A comprehensive model of natural language processing in the brain must accommodate four components: representations, operations, structures and encoding. It further requires a principled account of how these components mechanistically, and causally, relate to each another. While previous models have isolated regions of interest for structure-building and lexical access, many gaps remain with respect to bridging distinct scales of neural complexity. By expanding existing accounts of how neural oscillations can index various linguistic processes, this article proposes a neurocomputational architecture for syntax, termed the ROSE model (Representation, Operation, Structure, Encoding). Under ROSE, the basic data structures of syntax are atomic features, types of mental representations (R), and are coded at the single-unit and ensemble level. Elementary computations (O) that transform these units into manipulable objects accessible to subsequent structure-building levels are coded via high frequency gamma activity. Low frequency synchronization and cross-frequency coupling code for recursive categorial inferences (S). Distinct forms of low frequency coupling and phase-amplitude coupling (delta-theta coupling via pSTS-IFG; theta-gamma coupling via IFG to conceptual hubs) then encode these structures onto distinct workspaces (E). Causally connecting R to O is spike-phase/LFP coupling; connecting O to S is phase-amplitude coupling; connecting S to E is a system of frontotemporal traveling oscillations; connecting E to lower levels is low-frequency phase resetting of spike-LFP coupling. ROSE is reliant on neurophysiologically plausible mechanisms, is supported at all four levels by a range of recent empirical research, and provides an anatomically precise and falsifiable grounding for the basic property of natural language syntax: hierarchical, recursive structure-building.