Additivity of loudness across critical bands: a critical test

The use of magnitude estimation as well as axiomatic measurement theory has led to the suggestion that loudness adds across critical bands. In the present paper, we challenge this postulate by applying a more sensitive methodology, based on Falmagne's (1976) random conjoint measurement procedure. A necessary condition for additivity of loudness was investigated in tone complexes consisting of 2-kHz and 5-kHz (resp. 3-kHz) components; the results showed systematic deviations from additivity. We argue that these deviations are due to asymmetric masking of the higher component by the lower one, and we propose a tentative quantitative model to account for the data. Such a model is in line with results from tone-on-tone masking, which show masking to be effective over a range of several critical bands.