On loudness at threshold.
Absolute thresholds for and loudness matches between pure tones and four- and ten-tone complexes were used to assess the form of the function relating loudness to sensation level, SL, at low and moderate levels. The components of the tone complexes had equal SLs and were separated by one, two, four, or six critical bands. Six listeners with normal hearing were tested. The thresholds for the multitone complexes indicate that they generally can be detected even when the level of a single component is a few dB below the threshold. The average detection advantage is consistent with predictions for multiple observations in independent, frequency-selective auditory channels, but differences among listeners are apparent. The loudness matches also vary somewhat among listeners. Five of the six listeners matched tone complexes composed of subthreshold components to a pure tone a few dB above threshold. This indicates that the loudness of tones at or even below threshold is greater than zero for these five listeners. A simple model of loudness summation was used to obtain loudness functions from the individual listeners' loudness matches. The slopes of the loudness functions [log(loudness) plotted as a function of log(intensity)] generally exceed unity at low levels and are near 0.2 at 40 dB SL. This shallow slope at moderate levels agrees with loudness functions derived from data on temporal integration of loudness. The average loudness function derived from the present data also is in good agreement with a variety of previous data obtained by magnitude estimation, magnitude production, ratio production, and measurements of binaural loudness summation.