Numerous late twentieth-century composers grappled with the problem of using triads in non-tonal ways. Alfred Schnittke’s atonal music of 1974–85 offers a solution by relying on three triad-to-triad relations: P (parallel), S (slide), and M (minor third). The first two are familiar from neo-Riemannian theory; the third relates a major triad to the minor triad with a root three semitones higher (such as C major and E♭ minor). The PSM framework exhibits two properties ideally suited to an atonal triadic style. First, as each relation belongs to a different common-tone class (i.e., preserves a different number of common tones), the framework affords voice-leading flexibility. Second, each relation is maximally distant within its class, minimizing the possibility of suggesting a key. Examples drawn from Schnittke’s works demonstrate how the PSM framework is used to create chains (P/M, S/P, and S/M), polychords, and reharmonizations. The framework engages in similar voice-leading procedures as other atonal voice-leading practices, and its relations can be generalized to trichord types beyond the consonant triad. Schnittke’s triadic usage has been previously associated with polystylism, the importation of historical styles into contemporary compositions. This article argues that polystylism is a distinct practice from the PSM framework and that the very features of the framework are avoided in polystylistic reference. The PSM framework constitutes an integral aspect of Schnittke’s style, but it also addresses a broad concern of late twentieth-century composition—that of divorcing the triad from tonality.