Thermodynamic properties of MgSiO3 tetragonal majorite have been calculated at high pressures and temperatures within the quasi-harmonic approximation based on density functional theory using the local density approximation (LDA) and the generalized gradient approximation (GGA). The LDA results compare exceptionally well with measured thermodynamic properties. A classical Monte Carlo simulation based on results from a cluster expansion method demonstrates that disorder between magnesium and silicon in the octahedral sites in MgSiO3 majorite does not occur below 3600 K at transition zone pressures. The ensuing calculations on phase boundaries of MgSiO3 between majorite, perovskite, and ilmenite show that a much better agreement with experiment can be obtained by using GGA rather than LDA, for LDA underestimates the transition pressures by as much as 11 GPa. The Clapeyron slopes predicted by GGA and LDA are close to each other: 0.9-1.7 MPa/K for majorite-perovskite transition, 6.9-7.9 MPa/K for majorite-ilmenite transition, and -7 - 3 MPa/K for ilmenite-perovskite transition. The triple point predicted by GGA is located at 21.8 ± 1 GPa and 1840 ± 200 K which is ∼400 K lower in temperature than most experimental estimates. This result suggests that ilmenite is restricted to lower temperatures and that the majorite to ilmenite transition may occur in cold subducting slabs in the transition zone. Our calculation also reveals that wadsleyite decomposes to an assemblage of majorite plus periclase above 2280 K with a large negative Clapeyron slope (-22 - 12 MPa/K) and that ringwoodite decomposes to ilmenite plus periclase below 1400 K (1.2 MPa/K). These two decomposition transitions may influence hot plumes and cold slabs near 660 km depth, respectively. Further calculations show that discontinuities in density, bulk modulus, and bulk sound velocity associated with the majorite to perovskite transition in MgSiO 3 are much larger than those from the postspinel transition in Mg2SiO4 at conditions close to 660 km depth. This suggests that the large density discontinuity at 660 km depth as proposed by PREM (9.3%) might be accounted by a piclogite compositional model or marginally accounted by a pyrolite compositional model with, for example, 50 vol % ringwoodite, 45 vol % majorite, and 5 vol % other phases (such as calcium perovskite) at the bottom of the transition zone, provided that the density contrast between majorite and perovskite will not be greatly altered by the presence of other elements such as Fe, Al, Ca, and H. On the other hand, the smaller density discontinuity at 660 km depth as derived from impedance studies (4-6%) disfavors sharp contributions to seismic discontinuities from the majorite to perovskite transition.