We present the results of new partitioning experiments between metal and silicate melts for a series of elements normally regarded as refractory lithophile and moderately siderophile and volatile. These include Si, Ti, Ni, Cr, Mn, Ga, Nb, Ta, Cu and Zn. Our new data obtained at 3.6 and 7.7 GPa and between 2123 and 2473 K are combined with literature data to parameterize the individual effects of oxygen fugacity, temperature, pressure and composition on partitioning. We find that Ni, Cu and Zn become less siderophile with increasing temperature. In contrast, Mn, Cr, Si, Ta, Nb, Ga and Ti become more siderophile with increasing temperature, with the highly charged cations (Nb, Ta, Si and Ti) being the most sensitive to variations of temperature. We also find that Ni, Cr, Nb, Ta and Ga become less siderophile with increasing pressure, while Mn becomes more siderophile with increasing pressure. Pressure effects on the partitioning of Si, Ti, Cu and Zn appear to be negligible, as are the effects of silicate melt composition on the partitioning of divalent cations. From the derived parameterization, we predict that the silicate Earth abundances of the elements mentioned above are best explained if core formation in a magma ocean took place under increasing conditions of oxygen fugacity, starting from moderately reduced conditions and finishing at the current mantle-core equilibrium value.