Understanding compositional practices is a major goal of musicology and music theory. Compositional practices have been traditionally viewed as disembodied and idiosyncratic. This view makes it hard to integrate musical creativity into our understanding of the general cognitive processes underlying meaning construction. To overcome this unnecessary isolation of musical composition from cognitive science, in this conceptual analysis, we approach compositional processes with the analytic tools of blending theory, material anchoring, and enaction. Our case study is Iannis Xenakis’ use of sieves for distributing rhythmic patterns in Psappha . Though disregarded in previous accounts, the timeline and the gearwheel provide crucial conceptual templates for anchoring Xenakis’ idea of time for this score. This case study of conceptual integration templates for temporal representation seeks to gain insight into musical creativity, embodiment, and blending, especially into how virtual interactions with material structures facilitate the construction of complex meanings.