The beats of mistuned consonances (BMCs) result from the presentation of two sinusoids at frequencies slightly mistuned from a ratio of small integers. Several studies have suggested that the source of dichotic BMCs is an interaction within a binaural critical band. In one case the mechanism has been explained as an aural harmonic of the low-frequency tone (f1) creating binaural beats with the high-frequency tone (f2). The other explanation involves a binaural cross correlation between the excitation pattern of f1 and the contralateral f2 occurring within the binaural critical band centered at f2. This study examined the detection of dichotic BMCs for the octave and fifth. In one experiment with the octave, narrow-band noise centered at f2 was presented to one ear along with f1. The other ear was presented with f2. The noise was used to prevent interactions in the binaural critical band centered at f2. Dichotic BMCs were still detected under these conditions, suggesting that binaural interaction within a critical band does not explain the effect. Localization effects were also observed under this masking condition for phase reversals of tuned dichotic octave stimuli. These findings suggest a new theory of dichotic BMCs as a between-channel phase effect. The modified weighted-image model of localization [Stern and Trahiotis, in Auditory Physiology and Perception, edited by Y. Cazals, L. Demany, and K. Horner (Pergamon, Oxford, 1992), pp. 547–554] was used to provide an explanation of the between-channel mechanism.