Invariant characteristics of partial masking: Implications for mathematical models

The loudness of a tone in a noisy background increases very rapidly above its threshold with increasing intensity of the tone. The particular curve describing loudness growth as measured by a loudness matching paradigm depends on the level of the background noise. We introduce the hypothesis that an increment in masking noise induces a shift of the loudness matching curve in a diagonal direction (the matching curve being plotted in conventional log-log coordinates). This shift invariance is shown here to hold empirically for individual subjects within a monaural loudness matching task, based on a 2IFC paradigm using 1000-Hz tones and a wide band Gaussian noise. Shift invariance places considerable restrictions on models feasible for such data. In conjunction with a very general class of models involving the notion of gain control, the shift invariance property determines all parametric forms possible for the loudness matching functions. The fit of such parametric expressions to the data reported here yields very satisfying results. The resulting model is also found to be consistent with relevant results in the literature.