Pressure - volume - temperature measurements, calorimetry, and dielectric spectroscopy at ambient and elevated pressures were carried out on poly(cyclohexyl methacrylate) (PCHMA) and its blend with poly(alpha-methylstyrene) (PaMS). Both the glass transition temperature and local segmental relaxation times, tau(alpha), go through a maximum as a function of blend composition, plausibly due to a negative excess volume. Using a nonlinear function for the composition dependence of T-g, a value of the self-concentration parameter of the Lodge - McLeish model is determined, which is close to that calculated from the PCHMA chain statistics. For both neat PCHMA and the blend, the tau(alpha) superpose as a function of TV gamma. Since the breadth of the local segmental relaxation dispersion is a unique function of tau(alpha), this means that the parameter gamma defines both the magnitude and distribution of relaxation times. The thermodynamic scaling for the blend was corroborated by calculating the exponent gamma from the isochronal thermal expansion coefficient, determined from the pressure coefficient of T-g. gamma increases upon blending, consistent with a larger activation volume of PCHMA when mixed with the PaMS. PCHMA exhibits a weak beta-relaxation, which lacks correspondence to the segmental dynamics and thus is presumably due to local motion of the carbonyl group. A more intense gamma-relaxation and a frequency-insensitive loss at higher frequencies are also observed. Unlike the segmental process, these secondary relaxations are insensitive to blending.