A test of the equal-loudness-ratio hypothesis using cross-modality matching functions

This study tests the Equal-Loudness-Ratio hypothesis Florentine et al., J. Acoust. Soc. Am. 99, 1633-1644 (1996)], which states that the loudness ratio between equal-SPL long and short tones is independent of SPL. The amount of temporal integration (i.e., the level difference between equally loud short and long sounds) is maximal at moderate levels. Therefore, the Equal-Loudness-Ratio hypothesis predicts that the loudness function is shallower at moderate levels than at low and high levels. Equal-loudness matches and cross-modality string-length matches were used to assess the form of the loudness function for 5 and 200 ms tones at 1 kHz and the loudness ratio between them. Results from nine normal listeners show that (1) the amount of temporal integration is largest at moderate levels, in agreement with previous studies, and (2) the loudness functions are shallowest at moderate levels. For eight of the nine listeners, the loudness ratio between the 200 and 5 ms tones is approximately constant, except at low levels where it tends to increase. The average data show good agreement between the two methods, but discrepancies are apparent for some individuals. These findings support the Equal-Loudness-Ratio hypothesis, except at low levels.