Nitrogen, carbon, hydrogen and sulfur are essential elements for life and comprise about 1 % of terrestrial planet masses. These elements dominate planetary surfaces due to their volatile nature, but the Earth's interior also constitutes a major C-H-N-S reservoir. Resolving the origin of the surficial versus deep volatile reservoirs requires the past 4.5 Giga-years of mantle outgassing and ingassing processes to be reconstructed, involving many unknowns. As an alternative, we propose to define the primordial distribution of volatiles resulting from degassing of the Earth's magma ocean (MO). The equilibrium partitioning of C-H-ON -S elements between the MO and its atmosphere is calculated by means of solubility laws, extrapolated to high temperatures and over a large range of redox conditions. Depending on the redox conditions, the amount of volatiles, and the size of the MO considered, we show that the last MO episode may have degassed 40-220 bar atmospheres, whereas hundreds to thousands of ppm of C-H-ON -S can be retained in the magma. Two contrasting scenarios are investigated: reduced vs. oxidized MO. For reduced cases (IW+2) would be dry and C-N-S-rich. An intermediate redox state produces a C-N atmosphere. In many cases, the present-day surficial abundances (atmosphere+ocean+crust) of C and N, the most volatile elements, are very close to the calculated primordial MO-atmosphere distribution. This probably means that lithospheric recycling and post-magma ocean degassing only moderately alter the surficial abundances of these elements. Sulfur, in contrast, must have been mostly outgassed by post-MO events. Changes in redox conditions during magma ocean degassing played a first order role in the composition of the primordial atmosphere of planets. We suggest that the more oxidized conditions on Venus due to H-loss may have played a role in the growth of a dry MO atmosphere on this planet compared to an H-bearing one on Earth. To verify these first order assertions, constraints on volatile behaviour under extreme magma ocean conditions and upon magma ocean solidification are urgently needed.