The perceptual basis of loudness ratio judgments

In Experiment 1, subjects were required to estimateloudness ratios for 45 pairs of tones. Ten 1,200-Hz tones, differing only in intensity, were used to generate the 45 distinct tone pairs. In Experiment 2, subjects were required to directly compare two pairs of tones (chosen from among the set of 45) and indicate which pair of tones had the greaterloudness ratio. In both Experiments 1 and 2, the subjects’ judgments were used to rank order the tone pairs with respect to their judged loudness ratios. Nonmetric analyses of these rank orders indicated that both magnitude estimates of loudness ratios and direct comparisons of loudness ratios were based on loudnessintervals ordifferences where loudness was a power function of sound pressure. These experiments, along with those on loudness difference judgments (Parker & Schneider, 1974; Schneider, Parker, & Stein, 1974), support Torgerson’s (1961) conjecture that there is but one comparative perceptual relationship for ioudnesses, and that differences in numerical estimates for loudness ratios as opposed to loudness intervals simply reflect different reporting strategies generated by the two sets of instructions.     

Does stimulus context affect loudness or only loudness judgments?

Marks (1988) reported that when equal-loudness matches were inferred from magnitude estimates of loudness for tones of two different frequencies, the matches were affected by changes in the stimulus intensity range at both frequencies. Marks interpreted these results as reflecting the operation of response biases in the subjects' estimates; that is, the effect of range was to alter subjects' judgments but not necessarily the perception of loudness itself. We investigated this effect by having subjects choose which of two tone pairs defined the larger loudness interval. By using tones of two frequencies, and varying their respective intensity ranges, we reproduced Marks' result in a procedure devoid of numerical responses. When the tones at one frequency are all soft, but the tones at the other frequency are not all soft, cross-frequency loudness matches are different from those obtained with other intensity range combinations. This suggests that stimulus range affects the perception of loudness in addition to whatever effects it may have on numerical judgments of loudness.     

The additivity of loudness across critical bands: A conjoint measurement approach

Five subjects were required in each trial to compare directly two sounds and to indicate which sound was louder. Each of the 64 sounds employed consisted of a combination of one of eight intensity levels of a 2-kHz tone and one of eight intensities of a 5-kHz tone. If, as Fletcher and Munson (1933) argued, loudness is additive for tone combinations in which the frequencies are widely separated, then subjects’ judgments should reflect the summed loudnesses of the 2- and 5-kHz tones in a two-tone combination. Judgments of individual subjects were shown to satisfy the conditions for an additive structure, and individual loudness scales were constructed. These loudness scales varied from subject to subject. Since this paired comparison procedure minimized response biases, the results suggest substantial individual differences in the sensory representation of sound intensity. The relations among sensory scales derived from other structured sensory judgments, such as binaural loudness, are discussed.     

Individual loudness functions determined from direct comparisons of loudness intervals

Five subjects were required in each trial to directly compare two pairs of tones and indicate which pair of tones had the greater loudness difference. Ten 1,200-Hz tones differing only in intensity were employed. Subjects made binary comparisons among the 45 tone pairs that can be formed from these 10 tones. The loudness difference comparisons of each subject were found to satisfy two properties (transitivity and monotonicity) that are required for an interval scale representation of loudness. Therefore, individual loudness scales were constructed using a nonmetric scaling technique designed for comparisons of sensory intervals. These loudness scales differed significantly from subject to subject. Since a nonnumerical scaling procedure was employed, these individual differences could not be attributed to biases in the way in which observers use numbers or numerical concepts to describe the loudness of tones. Hence, they suggest strong individual differences in the coding of sound intensity.     

Auditory sensory storage in relation to the growth of sensation and acoustic information extraction

A brief, vivid phase of auditory sensory storage that outlasts the stimulus could be used in perception in two ways: First, all of the neural activity resulting from the stimulus, including that of the sensory store, could contribute to a sensation of growing loudness; second, the sensory store could permit the continued extraction of information about the sound's acoustic properties. This study includes a task for which these two processes lead to different predictions; a third prediction is based on the two processes combined. The task required loudness judgments for two brief tones presented with a variable intertone interval. The results of Experiments 1-3 were as one would expect if both the growth of sensation and information extraction contributed to the pattern of loudness judgments. Experiment 4 strengthened the two-process account by demonstrating the separability of the two processes. Approaches to mathematical modeling of these results are discussed.     

THE CONTINGENCY OF PERCEPTUAL PROCESSING: Context Modifies Equal-Loudness Relations

Abstract –The relative loudnesses of tones that differ in sound frequency can depend strongly on the stimulus context, that is, on the set of intensity levels m the stimulus ensemble Using a new paradigm, called matching in scaling, this investigation sought to confirm that context modifies loudness relations per se, and not, for example, only overt responses To this end, two experiments revealed that changes in stimulus context differentially affect direct comparisons of loudness of 500-Hz and 2,500-Hz tones, as well as numerical judgments of individual tones—when loudness matches and scaling judgments alike are obtained in the same experimental sessions These contingent effects vary dynamically over time as a function of the recent stimulus history A third experiment revealed analogous effects in a simple matching paradigm, with no numerical judgments at all These findings support the contention that basic properties of loudness perception—grounded in auditory processes often considered "low level"—nevertheless can be deeply contextual     

Intensity discrimination and loudness for tones in broadband noise

In two previous papers (Parker & Schneider, 1980; Schneider & Parker, 1987), we developed a model, based on Fechner's assumption, which successfully predicted the relationship between loudness and intensity discrimination for tones presented in quiet and in notched noise. In the present paper, pure-tone intensity-increment thresholds and loudness matches were determined for several levels of a standard tone in the presence of a broadband masker whose spectrum level was set to 35 dB below that of the standard tone. The model was unable to relate loudness to intensity discrimination under these conditions. Thus, the spectral composition of the masker affects the relationship between loudness and intensity discrimination in ways that cannot be accounted for by the model.     

Posttransient shifts in auditory lateralization

Presenting an intense (e.g., 80-dB [SPL]) "transient" (e.g., 50-msec) inducer to the ear reduces the loudness of subsequent signals at or near the frequency of the inducer. In this study, we ask whether similar inducers also affect lateralization. In two experiments, we asked how inducing tones presented to one ear (the exposed ear) affect judgments of the lateral position of subsequent target tones having various interaural intensity differences. In Experiment 1, inducers had the same frequency as the targets, and, as predicted, reduced the tendency to lateralize the targets to the exposed ear. In Experiment 2, the frequency of the inducers and the target differed (different critical bands), thereby eliminating the effect on lateralization. These results are consistent with the hypothesis that inducers temporarily reduce the magnitude of the representation of intensity signals in the frequency region around them and that this reduction occurs, at least partly, peripherally to the site at which binaural intensity differences are encoded. The results imply further that the reduction in loudness previously reported under similar stimulus conditions reflects a more general reduction of intensity-based information in hearing.     

Psychophysical judgment: Wundt's theory revisited

Summary Wundt's psychological interpretation of Weber's and Fechner's laws rests on two main postulates. First, the magnitude of sensory excitation is proportional to the intensity of the stimulus that produces it. Second, in apperception, sensory comparisons and judgments are made according to psychological relationships: Two sensations are just-noticeably different when they fall in a constant psychological ratio. Wundt's theory implies a hierarchical organization, in which sensory-perceptual processes are embedded within higher-level, apperceptive processes. Such an organization is compatible with recent psychophysical research on loudness and with a model that goes toward resolving some controversies in loudness scaling, notably the seeming incompatibility of Stevens's sone scale and Garner's lambda scale.     

Range and regression, loudness scales, and loudness processing: toward a context-bound psychophysics

How does context affect basic processes of sensory integration and the implicit psychophysical scales that underlie those processes? Five experiments examined how stimulus range and response regression determine characteristics of (a) psychophysical scales for loudness and (b) 3 kinds of intensity summation: binaural loudness summation, summation of loudness between tones widely spaced in frequency, and temporal loudness summation. Context affected the overt loudness scales in that smaller power-function exponents characterized larger versus smaller range of stimulation and characterized magnitude estimation versus magnitude production. More important, however, context simultaneously affected the degree of loudness integration as measured in terms of matching stimulus levels. Thus, stimulus range and scaling procedure influence not only overt response scales, but measures of underlying intensity processing.     

Time errors and differential sensation weighting

Sixteen pairs of successive tones, with different amplitude combinations, were presented with 16 combinations of tone duration and interstimulus interval. A separate group of 12 subjects was assigned to each presentation condition and made comparative loudness judgments for each of the pairs. Perceived within-pair loudness differences were scaled by a Thurstonian method using the subjective width of the "equal" category as the unit. The scale differences were well described by weighted linear combinations of the sensation magnitudes of the tones in the pairs. The time error can be regarded as an effect of this differential weighting. For the longer interstimulus intervals, the weight of the second tone was the greater, causing the usual inverse relation between time error and stimulus intensity level. For the shorter interstimulus intervals, these effects were reversed. An analysis of the pattern of weights led to the development of two models, one of which is a generalization of Michels and Helson's time error model. The weights could be interpreted as reflecting the differential efficiency of the loudness information from the two compared stimuli.     

The measurement of loudness using direct comparisons of sensory intervals

Subjects were required in each trial to directly compare two pairs of tones and indicate which pair of tones had the greater loudness difference. Ten 1200 Hz tones differing only in intensity were employed. Subjects made binary comparisons among the 45 tone pairs which can be formed from the set of ten tones. The subjects' binary comparisons of the tone pairs were found to satisfy the transitivity and monotonicity requirements of a positive difference structure. These comparisons of loudness intervals were used to construct a rank order of loudness difference. A loudness scale was constructed from a nonmetric analysis of the rank order of loudness difference for the 45 tone pairs and indicated that loudness was a power function of sound pressure with an exponent of 0.26.     

Response bias in category and magnitude estimation of difference and similarity for loudness and pitch

Interval scales of sensory magnitude were derived from magnitude and category estimates of loudness differences, loudness similarities, pitch differences, and pitch similarities. In each of the four loudness experiments, a loudness scale was constructed from a nonmetric analysis of the rank order of the judgments. The four loudness scales so constructed were found to be equivalent to one another and indicated that loudness was a power function of sound pressure with an exponent of .29. A similar analysis for the four pitch experiments found the pitch scales derived in each case to be equivalent to one another and linear with the mel scale of pitch. Thus the same sensory and similarities for two distinct perceptual continua. For both pitch and loudness, these sensory scales were used to generate scales of sensory differences. A comparison of the category and magnitude estimates of sensory differences with the scale of sensory differences derived from the nonmetric analyses indicated the presence of significant response biases in both category and magnitude estimation procedures.     

Slippery context effect and critical bands.

This article explored the slippery context effect: When Ss judge the loudness of tones that differ in sound frequency as well as intensity, stimulus context (relative intensity levels at the 2 frequencies) can strongly influence the levels that are judged equally loud. It is shown that the size of the slippery context effect depends on the frequency difference between the tones: Small frequency differences (less than a critical bandwidth) produced essentially no slippery effect; much larger differences produced substantial effects. These results are consistent with a model postulating the existence of a central attentional or preattentive "filter-like" process whose weighting coefficients represent the size of the absolute as opposed to the relative (contextual) component of loudness perception and judgment.     

Stimulus context and absolute magnitude estimation: a study of individual differences

The effect of stimulus context on absolute-magnitude-estimation (AME) judgments was examined by determining whether the loudness judgment of a tone is influenced by the intensities of other tones presented within the session. A group of 18 subjects was tested in separate sessions in which they judged stimuli within either a low (10-60 dB SL) or a high (40-90 dB SL) range of intensities. Examination of the results of individual subjects revealed that judgments of stimuli common to the two ranges were, in most subjects, unaffected or only slightly affected by the position of the range. The judgments of 2 subjects who failed to follow the instructions, however, showed very large context effects due to changing the stimulus range. The results of a second experiment, in which 22 subjects judged the loudness of tones within either a narrow (35-65 dB SL) or a wide (20-80 dB SL) range, revealed that, in all but 1 subject, the width of the range had no systematic effect on the loudness judgments of stimuli common to both ranges. This was also true 1 month later when 16 of the subjects returned to the laboratory to judge the loudness of tones within an even wider range of 10-90 dB SL. It was concluded that AME judgments are relatively insensitive to the potential biasing influences of stimulus context.     

Individual differences in loudness processing and loudness scales

Parameters of the psychophysical function for loudness (a 1000-Hz tone) were assessed for individual subjects in three experiments: (a) binaural loudness summation, (b) temporal loudness summation, and (c) judgments of loudness intervals. The loudness scales that underlay the additive binaural summation closely approximated S. S. Stevens's (1956) sone scale but were nonlinearly related to the scales that underlay the subtractive interval judgments, the latter approximating Garner's (1954) lambda scale. Interindividual differences in temporal summation were unrelated to differences in scaling performance or in binaural summation. Although the exponents of magnitude-estimation functions and the exponents underlying interval judgments varied considerably from subject to subject, exponents computed on the basis of underlying binaural summation varied less. The results suggest that interindividual variation in the exponent of magnitude-estimation functions largely reflects differences in the ways that subjects use numbers to describe loudnesses and that the sensory representations of loudness are fairly uniform, though probably not wholly uniform, among people with normal hearing. The magnitude of individual variation in at least one measure of auditory intensity processing, namely, temporal summation, seems at least as great as the magnitude of the variation in the underlying loudness scale.     

The stimulus range effect: Evidence for top-down control of sensory intensity in audition

The influence of intensity range on the perceived magnitude of a stimulus is well documented and usually attributed to response biases. Recent studies, however, have suggested that the range effect might be sensory in origin. To test this notion, we had one set of subjects compare loudness intervals in three conditions : a broad-range condition (15 tones, 23–95 dB SPL), a soft shortrange condition (the lowest 10 tones from the broad-range condition), and a loud short-range condition (the highest 10 tones). Nonmetric scaling showed that the broad-range and loud short-range conditionshad identical loudness functions, However, the second derivative of the loudness function was larger for the soft short-range condition than fox the broad-range condition. This pattern of results is consistent with the notion of a nonlinear ampler whose gain and degree of nonlinearity are adjusted under top-down control, so as to prevent distortion and increase discriminabztity.     

The dimensions of tonal experience: A nonmetric multidimensional scaling approach

Subjects were required in each trial to directly compare two pairs of tones and indicate which pair of tones had the greater subjective difference or dissimilarity. Eleven tones differing in both intensity and frequency were employed. Subjects made binary comparisons among the 55 tone pairs which can be formed from the set of 11 tones. These paired comparisons of tonal intervals were used to determine a two-dimensional Euclidean representation for tonal experience. Loudness and pitch appeared as orthogonal dimensions in this representation. However, a 45-deg rotation of loudness and pitch axes produced axes which could be identified as volume and density. This relationship suggested that volume and density were simple functions of pitch and loudness. Volume and density predictions based on this two-dimensional representation were shown to provide a good account of the data from three experiments on volume and density.     

Sequential dependencies and response range in cross-modality matches of duration to loudness

Subjects matched durations of keypresses to loudnesses of pure tones. Resulting duration responses were found to be assimilated to the value of the immediately preceding stimulus and responses from one to at least six trials back in the sequence of loudness stimuli. Responses were contrasted with the values of stimuli two through six trials back in the sequence. These sequential dependencies and other properties of the data were predicted by a cognitive model in which cross-modality matches are mediated by category judgments of stimuli on both continua, and subjects use heuristic strategies to reduce response uncertainty.     

Bisection of loudness

In a loudness bisection task, subjects varied one sound to lie halfway between two given sounds in terms of loudness. The two given sounds were varied from 30 to 90 dB in a 4 by 9 factorial design. Functional measurement methods based on monotone analysis provided good support for the bisection model, and yielded a loudness scale with an exponent of about .3, except for a falloff at lower intensities. Two other tasks, judging average loudness and difference in loudness of the two given sounds, yielded mixed results. In Experiment 2, in particular, the differencing judgments were not additive, even under monotone transformation. These analyses also indicated that previous applications of monotone analysis have typically lacked adequate power to allow any conclusion about the operative model. Overall, the present bisection scale agrees with Garner’s lambda scale, and the present theoretical approach agrees with that of Garner in its emphasis on algebraic models as a foundation for psychological measurement.