Two correlations for the RON and MON are found to be optimal. These achieve maximum absolute errors (MAE) of less than 2 octane numbers across TRF/ethanol mixtures with a RON between 80 and 120. These two correlations use mole fractions as the correlating variables, are consistent with previously published, linear TRF correlations, and show that binary (non-linear) interactions between iso-octane/ethanol, n-heptane/ethanol and toluene/ethanol are all significant. The use of liquid volume fractions is also shown to lead to poor correlation performance, thereby demonstrating the superiority of mole fractions as the correlating variables.