Gabo's interest in sound was peripheral, essentially a by-product of his fundamentalist approach to sculpture and space. Like many artists of his time his space was shaped by emerging mathematical and physical models, many works adopting their techniques, processes and forms.⁵ His Constructed Heads applied the engineering technique of stereometric construction, the Construction in Space-Crystal (1937) closely resembled a mathematical model, and the Spheric Theme (1936) also had mathematical precedents.⁶ Nevertheless his space remained phenomenal; he always sought to capture visual space,

as he saw it, in sculpture.

The twisted surfaces that characterised much of his work following the mid 1930s satisfied a long quest for a means of expressing his vision of space. Gabo strove for sensations of continuity, surroundedness, dynamism, self-sufficiency, and of force as much as mass. These works are formations of complex surfaces of double curvature, often made up of innumerable threads or wires, strung on a frame which is sometimes a heavy counterpoint to the lines, sometimes transparent and empty. The multiple layers of lines found in many of these constructions give a heightened sense of movement as the viewer circumnavigates the work. These works are primarily about engaging with space.

The Linear Constructions verge on audibility in a number of ways. The hundreds of taut threads form a vibrant mass, the sculpture becoming an incredible harp. Were this harp to sound, it may well approach Xenakis' stochastic music.⁷ A musical potential also exists in the stave-like image of ruled lines, but a stave exploding in the spirit of modernity. Or, as Xenakis shows in Metastasis and Concret PH, the lines can be trajectories in musical space.

The ruled lines also draw on two images of abstract visual space: the Cartesian grid and lines of ruled perspective. These interpretations are compelling in an art that concerns itself with revealing and mapping spatiality. In the first instance, the lines form distorted surfaces -- Euclidean planes but for the work's internal forces. Indeed this tension between

a simple and strongly articulated geometry and the curvilinear form gives a sense of instability, again contributing to its dynamism. As lines of perspective, the image is complicated, suggesting multiple viewpoints, multiple depths, and higher dimensionality. Space recedes and expands in several directions at once; the sculpture represents a multi-stable⁸ and shifting space even as it exists in real space.

Gabo's visual space is not the angular space of Euclid or that of ruled perspective; it is continuous and surrounding. In psychology there have been a number of attempts to formalise such a model of visual space, a notable one being that of Rudolf Luneburg and

his successors.⁹ Patrick Heelan has reinterpreted Luneburg's model and proposed a 'quasi-stable', 'hermeneutic visual space'.¹⁰ This model recognises that a viewer is inevitably well-versed in Euclidean spatial models, and is likely to interpret visual space in such terms when Euclidean structures are the focus of vision. The model also recognises a natural visual space surrounding the viewer. Here the size and shape of objects varies depending on their position in visual space -- unlike Euclidean space, where dimensions are constant. In the far zone, depth is compressed and objects are flattened onto the visual horizon. Space is limited in extent: the stars are on the sky, not in the infinite cosmos. In the near zone, depth is expanded and objects bulge towards the viewer. There is an area between these extremes where Euclidean space is approximated. These phenomena are commonly experienced in 'uncarpented' environments: in the open sea, for example, the water curves up to the horizon. Space envelops this embodied viewer through a heightened sensitivity to depth. Following Luneburg, this subjective visual space is mapped to approximate a Riemannian hyperbolic space.11

This space has also been observed in phenomenology. Maurice Merleau-Ponty invokes depth, not as the third dimension, but as the single dimension of a visual body-centred space.¹² Depth is the vertigo-like sensation of space receding around oneself, or the sensation that occurs in intense darkness of space pressing up against the skin. He describes night as 'pure depth' because of the darkness' cohesion and its intimate, even invasive, contact with the body.¹³ Euclidean space is the space of measurement; a depth-based space is the space of the body.

Gabo's Linear Constructions sensitise the viewer to depth by vibrating between Euclidean motifs and surrounding space. The simplicity, singularity and precision of the lines speak of a measured and ruled space. Yet even as they accumulate the forms of advanced geometry, the constructions become elusive except as algorithms: one can see how the surfaces are made, but the surface itself is difficult to grasp as a geometric entity. The overall wave-like form, however, is readily appreciated as shifting depth. This is partly a function of the subtle curvature itself, but also of the representational aspect of the ruled surfaces. Their sometimes hyperbolic contours (especially in Xenakis' hyperbolic paraboloids) are an apt cue for a perception of hyperbolic space.

Gabo-like constructions are primarily purist expressions of space: non-figurative, with a strong abstract theme, but also compellingly concrete. To claim them as images of sound space is partly arbitrary; after all, how could one find a definitive visual representation of an auditory phenomenon? Their use also reflects a shared ideology about the nature of space, space being a thing in itself, expressed substantially through insubstantial forces and sounds. The spaces have general qualities in common such as a vibration between extension and depth, but specific forms suggest an idealised mathematical sound space. But even when these spaces are constructed in a scientific or mathematical imagination, they must speak through perception. For Varèse the use of hyperbolic and parabolic trajectories represented a break from the established discrete space of musical proportions, heralding a new, continuous sound space grounded on the physicality of sound. Xenakis imagined a geometric space, where sound particles and trajectories might be precisely defined, but which was experienced in performance on a non-mathematical level. In the case of early stereophony Gabo-like images lent a pseudo-scientific aura (reminiscent of relativity) to the technology that promised to bring sound space into the home. Sound space was partly imaginary.

Merleau-Ponty's night becomes a sound space: much more than for vision, sound surrounds and invades the listener. It is scarcely possible to imagine an auditory Euclidean world. The depth apparent in the Linear Constructions is the same depth as that discussed by many sound theorists (especially from the fields of psychology and music), often as the distinguishing and overwhelming feature of auditory space.¹⁴ Depth might be found in music, in surround-sound installations, in reverberation and resonance, and in synaesthetic sensations of sound.

The strong counterpoint of geometry and depth in the Linear Constructions parallels one of the major projects of modernist sound -- the expansion of the frequency range to the extremes, wherein audition is most physical. At the high extreme, acoustics often approximates optics, wavelengths being short with respect to their environment. A geometric or ray model of sound propagation can be applied, and sound is often heard as directional and discrete. Wavelengths of deep sound are large, and sound propagates more like a fluid. There is often a sensation of immersion, as the body is caught up in vibration. While both extremes can give a sensation of proximity, high frequencies tend towards immediacy, while low frequencies are more intimate. The comparable juxtaposition of spatial extremes in Gabo's work may have held some attraction to proponents of modernist sound space.