This study presents a new approach to quantitatively assess the relationship between the composition and seismic P-wave velocity of anhydrous igneous and meta-igneous rocks. We perform thermodynamic calculations of the equilibrating phase assemblages predicted for all igneous composition space at various pressure and temperature conditions. Seismic velocities for each assemblage are then estimated from mixing theory using laboratory measurements of the elastic parameters for pure mineral phases. The resultant velocities are used to derive a direct relationship between Vp and major element composition valid to ¿0.13 km/s for pressure and temperature conditions along a normal crustal geotherm in the depth range of 5--50 km and equilibration pressures ≤12 kbar. Finally, we use the calculated velocities to invert for major element chemistry as a function of P-wave velocity assuming only the in situ temperature and pressure conditions are known. Compiling typical velocity-depth profiles for the middle and lower continental and oceanic crust, we calculate compositional bounds for each of these geologic environments. We find that the acceptable compositional range for the middle (15--30 km) and lower continental (≥35 km) crust is broad, ranging from basaltic to dacitic compositions, and conclude that P-wave velocity measurements alone are insufficient to provide fundamental constraints on the composition of the middle and lower continental crust. However, because major oxides are correlated in igneous rocks, joint constraints on Vp and individual oxides can narrow the range of acceptable crustal compositions. In the case of the lower oceanic crust (≥2 km), observed velocities are 0.2--0.3 km/s lower than velocities calculated based on the average bulk composition of gabbros in drill cores and exposed ophiolite sequences. We attribute this discrepancy to a combination of residual porosity at crustal depths less than ~10 km and hydrous alteration phases in the lower crust, and suggest caution when inferring mantle melting parameters from observed velocities in the lower oceanic crust.