Ever since in Greek antiquity the Pythagorean philosophers linked music with a classification system based on number theory, musical composition - in the form of a theory of harmony - has also been bound to architectural design - in the form of a theory of proportion.
For centuries, the shared basis in number theory remained the constituting esthetic principle for musical composition and architectural design. The analogies between the beauty or equilibrium of a building or space, and musical harmony and euphony were elaborated in particular in the Renaissance. The affinity of music to architecture ultimately became a dictum with the Romantic thesis that architecture is petrified or frozen music. It was not until the twentieth century that the objective basis of music and architecture in number theory was relativized and finally suspended. New, shared esthetic attitudes took the place of a universal concept of harmony - such as, for example, machine esthetics, the synthesis of the arts, or utilitarianism, which bespeak direct connections between musical composition and architectural construction. In the second half of the twentieth century, the interface between architecture and music became increasingly extended by the aspects of sounding urban space and landscape in terms of a sound architecture.
The close affinity between music and architecture has been passed down for nearly three thousand years by the Chinese, the Egyptian, and in particular the Greek history of culture and philosophy. According to this ancient understanding, music and architecture are based in equal measure on order structures that we can express in the form of numeric relationships and which find their particular exemplification in the theory of musical harmony and the theory of architectural proportion.
In antiquity, the Pythagorean theory of harmony was considered the universal standard of musical composition and, in derivation from this, also the standard of architectural design – be it, for example, in the form of the arrangement of columns, the dimensional ratio of the ground plan of a building, or the organization of facades. In the Platonic dialogue Timaeus, which deals with the creation of the world soul and the cosmic order in terms of a harmony of the celestial spheres, the Pythagorean relationships of the whole to its parts is explained. According to the Pythagoreans, number harmonies manifest themselves both in the constitution of the entire cosmos as well as in the structure of the human soul. The earliest application of the Pythagorean theory of harmony in architecture was handed down in Vitruvius’s treatise De architectura libri decem from the first century B.C., in which it is said to serve the successful creation of the proportions of crafted objects. Vitruvius called for a knowledge of music to be part of an architect’s education.
In the following centuries, the numeric aesthetics based on the Pythagorean concept of harmony was – in different variations and adaptations – definitive for the theory and practice of music and architecture. In the Middle Ages, the ancient cosmic theory of harmony was elevated with Christian symbols and associated with special construction methods (for instance, the golden cut and Fibonacci numbers). These developments in the relationship between music and architecture were again taken up theoretically in tracts by Augustinus or Boethius, for example, and were used both in Christian cult buildings, such as medieval minsters and Gothic cathedrals, and in the famous lodge book by Villard de Honnecourt of the early thirteenth century.
There is a special relationship in terms of architectural and musical harmony between the Florentine cathedral Santa Maria del Fiore and Guillaume Dufay’s motet Nuper rosarum flores from 1436, which was performed on the occasion of its consecration. Analogies can be identified between the numeric structure of the motet and the proportional dimensions of the cathedral.
Pythagorean number aesthetics was again taken up in the Renaissance and further developed into a comprehensive theory of proportion in architecture. Leon Battista Alberti’s arrangement of the facade of the Florentine Palazzo Rucellai from 1455 is a striking example of the analogy between music and architecture passed down from antiquity. In his design of the exterior facade of the palace, Alberti, who, with reference to music, had already presented the ideal proportions for various room dimensions based on Pythagorean numerical ratios in his treatise De re aedificatoria (1485), realized a proportional arrangement that even went beyond Pythagorean consonances. In the facade’s organization, in addition to the eighth, the fifth, and the fourth, i.e., in addition to the ratios 1:2, 2:3, and 3:4 as well as their multiples, he also included proportions that are made up out of the number five and in terms of music correspond with pure thirds (major third 4:5, minor third 5:6) and sixths (major sixth 3:5, minor sixth 5:8). The inclusion of these proportions, which have major significance in the proportional organization (facade design, ground plan, and room arrangement) of Andrea Palladio’s buildings, incorporated an important music-theoretical innovation of the fifteenth and sixteenth centuries, according to which in addition to the eighth, fifth, and fourth, the thirds and sixths are now also acknowledged as consonant intervals. Thus, the musical way was clear for triad harmony, which replaced the medieval fifth and fourth organum and advanced to become a definitive musical feature that would remain valid until the late Romantic period.
Criticism of the Pythagorean theory of harmony can to some extent already be discovered in Gothic architecture. The aesthetic premise that beauty or harmony is based on abstract and thus unalterable numeric proportions was increasingly called into question in the architecture-theoretical discourses of the seventeenth and eighteenth centuries – exemplary for this was Claude Perrault’s debate with the neo – Platonist Jacques – François Blondel. The objective basis of the Pythagorean theory of harmony was eventually invalidated in the Romantic period by the notion that aesthetics – as explicated in Immanuel Kant’s Critique of Judgment – is a theory of subjective taste and that musical-harmonic proportions are only subject to a subjective interpretation or personal perception.
The Romantic thesis – variations of which can be found in Friedrich Wilhelm Joseph Schelling and Johann Wolfgang von Goethe – that architecture is to be regarded as petrified, solidified, or frozen music, must be viewed in this context. The concept of a harmonia mundi and the notion of musical and architectural analogies, for example in Schelling’s Philosophy of Art, was certainly not completely invalidated, but the relationship between music and architecture shifted in a special way. On this view, because of its non – objective nature, music – alongside poetry – ranks highest in the canon of arts, whereas architecture ranks far below it due to its coarse materiality. This metaphysical foundation in the arts, which pits non-objectivity and objectivity against one another, becomes clearer if one compares two art – philosophical theses. Those concerned here are the rationalistic thesis put forth by Gottfried Wilhelm Leibniz – quite in the tenor of Pythagoreanism – according to which music is a secret arithmetical exercise of the counting mind, and Arthur Schopenhauer’s parody of this thesis, according to which music is more a secret metaphysical exercise of the philosophizing mind. In summary, however, it can be established that for centuries the Pythagorean theory of harmony in music and architecture – either with enhancements or modifications or in latent form – was the normative foundation of composition and construction.
In the first half of the twentieth century, aesthetic attitudes that tied in both with the synthesis of the arts proclaimed by the artistic avant-garde and with the aesthetics of the machine constituted the standards of comparison and reference for musical composition and architectural design. The characteristics of progressing industrialization, the large city, and modern life influenced the visual arts and music. In particular in Italian futurism, the model character of the machine became especially noticeable for sound composition, for instance in the manifestos and works by Francesco Balilla Pratella and Luigi Russolo, and for New Architecture, such as in designs by Antonio Sant’Elia. In much the same way Russolo generated new musical forms with his intonarumori (noise-generating instruments) on the basis of a sound-related machine aesthetics, the futurist building was to resemble a gigantic machine that rose up from the edge of a tumultuous abyss. The machine as a perfectly functioning apparatus and expression of modern urban life played a major role both in French purism of the 1920s (Le Corbusier) – and, derived from this, in the constructivist phase of Bauhaus architecture (for example, Walter Gropius, Hannes Meyer) and the International Style – as well as in the early forms of machine music in the 1910s and 1920s. Eric Satie’s Parade (1916-1917) as well as Edgard Varèse’s Amériques (1921, revised 1927) and Ionisation (1931) can be cited as examples. Le Corbusier’s thesis that the house is a machine for living in as well as his early living machines – from the Villa La Roche (1925) to the Villa Savoye (1928-31) – and the conceptions by other architects of a mechanical house, for instance, Georg Muche’s experimental Haus am Horn (1923) in Weimar, found their counterparts in compositions such as George Antheil’s Ballet mécanique (1924) and in numerous mechanical compositions such as Paul Hindemith’s composition for mechanical organ for Oskar Schlemmer’s Triadic Ballet.
On the one hand, New Architecture’s living machines of the 1920s represent forms of functionalist architecture that, like the forms of popular utility music found in the 1920s, are to essentially be considered under function-oriented aspects; on the other hand, they lead to a new standardized canonization of architectural forms that tie in with traditional standardized concepts of architecture (for example, Platonic bodies and neoclassicism). These neoclassicist tendencies in modern architecture, for example in Le Corbusier’s work, have their analogy in the new classicism of modern music, such as in works by Erik Satie, Ferruccio Busoni, and Igor Stravinsky. Satie’s compositions, which in an exceptional way conceptually make reference to a space (his Musique d’ameublement, for example, which as a background in the form of ribbons or carpets of sound is meant to belong to the space’s furnishings; or his piano pieces Ogives , which were inspired by Gothic architecture and his having read Eugène Emmanuel Viollet – Le – Duc), were intended to be white and pure like antiquity, as can be read in the preface to his score Socrate (1916). Reference to antiquity as well as features of Satie’s white and pure music, such as lack of ornamentation, simplicity, clarity, precision, and balance, can also be perceived as aesthetic exemplifications in classic modern architecture and, in particular, in the purist architecture of Le Corbusier, whom Satie presented as the central figure in a new aesthetics of music in the journal L’Esprit Nouveau, of which he was co-editor.
In addition to the outlined analogies between machine aesthetics and neoclassicist trends in architecture and music as well as between utility music and functionalist architecture, expressionist analogies in music, art, and architecture can also be identified at the Bauhaus.
Architectural expressionism linked back to the Romantic notion of architecture as solidified sound or frozen music, and in subjective series of associations united architectural design with musical composition. This applies equally to Hans Poelzig’s designs for the Salzburg Festspielhaus and his sketches for the Dresden concert hall, as well as for the theater and music-hall designs by Wenzel Hablik, Hans Scharoun, and Wassily Luckhardt: expressionist architectural designs were meant to ascend and precipitate so as to become absolute music and absolute plays on color and form. The maxim compose like a musician was expounded in the manifestos (e.g., Hermann Finsterlin’s Casa Nova – Architecture of the Future, 1919) and publications by the German group of artists and architects Gläserne Kette (Crystal Chain), for instance in Bruno Taut’s book Der Weltbaumeister (The World Master Builder), which bears the subtitle Architekturschauspiel für symphonische Musik (Architectural Drama for Symphonic Music).
The references and formal analogies between architectural or urbanist designs and musical compositions to a large extent define the relationships between architecture and music from the second half of the twentieth century to the present. The latent Pythagoreanism in Le Corbusier’s design for the musical glass panes for the monastery Sainte-Marie de La Tourette (1956-1960), which is based on the numerical series of the Modulor, and in Iannis Xenakis’s transposition of the graphic notation of string glissandi in his composition Metastases (1954) to the construction principles of the Philips Pavilion (1958) are exceptions. Subjective or metaphorical reference to sound phenomena in architecture can be identified, for example, in Le Corbusier’s design for the chapel Notre Dame du Haut (1950-1955) in Ronchamp. He referred to the chapel as a kind of acoustic sculpture that projects its forms into the distance and in turn receives the respondent light energy of the surrounding spaces. This concept corresponds with the terms sound projection and spatial music coined by Edgard Varèse. Examples for the free translation of musical notation systems can be found in the urbanist project Bloch City (1983) by Peter Crook, in which the notes, bars, and staves in Ernest Bloch’s concerto for violin (1937-1938) were interpreted as high-rise buildings, bridges, and traffic lanes; in Bernhard Tschumi’s deconstructivist designs; and in Steven Holl’s design for Stretto House (1989-1992), in which Béla Bartók’s composition Music for Strings, Percussion, and Celesta (1936) is translated into architecture. Conversely, architectural attitudes or buildings also inspired composers. These include, for example, the universal, utopian thinking of R. Buckminster Fuller for John Cage’s forms of indeterminate aleatory music, and the structures designed by the Venetian architect Carlo Scarpa for compositions by Luigi Nono. Finally, found urban sounds are processed in the Musique Concrète of Pierre Schaeffer and Pierre Henry; in minimal music, for instance in compositions by Steve Reich and sound installations by artists such as Bill Fontana or Rolf Julius; and in general in city soundscapes. In the genres of New Music, sound art, and audio performances, space or the concrete location and thus a reference to architecture and urbanism is advancing to become a decisive formative criterion. Finally, sound architecture deals with the questions as to what is auditorily perceived in an existing architectural environment and how it is perceived. Works such as Andres Bosshard’s Riflessione di una diga (Reflection of a dam; 1987), in which the acoustic properties of a dam in Fusio in the Italian district of Vallemaggia are revealed, show that the experience of architecture is always also marked by auditory perception.
 Le Corbusier, Toward an Architecture, trans. John Goodman (London: Francis Lincoln Publishers, 2008), 164.
 The Modulor is a proportion system developed by Le Corbusier between 1942 and 1955 and derived from both the physical proportions of the human body and the ‘golden cut.’
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