Dichotic pitches are binaural perceptual phenomena which occur when broadband noise with specific interaural phase/time relationships is presented simultaneously to the two ears. Four dichotic pitches have been described: Huggins' pitch; the binaural edge pitch; the Fourcin pitch; the dichotic repetition pitch (DRP). This paper shows that the perceived pitch and timbre of the first three dichotic pitches are correctly predicted using a model of binaural unmasking [Culling and Summerfield, J. Acoust. Soc. Am. 98, 785--797 (1995)]. The model detects across-frequency variations in interaural correlation; the resulting central spectrum shows peaks which correspond to the frequencies listeners hear. These pitches are probably, therefore, illusions produced by the mechanism of binaural unmasking. The DRP is not predicted by the model. The DRP could be produced through binaural cross talk, but experiments using insert earphones which produce minimal cross-talk confirmed that the phenomenon persists when cross talk is effectively eliminated. The DRP is probably, therefore, produced by a separate mechanism from the other dichotic pitches.