Three-pion interferometry is investigated for new information on the space-time structure of the pion source created in ultra-relativistic heavy-ion collisions. The two- and three-pion correlations are numerically computed for incoherent source functions based on the Bjorken hydrodynamical model, over a wide range of the kinematic variables. New information provided by three-pion interferometry, different from that provided by two-pion interferometry, should appear in the phases of the Fourier transform of the source function. Variables are identified that would be sensitive to the phases and suitable for observation. For a positive, chaotic source function, however, a variation of the three-pion phase is found to be difficult to extract from experiments. Effects of asymmetry of the source function are also examined.
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