An empirical equation from Riesz’s classic study on difference thresholds is treated in a new manner. Reformulating the expression for the Weber fraction allows one to account for the shape of the loudness function at different frequencies. Furthermore, the emerging loudness function unifies both the commonly used power and logarithmic laws of sensation. In principle, equal loudness contours can be derived from Riesz’s data. While the derived contours are imperfect, the theoretical method provides a basis for further experimental work.