Temporal integration of loudness, loudness discrimination, and the form of the loudness function

Temporal integration for loudness of 5-kHz tones was measured as a function of level between 2 and 60 dB SL. Absolute thresholds and levels required to produce equal loudness were measured for 2-, 10-, 50-, and 250-ms tones using adaptive, two-interval, two-alternative forced-choice procedures. The procedure for loudness balances was new and employed ten interleaved tracks to obtain concurrent measurements for ten tone pairs. Each track converged at the level required to make the variable stimulus just louder than the fixed stimulus. Thus, the data yield estimates of the just-noticeable difference (jnd) for loudness level and temporal integration for loudness. Results for four listeners show that the amount of temporal integration, defined as the level difference between equally loud short and long tones, varies markedly with level and is largest at moderate levels. The effect of level increases as the duration of the short stimulus decreases and is largest for comparisons between the 2- and 250-ms tones. The loudness-level jnds are also largest at moderate levels and, contrary to traditional jnds for the level of two equal-duration tones, they do not appear to depend on duration. The latter finding indicates that loudness discrimination between stimuli that differ along multiple dimensions is not the same as level discrimination between stimuli that differ only in level. An equal-loudness-ratio model, which assumes that the ratio of loudnesses for a long and short tone at equal SPL is the same at all SPLs, can explain the level dependence of temporal integration and the loudness jnds. It indicates that the loudness function [log(loudness) versus SPL] is flatter at moderate levels than at low and high levels in agreement with earlier findings for 1-kHz tones [M. Florentine et al., J. Acoust. Soc. Am. 99, 1633-1644 (1996)].