As we've discussed at the Hearing Seminar, neither pitch perception or the binaural system are completely understood.
Most people think of pitch as a monaural effect.
You hear a sound with either ear and perceive a pitch. But there are dichotic stimuli for which neither ear hears a pitch, but when you play the sounds to both ears you hear a musical note. Bob Dougherty is currently a PostDoc in the vision group here at Stanford. He did his work on dichotic pitch while he was a PostDoc at Univ. Check out the web sites at the end of his abstract to hear some sample sounds.