On the Lambda Loudness Function, Masking, and the Loudness of Multicomponent Tones

A computational procedure is presented for determining the loudness of multicomponent tones. The procedure uses the lambda loudness function and has just two basic assumptions: (1) loudness of components add as the sum of their squares, and (2) the effect of masking is to subtract a constant amount of loudness. With these two assumptions, the loudness data of Fletcher and Munson for multicomponent tones are predicted, using the lambda function and the masking data of Wegel and Lane for the necessary predictive terms. This procedure gives better accuracy than the original calculational schema of Fletcher and Munson, even though no constants are determined from the data. In fact the three sets of data (loudness scaling, masking, and multicomponent loudness) can be used such that any two will correctly predict the third. It seems possible that the lambda function may provide better integration of auditory data than other loudness functions.