A test of the binaural equal-loudness-ratio hypothesis for tones

It is well known that a tone presented binaurally is louder than the same tone presented monaurally. It is less clear how this loudness ratio changes as a function of level. The present experiment was designed to directly test the Binaural Equal-Loudness-Ratio hypothesis (BELRH), which states that the loudness ratio between equal-SPL monaural and binaural tones is independent of SPL. If true, the BELRH implies that monaural and binaural loudness functions are parallel when plotted on a log scale. Cross-modality matches between string length and loudness were used to directly measure binaural and monaural loudness functions for nine normal listeners. Stimuli were 1-kHz 200-ms tones ranging in level from 5 dB SL to 100 dB SPL. A two-way ANOVA showed significant effects of level and mode (binaural or monaural) on loudness, but no interaction between the level and mode. Consequently, no significant variations were found in the binaural-to-monaural loudness ratio across the range of levels tested. This finding supports the BELRH. In addition, the present data were found to closely match loudness functions derived from binaural level differences for equal loudness using the model proposed by Whilby et al. [J. Acoust. Soc. Am. 119, 3931-3939 (2006)].