Converging evidence from a series of recent lab and corpus-based studies has suggested that a composite model, including a number of predictors that are either intrinsic (e.g., spectral interference) or extrinsic (e.g., cultural familiarity) to chord structure (Smit et al., 2019), best accounts for pleasantness judgments of isolated chords (i.e., simultaneous consonance; Harrison & Pearce, 2020). In the present study, we aimed to explore whether the effects of the 2 most prominent intrinsic predictors in this literature, spectral interference (SI) and harmonicity, are moderated by the presentation of constituent chord tones to both ears (diotically) versus different ears (dichotically). To this end, we conducted 2 experiments in which we presented participants with a set of dyads and collected consonance ratings for each under both diotic and dichotic presentation conditions. To reduce extraneous variance due to chord familiarity, we selected dyads from an unconventional tuning system, the Bohlen-Pierce Chromatic Just scale. Results replicated earlier findings suggesting that both SI and harmonicity independently contribute to consonance judgments of unconventionally tuned chords. Moreover, they provided new evidence that the association between harmonicity and consonance is reliably moderated by presentation mode: In both experiments, the magnitude of this positive association was bolstered when Bohlen-Pierce Chromatic Just dyads were presented diotically rather than dichotically. There was no evidence that presentation mode moderates the association between SI and consonance. Discussion focuses on potential implications of these findings for understanding the low-level processes by which SI and harmonicity independently contribute to simultaneous consonance.