Rhona P. Hellman

Loudness, annoyance, and noisiness produced by single‐tone‐noise complexes

Single tones centered within the noise spectrum were added to three different broadband spectra: flat, low pass, and high pass. Judgments of overall loudness, annoyance, and noisiness (perceived magnitude) were obtained by absolute magnitude estimation (AME) supplemented by loudness matching. The data were evaluated to determine how the overall SPL of the noise-tone complex, and tone-to-noise ratio effect judged perceived magnitude. In addition, the relationship among the tree judged attributes was assessed. Results obtained with the different noise spectra show that the growth of perceived magnitude is a nonmonotonic function of the overall SPL of the noise-tone complex. More summation between tone and noise was found for relatively small tone-to-noise ratios (+5, +10, +15 dB), as measured in 1/3-octave bands, than for relatively large tone-to-noise ratios (+20 dV and greater). Data analysis suggests that the extent of the increments and decrements in perceived magnitude depends on the absolute loudness of the component stimuli, the interaction between a specific tone frequency and noise spectrum, and the attribute judged. An attempt is made to quantify the observed effects and to relate them to the published results of other investigators.

Growth of loudness at 1000 and 3000 Hz

Loudness growth at 1000 and 3000 Hz was measured directly by magnitude estimation and production, and indirectly by loudness matches between tone and wide‐band noise and by interfrequency matching. The outcome of the three series of experiments does not reveal any systematic difference in shape of the loudness curves at 1000 and 3000 Hz. To a first approximation, above about 30 dB SL the loudness functions at 1000 and 3000 Hz are power functions of sound pressure with an exponent close to the accepted ISO standard of 0.60 (0.30 re sound intensity). Below 30 dB SL both loudness curves become progressively steeper than a simple power function and approach the same limiting slope, re sound intensity, of unity. Consistent with Steven’s calculation system [J. Acoust. Soc. Am. 51, 575–601 (1972)], the data also show that loudness equality is achieved when a 3000‐Hz tone is about 8 dB below the SPL of a tone at 1000 Hz.Subject Classification: [43]65.50, [43]65.75.

Growth rate of loudness, annoyance, and noisiness as a function of tone location within the noise spectrum

The relation between overall perceived magnitude (loudness, annoyance, and noisiness) of noise-tone complexes and the location of the tone within the spectrum was investigated by absolute magnitude estimation (AME). Single tones at 250, 1000, 2000, and 3000 Hz were added to low-and high-pass noises. In contrast to noisiness, loudness and annoyance growth behavior depends on the relationship between the frequency of the added tone and the spectral shape of the noise. Tones centered in noise produce nonmonotonic loudness and annoyance growth functions; those added to the skirt produce power functions. The measured exponents are invariant across tone-to-noise ratio when the tones are positioned within the spectrum, but not when they are added to the skirt. Moreover, for complexes at approximately the same overall SPL, the tones position determines the functional relationship between loudness (or annoyance) and tone-to-noise ratio. Although a tone correction for annoyance is warranted for certain noise-tone configurations, none of the proposed calculation procedures considers all the variables relevant to perceived annoyance of tonal components. To a large extent, complex auditory interactions generated by the simultaneous presentation of noise and tone can account for the observed effects.

Why can a decrease in dB(A) produce an increase in loudness

Loudness measured by the method of absolute magnitude estimation is compared to loudness calculated in accordance with ISO 532 B (International Organization for Standardization, Geneva, 1966). The measured and calculated loudness functions exhibit a similar pattern of loudness growth. Both measured and calculated loudness of a complex sound composed of a 1000-Hz tone and broadband noise is a nonmonotonic function of the overall SPL of the complex. The nonmonotonic loudness-growth pattern holds over a 30-dB range from 73.5 to 103.5. To facilitate understanding of the results, a single cycle of data is analyzed in detail. The analysis shows that loudness patterns produced in the auditory system by the tone-noise complex can account for the observed effects. Moreover, they show that the A-weighting and the loudness of the complex are negatively related. This inverse relation means that the A-weighted SPL is an inappropriate and misleading indicator of the loudness of sound combinations with heterogeneous spectral envelopes. Consequently, its suitability for noise control is diminished. A loudness meter that combines the spectral shapes of different sounds to produce an overall perceived magnitude offers greater promise.

Stability of individual loudness functions obtained by magnitude estimation and production.

A correlational analysis of individual magnitude estimation and production exponents at the same frequency was perfor.med, as well as an analysis of individual exponents produced in different sessions by the same procedure across frequency(250, 1, 000, and 3, 000 Hz). Taken together, results show, first, that individual exponent differences do not decrease by counterbalancing magnitude estimation with magnitude production, and, second, that individual exponent differences remain stable over time despite changes in stimulus frequency. Further results disclose that although individual magnitude estimation and production exponents do not necessarily obey the .6 power law, it is possible to predict the slope (exponent) of an equal-sensation function averaged for a group of listeners from individual magnitude estimation and production data. Assuming that individual listeners with sensorineural hearing loss also produce stable and reliable magnitude functions, it is also shown that the slope of the loudness-recruitment function measured by magnitude estimation and production can be predicted for individuals with bilateral losses of long duration. Thus, results obtained in normal and in pathological ears suggest that individual listeners can produce loudness judgments that reveal, albeit indirectly, the input-output characteristic of the auditory system.

Loudness relations for individuals and groups in normal and impaired hearing

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.

Model of Loudness Summation Applied to Impaired Ears

The loudness of complex sounds composed of three or four pure tones was measured as a function of the over‐all spacing ΔF between the lowest and highest components. The measured relation between loudness and ΔF was compared to calculations from Zwickers model of loudness summation. In eight ears with a conductive impairment, loudness summated normally and as predicted by the model; loudness remained approximately constant as a function of ΔF near threshold and increased with ΔF beyond the critical band at higher sensation levels. In eight ears with a cochlear impairment, loudness did not change with ΔF at any tested sensation level. This invariance of loudness was not predicted by tire model nor was it found in six normal ears tested in the presence of a 90‐dB uniform masking noise intended to simulate the cochlear impairment. Under masking, loudness summated as predicted. The unexpected results in cochlear pathology were ascribed, tentatively, to a possible widening of the critical band.

Rate of loudness growth for pure tones in normal and impaired hearing.

The present article provides an analysis of loudness growth rates in normal and cochlear-impaired hearing for diverse groups with respect to age and backgrounds. Slopes are obtained from absolute magnitude estimation and magnitude production of loudness (measured values), and from cross-modality matching and absolute magnitude estimation of apparent length (predicted values). Consistent with an earlier study [R. P. Hellman and C. H. Meiselman, J. Acoust Soc. Am. 88, 2596-2606 (1990)], slopes calculated within the 15-30 dB stimulus range above the elevated threshold increase in size with the degree of hearing loss. The corresponding range of loudness values in normal hearing yields a slope near 0.60 independent of the threshold levels. This pattern of loudness growth holds for individuals and groups. But the intersubject variability of the slope is more labile, being larger across than within groups and larger for the measured slopes than for the predicted values. Determined from the predicted slopes, the coefficient of variation, sigma/m, is approximately constant in normal and impaired hearing ranging from 20%-27%. In contrast, sigma/m, obtained from the measured slopes, increases with the degree of hearing loss to a value of almost 50% for a 75-dB loss. The overall stability and systematics of the observed effects further demonstrate that the loudness-intensity relation can be specified with reasonable precision and accuracy from cross-modality matching.

On the relation between the growth of loudness and the discrimination of intensity for pure tones.

The intensity jnd is often assumed to depend on the slope of the loudness function. One way to test this assumption is to measure the jnd for a sound that falls on distinctly different loudness functions. Two such functions were generated by presenting a 1000-Hz tone in narrow-band noise (925-1080 Hz) set at 70 dB SPL and in wideband noise (75-9600 Hz) set at 80 dB SPL. Over a range from near threshold to about 75 dB SPL, the loudness function for the tone is much steeper in the narrow-band noise than in the wideband noise. At 72 dB SPL, where the two loudness curves cross, the tones jnd was measured in each noise by a block up-down two-interval forced-choice procedure. Despite the differences in slope (and in sensation level), the jnd (delta I/I) is nearly the same in the two noises, 0.22 in narrow-band noise and 0.20 in wideband noise. The mean value of 0.21 is close to the value of 0.25 interpolated from Jesteadt et al. [J. Acoust. Soc. Am. 61, 169-176 (1977)] for a 1000-Hz tone that had the same loudness in quiet as did our 72-dB tone in noise, but lay on a loudness function with a much lower slope. These and other data demonstrate that intensity discrimination for pure tones is unrelated to the slope of the loudness function.

Intensity discrimination as the driving force for loudness. Application to pure tones in quiet

Loudness functions and their associated neural-count functions are derived for steady-state tones at 250 and 1000 Hz from measurements of intensity discrimination obtained under gated and continuous conditions. The calculations are based on a multichannel generalization of the McGill-Goldberg counting model [J. Acoust. Soc. Am. 44, 576-581 (1968)]. Using the data for just noticeable differences (jnd) in intensity as input, the generalized version gives an integral relation between the neural-count function N(x) and the intensity-jnd function, where x = I/I0 and I0 is the reference intensity. Loudness functions are generated through the prescription L(x) = AN(x)--B. To determine how the detailed shapes of the intensity-jnd functions affect the form of the loudness function within the model, integration was performed over the intensity-jnd functions with and without a power-function approximation. Over a range of intensity levels from 20-95 dB, the best agreement between the calculated and measured loudness functions is obtained from the unaltered intensity-jnd functions. Consistent with psychophysical evidence and several models of intensity coding, the results predict that the output of the whole auditory nerve is unnecessary to maintain the large dynamic range observed for loudness and intensity discrimination.