Loudness and the power series transformation

Abstract

A nonlinear-algebraic approach to monaural intensity processing is proposed: the purpose is to integrate the conscious loudness attribute evoked by a pure tone with the power-series description of auditory distorition. The preliminary model consists of six postulates leading to a mathematical definition for loudness. To evaluate this equation, two task-specific sets of loudness judgments from each of seven subjects are examined. When linked to loudness-interval responses via the equisection assumption, the equation describes the behaviors quite well. Extrapolations into other intensity ranges predict similar responses with relatively slight overestimates. By relaxing the assumption that subjects will adjust the loudness proportions exactly as instructed, their ratio productions also can be described and predicted with sometimes surprising accuracy. Particularly striking is the prediction of overall levels and the curvilinearities of “doublings” from the “halvings”. In addition, the theory proposes absolute loudness measurement, an explanation for the growth of loudness including the principle underlying Steven's Power Law, and might prove useful in examining some exceptions to this relationship. Several aspects of this model differ from traditional approaches to intensity processing, but it appears to warrent further critical evaluations.