische Nationalbibliothek, Cod. Ser. n. 2649, fol. 32v

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Villa II

The plate represents a building of medium size (about 7000 square feet). It seems quite evident how the composition of the building arises from the subdivision of a base square. It is possible to hypothesize that the organization of the plan in a 3 × 3 grid follows the criterion of subdividing the sides of the square into 1, √2, and 1 modules.

The scheme proposes the octagonal main hall (30 × 30 feet) with niches in a central position, to occupy the largest field of the base grid, emphasizing a double longitudinal and transversal axiality. The angular fields of the grid are occupied by square bedrooms of average size, while the axial fields of the perimeter, characterized in our hypothesis by a ratio of 1:√2, are divided into rooms that differ as follows:

  • on the entrance axis, two lodges of elongated ratio are located—conferring particular strength on the longitudinal axis—and rooms linked to the ceremonial entry and reception (vestibule 2:3 and accessory rooms 3:4);

  • on the transversal axis, there are two further vestibules (very elongated), two rooms serving the corner rooms, small dressing rooms, and spiral staircases. The rooms (apart from the square dressing rooms) do not follow a codified ratio: rather they seem to respond, within the limits of the space dedicated to them, to functional needs (Fig. 10).

    Fig. 10
    figure 10

    reproduced by permission; graphic overlay: Marco Vitali

    Sebastiano Serlio, Villa II. Graphic overlay of the proportional-geometric and functional-distributive analyses. Image: Vienna, Österreichische Nationalbibliothek, Cod. Ser. n. 2649, fol. 33

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Villa III

The built area (about 6500 square feet) is organized “in the form of a cross” (Serlio n.d. [Vienna Manuscript]: fol. 1r, our trans.). The general organization is a grid of nine fields, defined in their dimensions by the central field on which sits the main hall, which is the largest room in the whole villa (40 × 40 feet), occupying 25% of its built surface. The translation along the diagonals of the central square, with a partial overlap to the central field, defines the space occupied by the gardens, as is evident from the layout of the flowerbeds.

Almost all the rooms of the entire villa are designed on the square module, used for the main hall and the halls on the longitudinal axis, while the bedrooms and the service rooms are on the transverse axis. The other rooms (vestibules with adjoining rooms and dressing rooms) are dimensioned without reference to the rectangular ratios to fill, with the staircases, the areas of the cross left free by the square modules. The general organization follows an anti-symmetric setting; the balance between the axes is only partially offset by the presence, along the entrance axis, of the stairs connecting to the gardens (Fig. 11).

Fig. 11
figure 11

reproduced by permission; graphic overlay: Marco Vitali

Sebastiano Serlio, Villa III. Graphic overlay of the proportional-geometric and functional-distributive analyses. Image: Vienna, Österreichische Nationalbibliothek, Cod. Ser. n. 2649, fol. 34v

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Villa VI

The organization of Villa VI deserves special mention. As Serlio states, “its main façade will have partly the shape of a theater” (Serlio n.d. [Vienna Manuscript]: fol. 2r, our trans.). The plan is of medium size (about 6000 square feet) and includes rooms mainly defined by rectangular ratios, which seem to be juxtaposed to fill the rectangular outline of 3:5 ratio.

The layout of the villa is symmetrically configured with respect to the entrance axis, on which a vestibule (1:2) is placed: this symmetry is broken by the main hall on the right side, which does not correspond to the coupled hall on the left. The bedrooms (of medium size), the service rooms, the dressing rooms, and the staircases along the wings of the building are in symmetry. In the spaces within the hemicycle of the garden, a small vestibule with a dressing room, a chapel, and two staircases, disrupt the symmetry of the composition (Fig. 12).

Fig. 12
figure 12

reproduced by permission; graphic overlay: Marco Vitali

Sebastiano Serlio, Villa VI. Graphic overlay of the proportional-geometric and functional-distributive analyses. Image: Vienna, Österreichische Nationalbibliothek, Cod. Ser. n. 2649, fol. 37

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Villa X

The plan of the villa of medium size (about 7000 square feet) comes from the subdivision of the square: the central field of larger dimensions is occupied by the central hall (48 × 48 feet), which occupies almost 30% of the plan. In the corner fields are placed the square bedrooms of the four apartments into which the complex is sub-divided. The central fields on the sides of the figure can be assimilated into four modules of 3:5 ratio, which are attached on the expansions of the central hall, generating small recesses in the façade: the two modules positioned along the entrance axis are intended for a garden, underlining the longitudinal axial organization, while those positioned along the transverse axis host pairs of square service rooms (Fig. 13).

Fig. 13
figure 13

reproduced by permission; graphic overlay: Marco Vitali

Sebastiano Serlio, Villa X. Graphic overlay of the proportional-geometric and functional-distributive analyses. Image: Vienna, Österreichische Nationalbibliothek, Cod. Ser. n. 2649, fol. 42v

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Villa XIII

Villa XIII is one of the largest examples (about 12,000 square feet), important for the complexity of its geometric and distributive composition. The scheme of the plan can be read from the square shape that defines the space of the garden, which, rotated 45° around its center, defines the dimension of the building’s arms, articulated around a large octagonal courtyard (80 feet in diameter). The structure develops with an almost complete symmetry relative to the longitudinal and transversal axes and the diagonal axes: this symmetry is only partially weakened by the different configuration of the connections between the different arms of the building. The entrance axis is emphasized by the staircase bodies connecting with the garden.

The composition of the rooms seems to show, in each of the fields that form arms and courtyard ring, alternative distribution solutions, as Serlio explicitly suggests in the descriptions of Villa XII (Serlio n.d. [Vienna Manuscript]: fol. 4r): this would justify the differences in the depth of the courtyard ring, the positioning, often alternating, of staircases, and the different solutions for the organization of the apartments. The rectangular ratios, as already underlined, find little use here, perhaps because of the difficulties also constituted by the complex articulation of the plan.

The arms of the cross are proportioned by building four diagonal modules with a rectangular ratio (1:2), which define the positions of the other rooms:

  • the two arms facing the entrance house two apartments, each consisting of a bedroom and service areas (in one case with rooms defined by the repetition of the 24 × 24 square module, in the other by differently sized rooms, including a staircase).

  • the two arms facing the back façade of the villa hold, on one side, the main hall, almost corresponding to the rectangle of ratio 1:2, and on the other side, a hall with service rooms and a staircase.

The connecting curtains between the arms, of different depths, house:

  • in the direction of the entrance, aligned with the two accesses to the garden, a vestibule, and accessory compartments;

  • in the transversal direction, on one side a small room, and on the other a room with relative accessory compartments and staircases (Fig. 14).

    Fig. 14
    figure 14

    reproduced by permission; graphic overlay: Marco Vitali

    Sebastiano Serlio, Villa XIII. Graphic overlay of the proportional-geometric and functional-distributive analyses. Image: Vienna, Österreichische Nationalbibliothek, Cod. Ser. n. 2649, fol. 45

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Villa XXIII

Villa XXIII is presented in a plate that shows the building, of considerable size (about 12,700 square feet), inside a very large garden, characterized by corner pavilions. The general composition is governed by an additive logic, organized with respect to the two longitudinal and transversal axes. On the longitudinal axis is placed the vestibule to which the main hall is linked on one side, which approaches the ratio 1:2, and on the other side an antechamber and a large square room (30 × 30 feet). At the end of the sequence, there are two symmetrical rooms in rectangular ratio 4:5 (24 × 30 feet). In the wings that make up the arms of the H-shaped configuration, there are four apartments, each consisting of a square room (24 × 24 feet), a dressing room, and a staircase (Fig. 15).

Fig. 15
figure 15

reproduced by permission; graphic overlay: Marco Vitali

Sebastiano Serlio, Villa XXIII. Graphic overlay of the proportional-geometric and functional-distributive analyses. Image: Vienna, Österreichische Nationalbibliothek, Cod. Ser. n. 2649, fol. 58v

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Conclusion (Roberta Spallone, Marco Vitali)

The graphical analysis and the comparison between the drawings of the 24 villa models by Serlio has highlighted the relationships between geometry, proportional relationships, and architecture present in the composition of the plans, which had until now been unexplored. Notwithstanding the fact that the drawings present Serlio’s inventions and are not designs destined to be built, they reveal:

  • The relationships between the geometric characteristics of symmetry with respect to one or two axes and the morphological types of plans;

  • The presence of symmetries and anti-symmetries in the placement of the rooms;

  • Compositional recurrences and variations on the theme for the different types in relation to geometric transformations, rotations, translations, and expansions;

  • The wide application of rectangular ratios in the dimensioning of the rooms;

  • The application of the compositional method ad quadratum, based on which the outline figure is subdivided by a modular grid that governs the arrangement of buildings and gardens;

  • The importance of the main hall as a centralizing and regulating figure of the entire composition;

  • The use of different rectangular ratios depending on the functions of the rooms and the prevalence of some measures in each type of room.

A development of the present research foresees the study of the relationships between the proportions of the lengths and widths of the rooms and their heights, also verifying the morphological and constructive compatibility of the proposed roofing systems. In this sense, three-dimensional digital models of synthesis could facilitate the spatial recomposition of the 24 villas, providing an understanding of the paths and the use of the rooms. Further ideas could arise from a widespread comparison, including graphic analyses, of the drawings in Book VII and, above all, with the models of private houses drawn in the two manuscripts of Book VI. Moreover, the possible links between the works of Serlio and Palladio, including a strict comparison between Serlio’s and Palladio’s plans, should be the subject of future work.