Scale: a relationship between geometries and space | The Plan
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Scale: a relationship between geometries and space

Steven Holl Architects

Scale, our comprehension of the measure of geometry and space, remains essential to experience. Beyond the length, width, or mass of a structure, there is magnitude of measurement in scale. Central to the proportional relation of things to humans, scale can be mysterious.
Some cities are filled with enigmatig juxtapositions of large and small scales. Like force fields of different programs, these contrasting scales radiate an inner energy. In Manhattan the juxtaposition of a row of four-story brownstones set directly against a 20-story structure of mysterious scale creates a dynamic contrast equal to the dynamic events that might take place within. The displacement of scale, the juxtaposition of different scales, and the disorientation of apparent scale are all part of a metropolitan dynamic. The programmatic and spatial richness of metropolitan space is parallel to the displacement of habitual readings of scale.
In contrast to the homogenous scale of horizontal suburban sprawl, a dynamic juxtaposition of scales reflects the intense character of urban space. Qualities of contrast in dramatically different architectures give shape to a metropolitan character of variable scales. The preconception of many planning agencies to forcefully integrate and adapt architecture to “context” goes against the complexity of urbanism at its social, programmatic, and poetic core.
The homogenization of scale can stifle the verve and liveliness of urban spirit. However, the experiences of the sublime dimensions of metropolitan space depend on our body in space as an instrument of measure. Our sense of scale is consequently inseparable from proportion and the mystery of the quality of proportion.
The Golden Section is the simplest and most ancient tool for the organization of pleasing proportion. The Golden Section, defined by (1+√5)/2=1,618 produces a mysterious number whose amazing algebraic qualities are equal only to π or 3,14.
Matila Ghyka’s book The Geometry of Art and Life traces the Golden Section’s properties in nature, logarithmic spiral and shell growth, marine animal morphology and gnomonic growth as well as in architecture and music. Scale is central to the gnomic growth of the nautilus shell for example; the proportions of its spiraling chambers are arithmetically parallel to the Fibonacci series 1, 1, 2, 3, 5, 8, 13, 21, 34…
If the simultaneous scales of fractals challenge our senses with infinitely small scales and concepts of “self similarity,” scale in architecture in a perceptual sense is always experienced via the body. From a position of 5’6” off the horizontal plane or with a tilt of the head and one step forward, the experience of architectural space is bound to human proportions and to particular phenomena of the body in space.
Scale and proportion are central to the mathematical links between music and architecture. Unlike a painting or sculpture, which you can turn away from, music and architecture surround us, binding our experience to a time sequence.
Moving through a building, the stride of each step inscribes a sense of scale within the overlapping perspectives of space. We can turn and move in the other direction and the sequence can be a totally different experience yet it is still ordered by the scale of stride.
In twelve tone musical composition a “row” can be followed by a retrograde “row,” which is the same sequence played upside-down and backwards. The intervals remain similar and in a way, they are equivalents of the stride in the scale of walking through overlapping spatial sequences.
Digital techniques have opened a new world of possibilities in architecture. Modeling of space, however, can be without scale, without the essential relation of the human body to the spaces in question. Here, space can be warped in amazing plastic dimensions, however scalelessness underlies the process. One of the problematic aspects of new technology is the removal of scale. The designer working digitally in plastic space is without the sense of the body, without the measure of the scale of space being shaped. On the positive side, the digital presents unprecedented tools for experiment. Fresh geometries are explored. However, in the realized construction, the undeniable relation of the human body to its surroundings in space remains the central experiential dimension. The body, like a mirror of the enveloping space, reflects the measure of scale.
From the macro scale of the metropolis to the micro scale of an individual standing in an interior, the intertwining of space and the body are exhilarating. Like a large centrifugal force engaged with a centripetal force, these scales animate and frame our daily experience.
Throughout the history of architecture, scale and proportion have been a focus. Francesco di Giorgio Martini and Piero della Francesca, as well as Alberti, Serlio, Palladio, and Leonardo da Vinci have all reflected on scale. From Auguste Choisy’s book on the history of architecture devoted to the regulating lines (tracé régulateurs) to Le Corbusier’s Modulor, “a harmonious measure to the human scale”, the understanding of scale has been an aim.
The body in space - the experience of moving through overlapping perspectives with our eyes 5’6” above the horizon - has not changed. Today, perhaps more than ever, an understanding of scale - from the macro to the micro - remains crucial to our perception.
Scale is not a thing but a possibility of our comprehension; a fundamental experience of our world.

Steven Holl


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