This article reflects on the “flat” history of timbre space, tracking its emergence as a technical inscription in psychoacoustic experiments and its rise to become a dominant conceptual metaphor in timbre studies. Drawing on Bruno Latour's notion of “immutable mobiles,” the author shows how the idea of a multidimensional timbre space has been propagated through the circulation of diagrams, which make perceptual data on listeners accessible to remote viewers. After surveying laboratory tools and techniques required for the production of these diagrams, the article considers how models of timbre space have been built into new technologies for music composition, performance, and listening, as well as into audio classification schemes and metadata formatting standards like MPEG-7. Mapping connections between psychoacoustic discourses and design practices, the article sheds light on the technoscientific origins of timbre space, examining its articulation to research labs at Bell, CCRMA, and IRCAM, and interrogating its role in determining what counts as sound knowledge.