  We present the itinerant coherent-potential approximation(ICPA), an analytic,
translationally invariant and tractable form of augmented-space-based,
multiple-scattering theory in a single-site approximation for harmonic phonons
in realistic random binary alloys with mass and force-constant disorder.
  We provide expressions for quantities needed for comparison with experimental
structure factors such as partial and average spectral functions and derive the
sum rules associated with them. Numerical results are presented for Ni_{55}
Pd_{45} and Ni_{50} Pt_{50} alloys which serve as test cases, the former for
weak force-constant disorder and the latter for strong. We present results on
dispersion curves and disorder-induced widths. Direct comparisons with the
single-site coherent potential approximation(CPA) and experiment are made which
provide insight into the physics of force-constant changes in random alloys.
The CPA accounts well for the weak force-constant disorder case but fails for
strong force-constant disorder where the ICPA succeeds.
