This project attempts to visualise the relationship and translation between Architecture and Music, by studying Georgian and post-1950s modern facades. Through surveying the characteristics and mathematical ordering principles of these facades this project looks to make connections related to the mathematics of music.
Architecture is a form of art that has served people since their initial need for shelter. Throughout history, music has appealed to people's souls; it is a form of art that helps them to express their feelings. Mathematics enables this duo to exist, it creates connections to give both meaning but remains in the background. Both architecture and music have common terminologies, which include critical terms in their historical development processes. In this sense, their resemblance and relationships with one another cannot be ignored.
Palladio’s Villa Rotonda, designed with harmonic proportions
Architecture and Mathematics
Historically, mathematics has been part of architecture all along; it was believed that through proportion, man could achieve harmony in architecture, alongside order, arrangement, eurythmy, symmetry, propriety and economy as Vitruvius mentioned and emphasised that principles of temple designs could not be formed without symmetry and proportion. In ancient Greece and Rome, temple designs were considered important and it was believed that beauty and aesthetics were linked to mathematics. Several well-known architectural monuments around the world are designed and built with mathematical principles. For instance, Golden Ratio proportions are present on the facades of Parthenon, Notre Dame of Paris, Mies van der Rohe's Farnsworth House, Gaudi's Sagrada Familia, Le Corbusier's Unite d'Habitation...
Another dominant principle in architecture is the incorporation of rhythm, which arose from aesthetic apprehensions and aesthetic appeal, to achieve harmony. Therefore, the use of rhythm in designs becomes dominant and it is common all over the world, such as Classical, Gothic and Renaissance architecture in Europe, Taj Mahal in India and Pyramids in Egypt.
Rhythm in architecture, row-houses from the 15th century in Venice
Music and Mathematics
Music is completely interwoven with mathematics, to such an extent that even an essential major chord can be portrayed mathematically. It has been known that mathematical calculations determine musical harmonies. There are terms such as octaves, scales, chords and keys that can be understood logically with the help of pure mathematical thought. So one can say that music's scientific roots are in mathematics.
The mathematical ratios put forward by Pythagoras, Vitruvius and Plato have gained new importance since the end of the fifteenth century. In the Renaissance, Alberti, along with Palladio, was one of the architects that used harmonic proportions of music in his designs, in order to have proper balance and harmony. They both applied their musical knowledge to clarify architectural concepts.
Santa Maria Novella by Alberti, Florence , Italy
After analysis and research on varied architectural styles, this paper seeks to focus on Georgian and post-1950s modern facades. The reasons for this decision can be summarised as 'the rationalisation processes' which happened in these two different periods.
Georgian Architecture and Mathematics
Around 1700 "the prevailing opinion was that good architecture should be based on geometries rooted in harmonic proportions, as employed by the ancients." That is why proportion is vital for Georgian architecture and Palladian architecture, that is characterised by symmetrical facades and an appreciation of proportion. Buildings were built with a system of proportion and ratios, based on square and circle, which were proportioning principles of Ancient Greece and Rome. Symmetry, uniformity and balance were also important. In this sense, the ancient Greek philosopher Pythagoras' principles were the guide for the Georgian architects.
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Square proportions on Georgian facades and plans
One of the most used proportions in the Georgian Architecture, the square was used to arrange facades, window proportions and window opening locations since it was considered critical for achieving architectural beauty. In fact, square, cube, circle and sphere were represented as ideal forms. Room plans and facades could be divided into shapes and described by their relationship to a square.
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Square, circle and Golden Ration proportions on Georgian facades
Post-1950s Architecture Style & Mathematics
Modern architecture flourishes with improving from technical capabilities. With the development of computing and information systems, there is a growing power and complexity of mathematical processes in architecture, which is aesthetically driven.
By the end of the twentieth-century, geometric thinking dominated the architectural world. Developing technology, new software and computing systems allow architects to explore and experiment with new geometries, materials and structural systems based on complex mathematical languages.
There are several architects and artists that interpret mathematical and scientific rules into their artistic productions. Tessellation (tiling), "the process of fitting shapes together in a pattern with no spaces in between, or an arrangement of shapes that have been made in this way" is one way of doing it. Tessellation was used in many ancient civilisations and cultures across the world because it may also have symbolic, monetary and cultural meanings, rather than only aesthetic reasons. However, it has become more widely used in the last century than ever before. Undoubtedly, this is because tessellations are henceforth included in the structure with the developing production technologies and have outstanding advantages such as multiple design possibilities, structure-property, being adaptable with different problems.
Following the initial research, it was decided to make a musical and mathematical comparison of the facades belonging to the two periods according to specific features. For this purpose, three facades with the Georgian architectural style and three facades from post-1950s were selected. These facades were divided into pairs according to specific characteristics.
The first pair, which consists of Welbeck Street Car Park and Wood Street Police Station, was chosen because both contained clear indications of rhythm. Welbeck Street Car Park is a brutalist building that was completed in 1970. Its facade is formed of tessellated concrete units. Wood Street Police Station is a Grade II* listed building that was completed in 1966. The architects, McMorran and Whitby, designed the building based on a set of principles of Georgian buildings such as Golden Ratio. Both buildings facades have certain architectural features that create the perception of rhythm. This perception is created with regular repetition of the same elements that eventually creates the facade of Welbeck Street Car Park. On the other hand, on Wood Street Police Station's facade, some stone extrusions are used that gives the rhythm perception. The perception of rhythm created in different ways and with different materials on these two facades with different architectural styles made the comparison more significant.
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Rhythm & beat collages
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For the second pair, variable aperture types were decisive. The size and scale of the apertures are the main factors affecting the tone of music, pitch and beat. For this, the new building of Ravensbourne University and the building of the Museum of London Docklands were selected. Ravensbourne building was built in 2010. On its facade, three differently shaped aluminium tiles were used which enabled the facade design to be flexible in terms of tile combinations. There are various sized round windows that are created with these tiles. However, "the pattern of the tiles is determined by the size and positioning of window openings, while the size of windows depends on the corresponding interior function." The building of the Museum of London Docklands was built in 1802 as a warehouse. Brick was used for the exterior walls and there are differently shaped and located apertures on them, determined by the function of the building. Different sized and shaped apertures of these two facades are equivalent to different music pieces.
Aperture sizes and shapes
The third pair consists of 30 St. Mary Axe and Maison Assouline's building on Piccadilly Street. For this pair, layering and rhythm are determinant factors. 30 St. Mary Axe is a skyscraper by Foster and Partners built in 2003. This building is selected due to the materials used and the way they were arranged during the construction of the building. Apart from the double glazing effect that was achieved by two layers of glass, some other layers of materials were used vertical, horizontal and diagonally to create the shell of the building.
Maison Assouline was designed in 1922 as a bank by Sir Edwin Lutyens who is "known for imaginatively adapting traditional architectural styles to the requirements of his era”. When the facade is examined, it is seen that the design aims to obtain a different appearance by using different layers of materials on top of each other. The resultant music of these two facades is affected by the overlapping layers that also have a rhythmic pattern.
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Layering of the facades
Mathematical Analyses of the Facades
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Following the facade selections, mathematical analysis of the facades was made relating to their determining factors. Through this mathematical analysis, the terms of rhythm, aperture and layering on the facades were visualised by transformation into sound waves.
Sound waves
A sound wave is described as "a wave of compression and rarefaction, by which sound is propagated in an elastic medium such as air." by the Oxford University Dictionary.
As a translation step between architecture and music, sound waves were created from mathematical grids extracted from the features of the facades, while considering the intersection points of the mathematical grids.
These sound waves were used as a basis medium and translated into musical notes by overlapping music stave with sound waves. This overlapping enabled the translation of facades into music notes and to compose music. The sound waves produced on different facades differ. Some were more meandering and bumpy, while others were closer to flat. In this case, the effect of rhythm, apertures and layering, which had an effect on the grouping of the facades, is inevitable.
Welbeck Street Car Park
Wood Street Police Station
Ravensbourne University
Museum of London Docklands
30 St. Mary Axe
Maison Assouline
The resultant music pieces have been different from each other and it is evident that they are translated from different buildings from different periods and variety of sound waveforms, which are related to mathematical explanations. However, the most significant impact on the resultant music pieces is the attention to rhythm, aperture and layering during the translation process. Given the importance of rhythm, apertures and layering in architecture, music and mathematics, that is an expected result.