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

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 $5kHz$⁠) and two overall levels (45 and $65dB$ SPL). The results showed that loudness is not constant over sound incidence angles, with directional sensitivity varying over a range of up to $10dB$⁠, 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 $3dB$⁠, over competing models based on larger gains, or on the summation of monaural loudness indices.