<p>Time-periodic dynamical systems occur commonly both in nature and as engineered systems. Large-scale linear time-periodic dynamical systems, for example, may arise through linearization of a nonlinear system about a given periodic solution (possibly as a consequence of a baseline periodic forcing) with subsequent spatial discretization. The potential need to simulate responses to a wide variety of input profiles (viewed as perturbations off a baseline periodic forcing) creates a potent incentive for effective model reduction strategies applicable to linear time-periodic (<span>ltp</span>) systems. Classical approaches that take into account the underlying time-periodic system structure often utilize the Floquet transform; however, computation of the Floquet transform is typically intractable for large-order systems. In this paper, we develop the notion of a <i>partial Floquet transformation</i> connected to selected invariant subspaces of a time-varying differential operator associated with the <span>ltp</span> system. We modify and repurpose the <i>Dominant Pole Algorithm</i> of Rommes to identify effective invariant subspaces useful for model reduction. We discuss the construction of associated partial Floquet transformations and time-varying reduction bases with which to produce effective reduced-order <span>ltp</span> models and illustrate the process on a simple time-periodic system.</p>