Ana López Mozo

La construcción gótica de bóvedas evolucionó de forma diferente en las diversas regiones europeas, también en lo que concierne a los métodos de diseño tridimensional. La aplicación de estos procedimientos en una bóveda concreta no es deducible de la planta ni de la observación directa; requiere una explicación o el acceso a las trazas. Además, los métodos para obtener la elevación desde la planta sólo serían compartidos en el ámbito del oficio. Así, estudiar qué procedimientos se emplearon para el diseño tridimensional de bóvedas aparentemente similares, puede ofrecer información valiosa para distinguir entre repetición de un esquema y transferencia técnica. En el marco de un proyecto de investigación sobre transferencia de conocimiento técnico en el tardogótico, esta comunicación estudia la diseminación en Europa de un tipo de bóveda de terceletes singular, que presenta un rombo central alineado con las diagonales y ojivos con frecuencia parcialmente ausentes. No es un diseño simple y su difusión parece requerir una copia consciente, pero las similitudes entre distintos casos pueden ser sólo aparentes y no existir conexiones técnicas entre los artífices. Este tipo de bóveda ha sido documentado hasta el momento en 36 edificios, 7 de ellos en España, y en cinco fuentes escritas originales. Apoyándose en el levantamiento de 35 de las 46 bóvedas hasta ahora documentadas y en el análisis de las fuentes escritas, este trabajo aproxima la difusión temporal y geográfica de este tipo de bóvedas, propone posibles trazas de planta y elevaciones de arcos para comparar los procedimientos encontrados en Centroeuropa y en España y argumenta qué pudo contribuir al surgimiento de esta tipología. La toma de datos de las bóvedas se ha realizado mediante fotogrametría automatizada combinada con coordenadas obtenidas con mini-estación total láser para orientar y escalar los modelos.

In the 15th and 16th centuries a peculiar type of Late-Gothic vault lacking symmetry about longitudinal and transversal axes of the plan appears in at least thirty two buildings throughout Europe; the oldest examples could be located in Poland. They are tierceron vaults with diamond shaped liernes, where the main keystone and the whole or part of diagonal ribs are absent. A number of written European sources include instances of this type of vault: the Frankfurt Lodge Book of Master WG (c. 1560-1572), the Wiener Sammlungen collection (spanning from mid-15th century and the beginning of 16th century) and the Musterbuch of Hans Hammer (last decades of the 15th century).
The design of this kind of vault is not simple; it does not seem to arise from a mere process of ribs multiplication. Although some types of Late Gothic vault were developed in particular countries, master masons travelled throughout the continent, an a permanent exchange took place amongst the different lodges. In many occasions, conscious copies of models were likely made, perhaps reflected in travel sketchbooks nowadays missing. Lacking other documents, a method to go beyond superficial resemblance and look for deeper connections is to analyze how the geometrical layout for both plan and volume has been addressed, since methods for deriving overall elevation from plan were only exchanged among masons.
This paper deals with two examples of this kind of vault that use the same plan layout to span different types of bay: a square one at a corner of the cloister of Basel cathedral (c. 1440-1645), and a rectangular one at the crossing of the church of Bebenhausen Abbey (c. 1467) (fig. 1). This study, supported by a precise data gathering based on crossing-image photogrammetry, is focused on the layout of the rib network. Although both vaults seem to follow the same design, the geometrical construction of plan and elevation is entirely different. The two cases show an advanced use of Gothic design procedures to solve problems easily.

Due to the lack of clay and trees, Armenian architecture makes intensive use of hewn stone; this
fosters the use of complex geometrical schemes that may recall at first sight Western stereotomy
of later periods. The scriptorium or library of the Monastery of Sanahin is a notable example of
these constructions. Located in the northeastern corner of the monastery, between the churches of
Saint Astavacacin and Saint Gregory, the library was built in 1063, under the patronage of Princess
Anuš, the daughter of David Lackland, using only dressed stone as apparent material (Strzygowski
1918, I:67-68, II:822; Cuneo 1988, 290-294; Maranci 2001, 149-151). The library is laid out on a
square plan; a second rotated square is inscribed in the exterior one, with its corners placed at the
midpoints of the sides of the outer square. Without an obvious reason to do so, the four triangles
between both squares are covered with different members. Trumpet squinches are laid over two
diagonally opposed triangles, while pairs of ramping half-barrel vaults meeting at right angles are
placed over the other triangles; in Western terms, we could say this later triangles are covered by
one half of a cloister or pavilion vault, cut along the diagonal of the plan. The lesser, inscribed
square is materialized by four arches that support four approximately spherical pendentives, although
the bed joints are not exactly horizontal. On top of the spandrels lies a circular ring that
supports a vault with eight pseudo-cylindrical severies, featuring horizontal mouldings along the
bed joints and crowned by an oculus. Taking into account its early date, the precision of the execution
of this ensemble is quite remarkable. In this paper, we shall analyze the geometry of this
ensemble, using a precise survey based on crossing-image photogrammetry. This will allow us to
confront this building with Mediaeval European stereotomy: Armenian solutions to these problems
do not seem to arise from a preconceived idea about geometrical generation of forms, as usual in
the West, but rather from the will to materialize complex spaces, in apparently well-dressed stone.

Starting from the inaugural text of Philibert de L'Orme, stereotomic treatises and manuscripts are subject to the opposing forces of reason and fancy. The Nativity Chapel in Burgos Cathedral provides an outstanding case study on this subject. It was built in 1571-1582 by Martín de Bérriz and Martín de la Haya, using an oval vault resting on trumpet squinches to span a rectangular bay. Bed joints and rib axes are not planar curves, as usual in oval vaults. This warping is not capricious; we shall argue that it is the outcome of a systematic tracing method. As a result of this process, the slope of the bed joints increases slightly in the firstcourses, but stays fairly constant after the third course; this solution prevents the upper courses from slipping.Thus, in the Nativity Chapel of Burgos Cathedral, the constraints of masonry construction fostered a singular solution verging on capriccio. It is also worthwhile to remark that the warping of the joints is not easily appreciable to the eye and that the tracing process does not seem to start from a previous conception of the resulting form. All this suggests that we should be quite careful when talking about the whimsical character ofLate Gothic and Early Renaissance; in some occasions, apparent caprice is the offspring of practical thinking.

Choisy situaba en las ruinas de Gerasa el ejemplo más antiguo de bóveda vaída y llamaba la atención sobre el corte de piedra de sus pechinas. La solución canónica en Occidente para cubrir un crucero emplea pechinas como superficies de transición entre la planta cuadrada que definen las embocaduras de las naves y la planta circular de la imposta de la cúpula. Estas pechinas son porciones de la esfera que definen los arcos perimetrales, cuyos paralelos determinan las juntas aparentes entre hiladas, en las que se apoyan unos lechos normalmente troncocónicos. Sin embargo, según Choisy, los lechos de las pechinas de Gerasa son «simples superficies planas» que convergen en la diagonal transversal, a la altura del arranque de la bóveda, de manera que las juntas aparentes entre hiladas estarían inclinadas: si las pechinas fueran esféricas serían circunferencias y las hiladas husos de altura variable. Choisy no precisa si estas pechinas son esféricas o no, pero las dibuja como tales y representa todas sus hiladas iguales. Un reciente viaje de investigación a Armenia ha permitido documentar ejemplos construidos y comprobar que, en muchos casos, la forma de las pechinas armenias y las leyes que gobiernan la disposición de sus juntas no siguen la pauta de la solución canónica antes enunciada y podrían tener similitudes con el caso de Gerasa. Así, este trabajo retende analizar los casos armenios, apoyándose en el levantamiento riguroso de su configuración geométrica y corte de piedra, y situarlos en el contexto de la historia de la
construcción en cantería.

The ribbed vault is considered one of the four elements characterizing Gothic architecture. However, due to its constructive advantages, its success overtook the Middle Ages. Ribbed vaults were still built throughout Europe during the 16th and 17th centuries, when Gothic had already been replaced by Renaissance principles coming from Italy. For centuries, these Late Gothic vaults have been considered a decadent anachronism even by the staunchest defenders of the Gothic style. However, current research on Late Gothic vaults has revalued this rich heritage, showing that these vaults don't respond to an unnecessary complexity or to a mere stylistic mannerism , but to a deep understanding of Gothic construction system. The Late Gothic vault is now considered as part of an evolution, usually offering design or material advantages or expressing the mastery of a system. There is a huge Late Gothic vaults heritage in Europe and some interesting conclusions on this constructive element have already been achieved: stylistic and construction relationships between different countries have been identified, offering evidences of a knowledge transfer beyond a mere copy of patterns. Unfortunately, much of this rich heritage still remains unknown. Researches on these vaults are based on the analysis of particular examples, which doesn't allow tackling the problem as a whole. We cannot answer with confidence seemingly simple questions such as: How many Late Gothic vaults are there? How many vaults with a diamond design are there? Or where did curved rib first appear? We don't even know whether these questions are worth to be answered. This paper aims to present a work in progress that the authors are carrying out at the UPM School of Architecture of Madrid: to lay the foundations for a catalog of Late Gothic vaults, which is not based on formal or stylistic criteria but arises from a reflection on the constructive features of these vaults, from the point of view of Construction History. The catalog would allow tackling future research on this subject with confidence. This work is part of the research project «Spanish late Gothic vaults construction in the European context. Innovation and knowledge transfer», funded by the Spanish Ministry of Economy (BIA2013-46896-P).

Full-scale tracings, drawn in plaster surfaces or engraved in stone walls and floors, were used frequently in Renaissance construction to control the execution of ashlar masonry.  In many occasions, these tracings furnished the shape of the templates used in the dressing process, either in true size or orthogonal projection. A large example of these tracings appeared in 2009 in the vestry of Murcia Cathedral, when the sacristy drawers were disassembled to execute a conservation treatment against woodworm. At first sight, the tracing seemed to be related to the vault over the vestry, built in 1525 by Jacopo Torni l’Indaco, one of the first examples of ashlar sail vaults in Europe; a number of surveys confirmed that the tracing corresponds with the vault quite precisely. In this study, after an introductory section dealing with tracings and dressing techniques, the authors explain the measuring methods used in the surveys, describe the tracing, compare the tracing with the built vault, and discuss the relevance of the tracing, in order to advance knowledge of the evolution of European stonecutting.