Characterizing the dependence of pure-tone frequency difference limens on frequency, duration, and level

This study examined the relationship between the difference limen for frequency (DLF) of pure tones and three commonly explored stimulus parameters of frequency, duration, and sensation level. Data from 12 published studies of pure-tone frequency discrimination (a total of 583 DLF measurements across 77 normal-hearing listeners) were analyzed using hierarchical (or "mixed-effects") generalized linear models. Model parameters were estimated using two approaches (Bayesian and maximum likelihood). A model in which log-transformed DLFs were predicted using a sum of power-law functions plus a random subject- or group-specific term was found to explain a substantial proportion of the variability in the psychophysical data. The results confirmed earlier findings of an inverse-square-root relationship between log-transformed DLFs and duration, and of an inverse relationship between log(DLF) and sensation level. However, they did not confirm earlier suggestions that log(DLF) increases approximately linearly with the square-root of frequency; instead, the relationship between frequency and log(DLF) was best fitted using a power function of frequency with an exponent of about 0.8. These results, and the comprehensive quantitative analysis of pure-tone frequency discrimination on which they are based, provide a new reference for the quantitative evaluation of models of frequency (or pitch) discrimination.