Previous studies have demonstrated that absolute pitch (AP) possessors can directly perceive the musical pitch quality (pitch class) of a tone presented in isolation. However, an isolated tone without musical context has no relevance to music, and AP ability should be examined in musically meaningful situations. In this study, AP possessors tried to identify the musical intervals between pairs of successive tones. The first tone (a reference) was either in-tune C according to the conventional pitch standard or out-of-tune C (a quarter-tone higher than standard C). The identification performance was less accurate and slower in the out-of-tune reference condition than in the in-tune condition. In contrast, AP nonpossessors showed no significant difference in performance in the two conditions, as predicted by the principle of equality under transposition. These results suggest that AP subjects tend to adhere to AP in relative pitch tasks, and that at least some AP listeners may have developed a strong dependence on AP at the sacrifice of relative pitch. AP may not have any advantage in music, in which relative pitch, not AP, is essential. Rather, AP may conflict with relative pitch and, in some cases, harm musical pitch processing.