Directional loudness in an anechoic sound field, head-related transfer functions, and binaural summation

The effect of sound incidence angle on loudness was investigated using real sound sources positioned in an anechoic chamber. Eight normal-hearing listeners produced loudness matches between a frontal reference location and seven sources placed at other directions, both in the horizontal and median planes. Matches were obtained via a two-interval, adaptive forced-choice (2AFC) procedure for three center frequencies (0.4, 1, and 5 kHz) and two overall levels (45 and 65 dB SPL). The results showed that loudness is not constant over sound incidence angles, with directional sensitivity varying over a range of up to 10 dB, exhibiting considerable frequency dependence, but only minor effects of overall level. The pattern of results varied substantially between subjects, but was largely accounted for by variations in individual head-related transfer functions. Modeling of binaural loudness based on the at-ear signals favored a sound-power summation model, according to which the maximum binaural gain is only 3 dB, over competing models based on larger gains, or on the summation of monaural loudness indices.