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.     

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.     

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.     

Loudness and loudness discrimination

A model is developed which holds that pure-tone intensity discrimination and suprathreshold loudness judgments are based on the same sensory representation. In this model, loudness is a power function of sound intensity. When two tones are presented sequentially, each gives rise to a loudness value along the sensory continuum. In intensity-discrimination experiments, threshold is reached when the loudness difference between the tones exceeds a criterial value. For suprathreshold presentations of tone pairs, judgments of loudness differences are based on the loudness difference between the two tones. The model is shown to accord well with data from both classes of experiments.     

On cross-modal similarity: the perceptual structure of pitch, loudness, and brightness

Examined how pitch and loudness correspond to brightness. In the Experiment 1, 16 Ss identified which of 2 lights more resembled each of 16 tones; in Experiment 2, 8 of the same 16 Ss rated the similarity of lights to lights, tones to tones, and lights to tones. (1) Pitch and loudness both contributed to cross-modal similarity, but for most Ss pitch contributed more. (2) Individuals differed as to whether pitch or loudness contributed more; these differences were consistent across matching and similarity scaling. (3) Cross-modal similarity depended largely on relative stimulus values. (4) Multidimensional scaling revealed 2 perceptual dimensions, loudness and pitch, with brightness common to both. A simple quantitative model can describe the cross-modal comparisons, compatible with the view that perceptual similarity may be characterized through a malleable spatial representation that is multimodal as well as multidimensional.     

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 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.     

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.     

Dual loudness scales in individual subjects

Each of 7 subjects matched the loudness of a single tone to the loudness differences within tone pairs (Experiment 1), gave magnitude estimations of those differences (Experiment 2), and gave magnitude estimations of single tonal loudness (Experiment 3). Individual subjects used several loudness scales to perform these tasks, in accordance with Marks's (1979b) theory. At least 3 subjects used the same scale to match loudnesses to loudness differences and to give magnitude estimations of the loudness of single tones (Experiments 1 and 3), but used a shallower sloped scale when giving magnitude estimations of loudness differences (Experiment 2).     

Loudness “ratios” and “differences” involve the same psychophysical operation

Subjects judged both “atios” of loudness and “differences” in loudness between pairs of tones that varied in intensity. The pairs were constructed from factorial designs, permitting separation of stimulus and response scaling for each subject. Ratings of “differences” and estimations of “ratios” were monotonically related, inconsistent with the hypothesis that subjects perform both subtractive and ratio operations on a common scale. Instead, the data suggest that both tasks involve the same psychophysical comparison operation with different response transformations. If the operation can be represented by the subtractive model, then category ratings involve a nearly linear transformation and magnitude estimations involve a nearly exponential transformation.     

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 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     

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.     

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.     

Effects of expectations on loudness and loudness difference

To determine how expectations affect loudness and loudness difference, in two experiments we induced some subjects to expect loud sounds (condition L), some to expect soft sounds (condition S), and others to have no particular expectations (control). In Experiment 1, all subjects estimated the loudnesses of the same set of three moderately loud 1-kHz tones. Estimates were greatest for subjects in condition S and smallest for subjects in condition L. Control subjects’ estimates were intermediate but closer to those of condition S subjects. In Experiment 2, subjects estimated the difference in loudness for pairs of moderately loud 1-kHz tones. Again, estimates were smallest for condition L subjects; estimates were greatest for control subjects, and condition S subjects’ estimates were closer to control estimates than to condition L estimates. This pattern of results is explainable by a combination of (1) Parducci’s (1995) range-frequency theory and (2) a gain control mechanism in the auditory system under top-down governance (Schneider, Parker, & Murphy, 2011).     

Binaural loudness gain measured by simple reaction time

In order to yield equal loudness, different studies using scaling or matching methods have found binaural level differences between monaural and diotic presentations ranging from less than 2 dB to as much as 10 dB. In the present study, a reaction time methodology was employed to measure the binaural level difference producing equal reaction time (BLDERT). Participants had to respond to the onset of 1-kHz pure tones with sound pressure levels ranging from 45 to 85 dB, and being presented to the right, the left, or both ears. Equal RTs for monaural and diotic presentation (BLDERTs) were obtained with a level difference of approximately 5 dB. A second experiment showed that different results obtained for the left and right ear are largely due to the responding hand, with ipsilateral responses being faster than contralateral ones. A third experiment investigated the BLDERT for dichotic stimuli, tracing the transition between binaural and monaural stimulation. The results of all three RT experiments are consistent with current models of binaural loudness and contradict earlier claims of perfect binaural summation.     

Binaural and temporal integration of the loudness of tones and noises

Subjects judged the loudness of tones (Experiment 1) and of bursts of noise (Experiment 2) that varied in intensity and duration as well as in mode of presentation (monaural vs. binaural). Both monaural and binaural loudness, for both types of signals, obeyed the bilinear-interaction prediction of the classic temporal integration model. The loudness of short tones grows as a power function of both intensity and duration with different exponents for the two factors (.2 and .3, respectively). The loudness of wide-band noises grows as a power function of duration (with an exponent of approximately .6) but not of sound pressure. For tones, binaural summation was constant but fell short of full additivity. For noises, summation changed across level and duration. Temporal summation followed the same course for monaural and binaural tonal stimuli but not for noise stimuli. Notwithstanding these differences between tone and noise, we concluded that binaural and temporal summation are independently operating integrative networks within the auditory system. The usefulness of establishing the underlying metric structure for temporal summation is emphasized.     

Nomnetric scaling of loudness and pitch using similarity and difference estimates

In Experiment 1, nonmetric analyses of estimates of similarity and difference were used to generate a scale of loudness for 1,200-Hz tones varying in intensity. For both similarity and difference estimates, loudness was found to grow approximately as the 0.26 power of sound pressure. In Experiment 2, nomnetric analyses of estimates of similarity and difference were used to generate a scale of pitch for 83.3-dB pure tones varying in frequency. For both similarity and difference estimates, pitch was found to vary with frequency in accordance with the mel scale.     

Sensory and cognitive factors in judgments of loudness

One thousand Hertz tones were presented at equal or unequal intensities to the two ears. In a binaural-summation experiment, the presentation of components was simultaneous, the auditory system integrated the components automatically, and the subjects judged the loudness of the unitary sensation. In two cognitive-summation experiments, the presentation of components was successive, and the subjects had to integrate the two sensations consciously to judge their "total loudness." Results of all three experiments are consistent with models of linear summation of "loudness," but the loudness scales differ in the two tasks: The scales that underlie binaural summation and cognitive summation are nonlinearly related. This outcome suggests two nested processes: First, the auditory system transduces stimulus energy to loudness sensations by means of a nonlinear function; second, tasks that require subjects to judge combinational relations between sensations may impose additional nonlinear transformations on the sensations before the latter are combined.     

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.