Pitch is the perceptual dimension along which musical notes are ordered from low to high. It is often described as the perceptual correlate of the periodicity of the sound's waveform. Previous reports have shown that pitch can depend slightly on sound level. We wanted to verify that these observations reflect genuine changes in perceived pitch, and were not due to procedural factors or confusion between dimensions of pitch and level. We first conducted a systematic pitch matching task and confirmed that the pitch of low frequency pure tones, but not complex tones, decreases by an amount equivalent to a change in frequency of more than half a semitone when level increases. We then showed that the structure of pitch shifts is anti-symmetric and transitive, as expected for changes in pitch. We also observed shifts in the same direction (although smaller) in an interval matching task. Finally, we observed that musicians are more precise in pitch matching tasks than non-musicians but show the same average shifts with level. These combined experiments confirm that the pitch of low frequency pure tones depends weakly but systematically on level. These observations pose a challenge to current theories of pitch.