Effects of relative and absolute frequency in the spectral weighting of loudness

Abstract

The loudness of broadband sound is often modeled as a linear sum of specific loudness across frequency bands. In contrast, recent studies using molecular psychophysical methods suggest that low and high frequency components contribute more to the overall loudness than mid frequencies. In a series of experiments, the contribution of individual components to the overall loudness of a tone complex was assessed using the molecular psychophysical method as well as a loudness matching task. The stimuli were two spectrally overlapping ten-tone complexes with two equivalent rectangular bandwidth spacing between the tones, making it possible to separate effects of relative and absolute frequency. The lowest frequency components of the "low-frequency" and the "high-frequency" complexes were 208 and 808 Hz, respectively. Perceptual-weights data showed emphasis on lowest and highest frequencies of both the complexes, suggesting spectral-edge related effects. Loudness matching data in the same listeners confirmed the greater contribution of low and high frequency components to the overall loudness of the ten-tone complexes. Masked detection thresholds of the individual components within the tone complex were not correlated with perceptual weights. The results show that perceptual weights provide reliable behavioral correlates of relative contributions of the individual frequency components to overall loudness of broadband sounds.

FIG. 1.

(Color online) (A) Spectral configuration of the two ten-tone complexes. The lowest frequency of the High complex was the fifth component in the Low complex. This stimulus configuration was designed to test the effect of absolute frequency and relative position of the component in a tone complex on the perceptual weight it received. (B) Illustration of the task used to obtain perceptual weights. Level of each component in the “signal” and “non-signal” interval was selected from a distribution with a mean of 48 and 45 dB, respectively. Listeners were asked to pick the interval that was louder.

FIG. 2.

(Color online) Mean of the normalized perceptual weights and their standard deviations from experiment 1. The weights were obtained using a multiple regression model to predict a listener's responses on every trial using the difference in level between interval 2 and interval 1 for each individual component. Weights predicted by the loudness model are shown with a dashed line.

FIG. 3.

(Color online) Normalized perceptual weights for six individual subjects in experiment 1, plotted as a function of component number within the low and high complexes.

FIG. 4.

(Color online) (A) An illustration of the task used to obtain the masked threshold for individual components. The signal interval included the signal tone at a level which was changed adaptively. The non-signal interval contained only 9 tones presented at equal level with mean of 45 dB/component and their levels were roved across trials in 3 dB range. (B) Illustration of the loudness matching task used in experiment 3. The standard complex included one component that was either incremented or decremented by 8 dB. The level of the comparison tone complex was changed adaptively to match the loudness of the standard complex.

FIG. 5.

(Color online) Mean masked thresholds and their standard deviation for individual components of the ten-tone complexes in experiment 2. Predictions of the partial loudness model with a criterion of 5 phons are shown with dashed lines.

FIG. 6.

(Color online) Mean levels (and their standard deviations) of comparison complexes required to match the loudness of standard complexes in experiment 3. Upward triangles show conditions where the standard complex included one component with an increment of 8 dB and downward triangles show conditions with a decrement of 8 dB. Predictions of the loudness model are shown with dashed lines.