A model of frequency discrimination with optimal processing of auditory nerve spike intervals

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.

Psychometric functions for pure-tone frequency discrimination

The form of the psychometric function (PF) for auditory frequency discrimination is of theoretical interest and practical importance. In this study, PFs for pure-tone frequency discrimination were measured for several standard frequencies (200-8000 Hz) and levels [35-85 dB sound pressure level (SPL)] in normal-hearing listeners. The proportion-correct data were fitted using a cumulative-Gaussian function of the sensitivity index, d', computed as a power transformation of the frequency difference, Δf. The exponent of the power function corresponded to the slope of the PF on log(d')-log(Δf) coordinates. The influence of attentional lapses on PF-slope estimates was investigated. When attentional lapses were not taken into account, the estimated PF slopes on log(d')-log(Δf) coordinates were found to be significantly lower than 1, suggesting a nonlinear relationship between d' and Δf. However, when lapse rate was included as a free parameter in the fits, PF slopes were found not to differ significantly from 1, consistent with a linear relationship between d' and Δf. This was the case across the wide ranges of frequencies and levels tested in this study. Therefore, spectral and temporal models of frequency discrimination must account for a linear relationship between d' and Δf across a wide range of frequencies and levels.

Factors affecting the duration effect in pitch perception for unresolved complex tones

Previous research has shown that fundamental frequency (F0) discrimination thresholds for complex tones containing unresolved harmonics decrease as the duration of the tone increases [White and Plack, J. Acoust. Soc. Am. 103, 2051-2063 (1998)]. In this paper F0 discrimination was measured as a function of duration for complexes with F0s of 62.5, 125, and 250 Hz, bandpass filtered into two spectral regions (2750-3750 and 5500-7500 Hz). The harmonics were summed either in sine phase (SINE) or with alternating sine-cosine phase (ALT), which affects the envelope of the waveform and the pitch of the complex. Tone duration was 20, 40, 80, and 160 ms. The improvement in F0 discrimination with duration increased with decreasing F0. When harmonics where spectrally filtered between 2750 and 3750 Hz, for complexes with an F0 of 62.5 Hz, F0 discrimination thresholds decreased from approximately 30% for a 20-ms tone to approximately 3% for a 160-ms tone. For complexes with an F0 of 250 Hz, thresholds decreased from 3% for a 20-ms tone to 1% for a 160-ms tone: a lower envelope repetition rate led to a larger change in performance with increasing duration. The phase manipulation also affected the size of the duration effect, in that the effect was less for an ALT complex compared to a SINE complex with the same F0, consistent with the change in envelope repetition rate. Overall, the results suggest that for unresolved complex tones it is primarily envelope repetition rate, not spectral region, that determines both the F0 discrimination threshold and the size of the duration effect.

Transfer of learning across durations and ears in auditory frequency discrimination

Frequency-discrimination thresholds (FDTs) for 1-kHz tone pips with durations of 40, 100, and 200 msec were measured in the left and right ears of 10 normal-hearing listeners, before and after six 2-h frequency-discrimination training sessions involving, exclusively, the 200-msec duration and the right ear. In the trained ear, highly significant improvements in FDTs were observed at all durations. Further inspection of the data suggested complete generalization between 200 and 100 msec, but not at 40 msec. Posttraining FDTs were not found to differ between the two ears for the two untrained durations, but proved significantly smaller in the right (trained) than in the left (untrained) ear at the trained (200-msec) duration only. A control experiment involving 10 additional subjects allowed us to establish the absence of intrinsic differences in pretraining FDTs between the right and left ears. Overall, these findings indicate that frequency-discrimination learning generalizes widely across stimulus durations and across ears, but that part of the improvement is specific to the range of durations and to the ear used in training.