Two complex sounds were studied, one with a continuous energy frequency spectrum corresponding to connected speech, the other a test tone having discrete frequency components. By means of filters the energy was removed from all frequencies either above or below a certain frequency, and the resulting decrease in loudness was measured by attenuating the original sound without distortion until equal in loudness to the filtered sound. Taking the average results for six observers, this decrease was found to depend on the absolute values of the loudness. For a loudness of 22 units above threshold, each frequency region contributes to loudness in proportion to the energy in that region weighted according to the threshold energy for that frequency. For a loudness above 30 units, however, this is no longer true, because of the non-linear character of the response of the ear. By assuming each frequency region contributes in proportion to a fractional power of the weighted energy of that region, values of the total loudness in agreement with observed values are obtained if proper values are taken for the fractional power, decreasing to 1/3 as the loudness increases to 100 units.

• Received 8 February 1924

DOI:https://doi.org/10.1103/PhysRev.24.306