Development and Current Status of the “Cambridge” Loudness Models

This article reviews the evolution of a series of models of loudness developed in Cambridge, UK. The first model, applicable to stationary sounds, was based on modifications of the model developed by Zwicker, including the introduction of a filter to allow for the effects of transfer of sound through the outer and middle ear prior to the calculation of an excitation pattern, and changes in the way that the excitation pattern was calculated. Later, modifications were introduced to the assumed middle-ear transfer function and to the way that specific loudness was calculated from excitation level. These modifications led to a finite calculated loudness at absolute threshold, which made it possible to predict accurately the absolute thresholds of broadband and narrowband sounds, based on the assumption that the absolute threshold corresponds to a fixed small loudness. The model was also modified to give predictions of partial loudness—the loudness of one sound in the presence of another. This allowed predictions of masked thresholds based on the assumption that the masked threshold corresponds to a fixed small partial loudness. Versions of the model for time-varying sounds were developed, which allowed prediction of the masked threshold of any sound in a background of any other sound. More recent extensions incorporate binaural processing to account for the summation of loudness across ears. In parallel, versions of the model for predicting loudness for hearing-impaired ears have been developed and have been applied to the development of methods for fitting multichannel compression hearing aids.