This article deals with a way that algorithmic composition systems can be informed by material realities of musical performance. After a general discussion of the relation of abstract algorithms to concrete materiality, the article focuses on the idea of an instrument's space of possibilities. It briefly discusses a number of compositional approaches that seek to derive musical structure from bodily movements and from the physical properties of instruments. The last part describes a new open-source JavaScript library called OboeJS and a Web application based on this library. The system is an experimental exploration of the idea of instrumental space and an attempt to bring together abstract algorithmic processing and the concrete possibilities of a musical instrument. The system implements a flexible constraint-based search algorithm for the generation of oboe fingering sequences. This tool is presented as part of a wider approach to algorithmic composition that aims not to map data output of generative procedures to “sound generators” (e.g., performers, instruments, sound synthesis processes). Instead, I propose to derive structure from the space of possibilities of the instrument itself, which in this case is the oboe.