A monaural loudness function is determined for 1000 cps and compared to a previously obtained binaural loudness function. Although the monaural function appears to have a somewhat smaller exponent than the binaural one, the empirical evidence does not permit rejection of the hypothesis of a simple interaural loudness summation. The psychophysical methods of magnitude estimation with and without a designated standard and of magnitude production without standards are used. A combination of magnitude estimation and production without standards is accepted as a method with minimum bias and classified under a more general methodological category called “psychological magnitude balance.”

Loudness levels of a partially masked 1060-cps tone are determined by loudness-balance procedures and, indirectly, by the methods of magnitude estimation and production. It is shown that loudness balances obtained by the method of adjustment are consistent with the loudness judgments obtained by the combined method of magnitude estimation and production, called method of numerical magnitude balance. The final results are in good agreement with those of other investigations in which balanced procedures were followed.

A pure tone was used to mask narrow and wide bands of noise centered on the frequency of the tone. In a given experimental session, the sound-pressure level (SPL) of the tone was held constant and loudness balances were obtained between a masked and unmasked noise band of equal width. These results are compared to earlier measures of the partial masking of tone by noise. The comparison shows that noise masks a tone more effectively than the tone masks the noise. Although the effect of the tone on a critical band of noise is greater than its effect on either an octave-band noise or wide-band noise, it is considerably smaller than the effect of the noise on the tone. Decreasing the noise bandwidth still further to a subcritical width reduces the asymmetry of masking somewhat, but a difference at high intensities of about 20 dB between the masking effects of an equally intense noise and tone remains. Whether the masker is a tone or noise, masking ceases when the effective energy of the masked and masking stimuli is the same.

Individual and group loudness relations were obtained at a frequency in the region of impaired hearing for 100 people, 98 with bilateral cochlear impairment. Slope distributions were determined from absolute magnitude estimation (AME) and absolute magnitude production (AMP) of loudness; they were also derived from cross-modality matching (CMM) and AME of apparent length. With respect to both the means and the individual slope values, the two distributions closely agree. More than half of the measured deviations are less than 20%, with an overall average of -1.5%, meaning that transitivity is preserved for bilaterally impaired individuals. Moreover, over the stimulus range where cochlear impairment steepens the loudness function, both the group means and the individual slope values are clearly larger than in normal hearing. The results also show that, for groups of people with approximately similar losses, the standard deviation is a nearly constant proportion of the mean slope value giving a coefficient of variation of about 27% in normal and impaired hearing. This indicates, in accord with loudness matching, that the size of the slopes depends directly on the degree of hearing loss. The results disclose that loudness measurements obtained by magnitude scaling are able to reveal the operating characteristic of the ear for individuals.

Taken together, the results demonstrate that CMM can yield stable, accurate, and robust loudness growth measures in cochlear-impaired hearing. Given its apparent reliability, validity, and ease of application, CMM has the potential to become a powerful tool for assessing the growth of loudness in a clinical population. Loudness-level functions derived from CMM may well be important for determining the frequency-gain response of a hearing aid that most closely compensates for the distorted input-output function of the impaired auditory system.