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Rudolf Wittkower addressing the Milan conference 'De divina proportione', as part of the Ninth Triennale, Milan, September 1951. By permission of Fondazione La Triennale di Milano.
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The subject of architectural proportional systems in the history of architecture, the topic of this special collection of essays in 'Architectural Histories', has long been characterized by a fundamental ambiguity: the word and concept of proportion simultaneously signify two unrelated and in some ways opposite meanings. Proportion can refer to rat...
Contexts in source publication
Context 1
... ambiguous, metaphysically driven melding of the two kinds of proportion discussed in this section, propor- tion-as-ratio and proportion-as beauty, have found four main categories of expression in the art and architectural literature from Alberti to the present. Two of them, we have seen, are the terms 'proportion' and 'harmony'. 50 Indeed, today scholars and architects still commonly refer to 'harmony and proportion' without understanding spe- cifically what these words mean, or realizing that by using them they are perpetuating an ambiguity that traces back at least as far as the early Renaissance. The third category is the notion of regulating lines, which along with harmony Blondel also promotes in his Cours ( Fig. 6; Blondel, Cours, V.ix.752). The fourth, the virtual cult of the golden sec- tion, originated in Germany in the mid-19th century, and is only superficially related to the occasional and probably often inadvertent appearance of this ratio (1:1.618...) in medieval architecture. 51 These four categories of expression blended with par- ticular fervor in France during the second decade of the 20th century, in the discussions of several avant-garde groups composed of artists and others, including Section d'Or (Golden Section; also called Groupe de Puteaux), Les artistes de Passy, and Art et Liberté. Among the vari- ous members and officers of these groups were August Perret, Paul Valéry, Amédée Ozenfant, Gino Severini, Pablo Picasso and Charles-Édouard Jeanneret-Gris, the future Le Corbusier (Laurent 1998;Loach 1998; Jeunes Peintres ne vous frappez pas! 1912). 52 Out of this early 20th-century French cultural context, augmented by German and other influences, eventually emerged Le Corbusier's Modulor, a proportional system of the 1940s that combined all four of the above-noted categories of expression of the ambigu- ously quantitative/qualitative notion of proportion. 53 Out of this context also belatedly emerged, in 1951, the Milan conference, which for some of the older participants such as Severini and Le Corbusier must have carried a rather nostalgic air of reunion, albeit in a dramatically different, post-war world (Fig. 2). 54 The legacy of the Milan conference Dominated by the conspicuous participation of Le Corbusier and Wittkower, and given augmented pres- tige by the contributions of other leading intellectuals including Sigfried Giedion, Matila Ghyka, Pier Luigi Nervi, Andreas Speiser and Bruno Zevi, the 1951 conference gave voice to a spiritual yearning on the parts of the organiz- ers and participants for the development of a unified, orderly basis for the arts and sciences as a pathway toward the reformation of society, and ultimately, recovery from the trauma of World War II. 55 In his introduction to the recently published proceedings of the conference, Fulvio Irace describes this yearning as ...
Context 2
... diverse collection of essays presented in this special collection of Architectural Histories, written by leading scholars in the field of architectural history, grew out of the international conference 'Proportional Systems in the History of Architecture', held in Leiden in March 2011 ( Fig. 1). 1 The conference was scheduled to commemorate the sixtieth anniversary of the last international confer- ence on proportional systems in the arts, held in Milan in 1951 and titled 'De divina proportione', which similarly gathered leading thinkers of its day (Fig. 2). 2 This recent anniversary thus offers a valuable opportunity to reflect on where the study of proportional systems has gone over the past sixty years, and where it might most productively go from here. Although the premises of the two confer- ences were fundamentally different from one another - the Milan conference promoted the contemporary use of proportional systems in the arts for the aesthetic and spir- itual betterment of society, while the Leiden conference promoted the historical study of specifically architectural proportional systems for the advancement of scholarly knowledge -certain noteworthy attitudes toward the subject of proportional systems manifested in the Milan conference are still prominent today. 3 On the bright side, both conferences together demonstrate a sustained recog- nition of the importance of the multidisciplinary study of proportional systems as integral parts of human culture across time and geography. Less productively, while sym- pathy with the overtly mystical beliefs that drove the Milan conference is substantially more subdued in the scholarly community today, a fundamental ambiguity inherent in the concept of proportion that enabled those beliefs to flourish in 1951 continues to characterize much scholarly thinking about this subject today: when architectural his- torians use the word 'proportion', whether they intend it to signify a ratio, architectural beauty, or both simultane- ously, is often unclear to author and reader ...
Citations
... Similarly, the spirals of galaxies also develop according to the golden ratio. In the human body, you can also find many dependencies remaining with the golden ratio, as already mentioned above (Cohen 2014). By reviewing achievements in the field of biomimetics, one can observe numerous structures inspired by biological systems, which serve as inspiration for problem-solving by understanding the mechanisms of biological systems. ...
Wooden furniture design necessitates the integration of both technological requirements and aesthetic considerations. To guide designers in achieving this balance, this article explores how established design principles, such as proportions and preferred numerical sequences, can inform decision-making for both technological and aesthetic aspects. The goal is to demonstrate how these principles can be integrated with modern CAD tools. In reviewing the scientific literature, this study compiled and compared mathematical and non-mathematical models that support dimensional decision-making. These models included ancient canons (Egyptian, Greek, and Roman) alongside those of Leonardo da Vinci, Palladio, Dürer, Le Corbusier, Zeising, McCallum, and Brock. Additionally, the article examines numeral systems used in modern technology, such as Renard's series and convenient numbers. It is proposed that designers should experiment with geometric design templates to achieve balanced proportions. All geometric design principles contribute to aesthetics, creativity and effectiveness in design. The literature identifies two groups of dimensional design templates: organic, inspired by the human body or the Fibonacci sequence, and inorganic, based on numerical order. It's impossible to pinpoint a single "optimal algorithm" to support dimensional decisions in design. Specific geometric design principles serve as valuable tools, not the ultimate answer.
... Using basic geometric shapes to precisely control architectural scale and proportion seems to be a universal principle in the pursuit of architectural aesthetics, appearing in the architectural history of different regions around the world. Padovan (2002), Wi kower (1998), Buthayna (2012), and Cohen (2013Cohen ( , 2014 have discussed the proportion systems and mathematical principles of European classical architecture [13,[22][23][24][25]. Oikonomou (2011), Eltrapolsi (2022), and Xavier (2022) have revealed the compositional proportions and geometric principles of traditional architecture in northern Greece, Tripoli, Libya, and Cuenca, Ecuador [26][27][28]. Arnold (2018) indicated that tenth-century geometry marked a shift to a new method distinct from the Roman era, guiding the compositional and spatial perception design of Islamic architecture in Córdoba [29]. ...
... Using basic geometric shapes to precisely control architectural scale and proportion seems to be a universal principle in the pursuit of architectural aesthetics, appearing in the architectural history of different regions around the world. Padovan (2002), Wi kower (1998), Buthayna (2012), and Cohen (2013Cohen ( , 2014 have discussed the proportion systems and mathematical principles of European classical architecture [13,[22][23][24][25]. Oikonomou (2011), Eltrapolsi (2022), and Xavier (2022) have revealed the compositional proportions and geometric principles of traditional architecture in northern Greece, Tripoli, Libya, and Cuenca, Ecuador [26][27][28]. ...
Investigating the mathematical and geometric principles embedded in ancient classic architecture is a significant tradition in the history of architectural development. Drawing inspiration from the modular design and creative ideology based on the geometric proportions of squareness and roundness in ancient Chinese architecture, we propose a new mode of squareness and roundness composition based on scale proportion specifically for the design of multi-story buildings. Taking Yingxian Wooden Pagoda as the case study, we not only re-evaluate the modular system and proportional rules followed in the design of the entire pagoda, but also reveal the technical approaches and geometric rules for effectively controlling the form of multi-story buildings. In particular, the mode of squareness and roundness composition based on scale proportion, utilizing a modular grid combined with squareness and roundness drawings as decision-making tools, can control the scale and proportion of buildings across different design dimensions and organically coordinate the design of multi-story buildings’ plans and elevations. Thus, it can achieve an effective balance of multi-story architectural forms. This study has potential applications in the creation of traditional multi-story buildings and heritage restoration projects, and offers valuable insights for future research on ancient multi-story buildings.
... 305-348. Different proportional systems and their quantitative and qualitative meanings in architectural history have recently been reviewed by Cohen (2014aCohen ( , 2014b. Proportion in ancient Greek architectural design has been treated by Coulton (1977, pp. ...
The Greek deity Dionysos had a particular affinity for war galleys, a relationship perhaps explained by the Homeric Hymn to Dionysos in which Tyrsenian pirates kidnap him on their galley. Soon grape vines entangle the rigging and some of the pirates attempt to escape their fate by jumping into the sea: Dionysos transforms them into dolphins. This hymn served as an occasional motif in pagan art and may explain the miniaturized replicas of seagoing oared ships that played an integral role in the ancient Dionysian cult. These flimsy Dionysian ship carts moved overland in parades, either on wheels or upon the shoulders of celebrants. While the earliest examples may date to the Late Bronze Age, they are best known from a series of three late Archaic-period representations on black-figure skyphoi, now in museums in Athens, Bologna and London. No two Archaic-period Dionysian ship-cart representations are identical in all details. While perhaps due to painters' whims, this diversity in appearance may reflect changes to the ship carts at each annual appearance, analogous to modern-day parade floats. Due to the two-dimensional nature of these ship-cart images, it is impossible today to determine whether the Dionysian ship carts reflected in them consisted of actual vessels-purpose-built and placed on wagons during the procession, employed solely for the Dionysian celebrations-or floats in the form of miniaturized galleys. This paper supplies context and explains the process of creating a three-dimensional digital reconstruction of a generic Late Archaic-period Dionysian ship cart employing contemporaneous imagery and artifacts.
... Since proportional systems are a part of human culture [5,6], in order to fully identify the value of an historic building, it is necessary not only to examine the building from a structural or architectural/aesthetical point of view, but to look further. Therefore, starting from the believes of the craft-guilds, and harmonic proportions used to define architecture, important buildings from the historic part of the city, from the main historic squares, were analysed from a multidisciplinary point of view, in order to identify how the use of geometric ratios changed over time and to identify the link between urban space and building from a geometrical point of view (figure 1). ...
... Therefore, in order to highlight these buildings, imposing towers were placed on the corner and pediments were used to highlight the main facades of the building. 5 Despite the fact that this building is presenting a different aesthetical approach from the adjacent buildings it still respects their geometric ratios. Therefore, the ratio between the height of the building and the roof at its highest point is (√2), while a golden ratio can be identified as a ratio between the roof at its lowest point and the height of the upper floors ( figure 6). ...
Heritage buildings and their surrounding are inseparably intertwined. Anthropological, cultural, symbolic, religious and technical factors are influencing the choice of constructive and architectural features and their interconnection. An important part of heritage buildings, influencing the general outlook, defining its aesthetics, shaping the relationship with the urban context and ultimately contributing to the skyline of the city is the roof. In recent years, numerous timber roof structure assessment methodologies have been developed, which assess the roof structure only by its structural features and state of conservation without taking the link between the roof and the building and its surrounding area into consideration. However, considering the principles of the European guilds, heritage buildings were built with no strict division between symbolic meaning, craftsmanship, architectural aesthetics and urban design methods. This results in a "Gesamtkunstwerk", a total work of art, with harmonically interlinked features and fully connected to its surrounding, leading to a full aesthetic experience. All these features highly influence the aesthetics of the heritage building but also the shape and height of the roof. During the late 19th century and early 20th century, at the dawn of modern architecture and urban design, a bold and aesthetically conscious use of traditional crafts and methods took place in most European cities - the Arts and Crafts movement, Art Nouveau, National Schools. This study aims to define how the relationship between building, roof and the urban context is changing in Timisoara during the late 19th and early 20th century. Ultimately the main scope of the paper is to identify the role of the roof structure in defining heritage structures built around the beginning of the 20th century through a transdisciplinary and interdisciplinary approach.
... Recurrently, behind proportioning is a tendency for architects to try to achieve beauty, harmony and order in design. In his text "Two kinds of proportions," Cohen (2014) speaks of "proportion-as-ratio" and "proportion-asbeauty." He explains how the quantitative/qualitative ambiguity of the term proportion is related to an object. ...
In this paper, an analysis of three Serbian medieval Raška churches highlights the significance of the interaction of regular geometric shapes in the composition of their underlying proportional scheme. The complex geometry recognised in the layouts and cross-sections of these monastery churches points to the potential use of a unique triangular proportioning system. This proportional system is derived from the initial geometry of Štambuk’s proportional canon, which employs two circles constrained by an equilateral triangle in a specific setting. As the essence of religious medieval structures is often related to their interior, in this paper 3D “empty space moulds” are created by the parametric modelling of each element of the structure. This research shows how the variation of the two critical points of the church interior, the centres of the dome and of the main apse, along with the key triangles incorporated in the proportional scheme, affect the final 3D structural model.
... 55 http://data.perseus.org/citations/urn:cts:greekLit:tlg0059.tlg034.perseus-eng1:1.625 56 For this distinction and its implications see (Cohen, 2014) and (Wittkower, 1960) ...
Today, architectural theories are replaced by instant discoursive positions, which are
mainly overwhelmed by a crisis of meaning and legitimacy. The examination of the
history of architectural theories showed that those instant positions are based on the
architectural theories of the 18th century. The reverse-chronological investigation of
the theories of the 18th century has revealed the emancipation of architecture from its
metaphysic knowledge, which distanced the theory from its origins dissociatively, in
the 17th century as the reason that crisis. That knowledge was defining the particulars
of architectural theory, such as origin, meaning, character, taste, and form from
antiquity to the late 17th century. The research showed that those particulars
constitute the universals of architecture. Their genuine origin and language defining
them were structured by Vitruvius in the 1st century BC on the basis of six essential
concepts: order, arrangement, symmetry, eurhythmy, propriety and economy. Those
concepts have been revisited and redefined in order to reflect upon the domain itself
by means of its own terminology, rather than imported concepts. This reflection,
considered as a further study, would proceed towards solid and valid architectural
theories corresponding the crisis of meaning and legitimacy.
The architecture of templon (stone sanctuary barrier), did not change significantly during the Middle Ages. Certain changes can be traced in relation to the position of the representations of Christ and the Holy Virgin, which are important for understanding the function of the templon. At the beginning of the fourteenth century, a rather small church, dedicated to Saints Joachim and Anna, was built in the Studenica Monastery. The remains of the marble closure slabs testify to the existence of a stone templon. A reassessment of the available data has led us to propose analysis of the original form of the templon, with the frescoes of Christ and the Holy Virgin being its constituent parts, painted directly to the north and south of the barrier.
In Iranian architecture, the emphasis on the use of geometric ratios such as human scale and modularization, caused beauty and harmony. Unfortunately, in contemporary architecture, the use of these scales has been forgotten, and their presence has been diminished. Therefore, the main goal of the present study was to analyze and evaluate the geometry and proportions used in six remaining traditional Iranian sunken courtyards in Yazd and Kashan. For each house, the length, width, height and the ratio between these dimensions were measured for the sunken courtyard, courtyard and earth of the case studies. Then, to find out which kind of proportions were used in these sunken courtyards, we proposed some statistical tests to compare our measurements with the traditional proportions used. In the end, the results showed that the proportions used in the design of the sunken courtyard, courtyard, and earth of the case studies are related and the traditional Iranian sunken courtyards have been designed mostly based on the use of Gereh (a unit of measurement), which was the most appropriate and most widely used scale in housing architecture.
Architecture in Ancient Central Italy takes studies of individual elements and sites as a starting point to reconstruct a much larger picture of architecture in western central Italy as an industry, and to position the result in space (in the Mediterranean world and beyond) and time (from the second millennium BC to Late Antiquity). This volume demonstrates that buildings in pre-Roman Italy have close connections with Bronze Age and Roman architecture, with practices in local and distant societies, and with the natural world and the cosmos. It also argues that buildings serve as windows into the minds and lives of those who made and used them, revealing the concerns and character of communities in early Etruria, Rome, and Latium. Architecture consequently emerges as a valuable historical source, and moreover a part of life that shaped society as much as reflected it.
