Spectral loudness summation as a function of duration

Loudness was measured as a function of signal bandwidth for 10-, 100-, and 1000-ms-long signals. The test and reference signals were bandpass-filtered noise spectrally centered at 2 kHz. The bandwidth of the test signal was varied from 200 to 6400 Hz. The reference signal had a bandwidth of 3200 Hz. The reference levels were 45, 55, and 65 dB SPL. The level to produce equal loudness was measured with an adaptive, two-interval, two-alternative forced-choice procedure. A loudness matching procedure was used, where the tracks for all signal pairs to be compared were interleaved. Mean results for nine normal-hearing subjects showed that the magnitude of spectral loudness summation depends on signal duration. For all reference levels, a 6- to 8-dB larger level difference between equally loud signals with the smallest (delta f = 200 Hz) and largest (delta f = 6400 Hz) bandwidth is found for 10-ms-long signals than for the 1000-ms-long signals. The duration effect slightly decreases with increasing reference loudness. As a consequence, loudness models should include a duration-dependent compression stage. Alternatively, if a fixed loudness ratio between signals of different duration is assumed, this loudness ratio should depend on the signal spectrum.