Deriving loudness growth functions from categorical loudness scaling data

The goal of this study was to reconcile the differences between measures of loudness obtained with continuous, unbounded scaling procedures, such as magnitude estimation and production, and those obtained using a limited number of discrete categories, such as categorical loudness scaling (CLS). The former procedures yield data with ratio properties, but some listeners find it difficult to generate numbers proportional to loudness and the numbers cannot be compared across listeners to explore individual differences. CLS, where listeners rate loudness on a verbal scale, is an easier task, but the numerical values or categorical units (CUs) assigned to the points on the scale are not proportional to loudness. Sufficient CLS data are now available to assign values in sones, a scale proportional to loudness, to the loudness categories. As a demonstration of this approach, data from Heeren, Hohmann, Appell, and Verhey [J. Acoust. Soc. Am. 133, EL314-EL319 (2013)] were used to develop a CU_sone metric, whose values were then substituted for the original CU values in reanalysis of a large set of CLS data obtained by Rasetshwane, Trevino, Gombert, Liebig-Trehearn, Kopun, Jesteadt, Neely, and Gorga [J. Acoust. Soc. Am. 137, 1899-1913 (2015)]. The resulting data are well fitted by power functions and are in general agreement with previously published results obtained with magnitude estimation, magnitude production, and cross modality matching.