The design and construction of an organised sound space to support information representations in the human–computer interface is described. The design of the sound space is guided by four principles which match perceptual structure with data structure to improve natural comprehension of an auditory display. These principles – completeness, comprehensibility, consistency, and cohesiveness – have been generalised from the use of colour displays in scientific visualisation. The choice of perceptual parameters to represent different types of data is informed by the body of psychoacoustic literature. The raw material for the construction of the sound space is the McGill University Master Samples (MUMS) palette of musical instrument samples. This is an important choice because this reference resource enables reproduction and confirmation of the results. The construction was carried out in four stages – the ‘pedestal’, the ‘skin’, the ‘skeleton’ and the ‘flesh’. The pedestal consists of eight equally discriminable timbres organised in a circle by perceptual similarity. The skin is the boundary of variation in the space, defining the limits of dynamic range for pitch and brightness at each timbre. The skeleton characterises the internal behaviour of the space at a number of perceptually measured points. The flesh is a continuous medium moulded to the skeleton and skin, realised by a three-dimensional (3D) regularised linear spline interpolation. The concrete realisation of the sound space can be investigated through a user interface, called the GamutExplorer. Colour visualisations of slices and wireframe views of the 3D space can be chosen, and sounds can be picked with a mouse.