1 Linear Perspective Models of Carlo Crivelli's Annunciation Abstract 1
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Linear Perspective Models of Carlo Crivelli’s Annunciation Natasha Rozhkovskaya Department of Mathematics, Kansas State University KEYWORDS Linear Perspective, Carlo Crivelli, The Annunciation Abstract Several linear perspective models of The Annunciation with Saint Emidius by Carlo Crivelli were proposed by different authors. Surprisingly, straightforward technical reconstructions often do not match each other. In this note we compare reconstructions, provide mathematical arguments, contribute new observations. We cover consistency of the one-point perspective of the painting, floor plans, side views of the buildings, comparison of the heights of characters, visual illusions. 1. Introduction Analysis of linear perspective proved to be an important geometric tool in studies of artists’ techniques, connections between schools, symbolic interpretations. Such analysis may even imply reinforcement of an attribution of an artwork, see e.g. (Ampliato Acosta 2020). This note is dedicated to the geometry of the space of The Annunciation with Saint Emidius by Carlo Crivelli (1486, National Gallery, London). As Golsenne (2002:161) points out, the elaborate perspective scheme of the ornamented painting serves as one more demonstration of the artist’s mastery. This intention was not left unnoticed: several scholars investigated the space of the painting, providing the floor plans, reconstructing buildings, analyzing the composition in a historical and social context. Surprisingly, not only symbolic interpretations of the artwork vary significantly, but straightforward technical reconstructions also often do not match each other. In this note we compare space reconstructions of (Zanobini Leoni 1984), (Arasse 1999), (Hart Robson 1999), (Hofmann 2000), and (Heldermann Hofmann Münder 2008) exclusively from the mathematical point of view. We comment on the observations of the peers, supply supporting mathematical arguments, contribute new findings. We address consistency of the one-point perspective of the painting, floor plans, side views of the buildings, heights of the human figures, visual illusions. 2. Composition of the Painting We briefly review the famous politico-religious subject of the painting (Rushforth 1900; Zampetti 1986, Arasse 1999; Lightbown 2004, etc.). The altarpiece is a commemoration of acquiring of the right of self-government issued to the city of Ascoli by Pope Sixtus IV. The document came on March 25, 1482, the Feast Day of the Annunciation. The scene traditionally features Archangel Gabriel and praying at prie-dieu Maria. As a unique variation, the figure of the saint patron of the town St. Emidius is kneeled behind Archangel Gabriel. He holds the model of the city, which, according to (Golsenne 2002:54), represents ex-voto offered by the city to Maria. In the middle ground on the top of the arch bridge a city official is reading the document delivered by the papal messenger. A group of two Franciscan monks, a noble man and a child are standing on the staircase to the left. Several other characters can be noticed in the far back. The composition echoes many other examples of Annunciations (Arasse 1999:191; Golsenne 2002:163). The canvas is bisected by architectural structures separating Archangel Gabriel and Maria. The left half of the canvas depicts an urban cityscape with a regular lattice of floor tiles, which serves as a reference grid for the perspective construction. The right half of the painting is divided vertically in two parts, featuring the interior of Maria’s palace in the lower section, and the lavish balcony in the upper section. 1 (Arasse 1999) states that Italian paintings of Annunciation played a crucial role in the development of the linear perspective method. The one-point perspective of Crivelli’s artwork is a special case even among those. It represents a remarkable artistic challenge that outstands many other similar compositions. In Crivelli’s composition the grid of the floor expands with a minimum of view obstructions of the positions of architectural structures in relation to this grid. This setup introduces a highly rigid scale through the whole depth of the painting and excludes any geometric ambiguity in measurements and distances. As a result, a quest for consistency implies the necessity of rigorous calculations. Crivelli virtuously demonstrated his skills of creating an imaginary three-dimensional space, turning The Annunciation into an exceptionally interesting case for geometric analysis. 3. General Remarks on Reconstructions To our knowledge, (Zanobini Leoni 1984) is the first publication that provides the floorplan of the foreground of the painting along with the side view of Maria’s palace. The position of the viewer of the scene in this work is estimated by a view angle. The floor plan in (Arasse 1999: fig 17:192) is attributed to Loïc Richalet. However, it is based on the diagram (Zanobini Leoni 1984) with some added background space behind the arch. The studies of (Hofmann 2000) and (Heldermann Hofmann Münder 2008) are focused on the technical reconstruction of the space. The later one of the two articles is the only work where the actual three-dimensional wooden model of the space of the painting was built and photographed. Yet, we find the diagrams of these two publications to be the least accurate in comparison to other studies, and we question the rationality of the methods used in the three- dimensional wooden model reconstruction given drastic digital alterations of the final image. From our point of view (Hart Robson 1999) is the most careful technical analysis of the geometry of The Annunciation. Our observations independently agree (up to insignificant variations) with many conclusions of the later study. The article provides the floor plan, the side view of Maria’s palace, discusses the distortion of the space and human figures in the background of the painting, the spatial position of the cloud with the nimbus of golden rays, possible position of the sun. We retain slight skepticism towards the interpretive analysis of the paper that is occasionally conducted through the prism of modern clichés and with a minimum of references to any historical context. Also, we would like to object gently the statement (Hart Robson 1999:56) that the provided reconstructions would be impossible without use of the computer, since in this study the use of the computer amounts to careful draftsmanship in a convenient design software rather than to any specific algorithms or computer calculations. We praise the accuracy of graphical constructions achieved through the benefits of the computer aided graphics design, but the arguments behind the conclusions of this study are of simple classical geometry nature. We refer to (Zampetti 1986; Arasse 1999; Golsenne 2002; Lightbown 2004) for the historical, stylistic, symbolic, and social analysis of The Annunciation. Readers may be also interested in essays (Randolph 2007, McCall 2009) on gender-related interpretations. 4. Basic Elements of the Perspective Diagrams of the perspective scheme are provided e.g., in (Arasse 1999: Fig 16:192; Golsenne 2002: Fig 9, after (Arasse 1999); Hart Robson 1999: Fig.1). All of those agree that the basic linear perspective rules are scrupulously observed by the painter: the orthogonals have the unique vanishing point P placed right in the center of the distant figure of the young man in the red cap (Fig.1). The position of the vanishing point P defines the horizon line, the eye level of the viewer of the scene. Note that the horizon line coincides with the eye level of the man standing in the middle ground by the staircase on the left. (Arasse 1999) and (Glosenne 2002) attribute to this character special function of the observer, identifying him with the viewer of the scene. We will refer to this man as the ‘internal observer.’ With such identification we may assume that the height of the viewer of the scene is the same as the height of the internal observer (Fig. 2). 2 Figure 1. Vanishing point P, horizon level, distance points L and R. Further consistency of perspective construction and of distances between the transversals can be checked against the convergence points of the diagonals of the tiles (Fig.1). The diagonals are called checkback lines, and their convergence points are called distance points. Most of compared here authors mark distance points L and R as well-placed at the horizon line. (Hart Robson 1999) challenge the accuracy of the convergence of checkback lines. They state that only diagonals of the first four rows of the floor accurately converge to the right distance point R. Our measurements confirm the presence of some deviation. At the Figure 2. The internal same time, we do not find the magnitude of the deviation to be observer. significant enough to provide any definite conclusions of intentional or unintentional artists’ manipulations with the linear perspective scheme. To proceed with such conclusions, one has at least to eliminate such factors as possible deformations of the painting itself, as well as the limits of the precision of measurements due to the use of a reproduction of the painting. To compare distances within the scene we set the side of the square tile to be the unit of measurements. Then the internal observer has the height of about 5 units. Assumptions on the height of this character may suggest an estimate of a length of this unit. For example, assuming that the height of the internal observer is about 170 cm, the length of the square tile could be about 34 cm. In (Hart Robson 1999) the measurements of human figures and distances depart from the height of Archangel Gabriel. The assumption is made that it is equal to be three Florentine braccia or five feet nine inches. We have few objections on such choice. First, the standard of the height of three braccia is usually applied to a standing figure, and Archangel Gabriel is kneeled. Second, it seems that across Italy there was no fixed measure for one braccio unit, and without additional research it is not clear, if Crivelli indeed would use the value proposed by the authors.