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.     

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.     

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.     

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.     

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.     

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.     

Induced loudness reduction as a function of frequency difference between test tone and inducer

When a high-intensity tone (inducer) is followed by a moderate-intensity tone (test tone), the loudness of the latter is reduced. This phenomenon, called induced loudness reduction (ILR), depends on the frequency separation of the two tones; as the difference in frequency increases, the amount of ILR decreases. However, the precise course of this decrease is not well known. This article presents two experiments that address this question. In the first experiment, the amount of loudness reduction produced by a 2.5-kHz 80-dB-SPL inducer was measured with the frequency of the test tone swept from 800 Hz to 6 kHz. In the second experiment, the amount of ILR was measured with the same inducer and with test tones set at 2, 2.5, 3, and 4 kHz. Both experiments show that some ILR occurs at frequency separations as wide as four critical bands.     

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).     

Auditory induction: Reciprocal changes in alternating sounds

When portions of a sound are replaced by a potential masker, the missing fragments may be perceptually restored, resulting in apparent continuity of the interrupted signal. This phenomenon has been examined extensively by using pulsation threshold, auditory induction, and phonemic restoration paradigms in which two sounds, the inducer and the inducee, are alternated (ABABA ... ), and the conditions required for apparent continuity of the lower amplitude inducee are determined. Previous studies have generally neglected to examine concomitant changes produced in the inducing sound. Results from the present experiments have demonstrated decreases in the loudness of inducers using inducer/inducee pairs consisting of tone/tone and noise/noise, as well as the noise/speech pairs associated with phonemic restorations. Interestingly, reductions in inducer loudness occurred even when the inducee was heard as discontinuous, and these decreases in loudness were accompanied by graded increases in apparent duration of the inducee, contrary to the conventional view of auditory induction as an all-or-none phenomenon. Under some conditions, the reduced loudness of the inducer was coupled with a marked alteration in its timbre. Especially profound changes in the inducer quality occurred when the alternating stimuli were tones having the same frequency and differing only in intensity-it seems that following subtraction of components corresponding to the inducee, an anomalous auditory residue remained that did not correspond to the representation of a tone.     

Facilitation by repetition in recognition memory for tonal pitch

Subjects made delayed pitch comparisons when the standard and comparison tones were separated by a sequence of interpolated tones. In some conditions, a tone of the same pitch as the standard tone was included among the interpolated tones. Recognition performance was superior for sequences where the standard tone pitch was repeated, even compared with control sequences of reduced size. The improvement in performance produced by the repeated tone depended on its position in the intervening sequence. Improvement was substantial and highly significant when the standard tone pitch was repeated in the second serial position of a sequence of six interpolated tones, but small and insignificant when it was repeated in the fifth serial position.     

Repeated magnitude estimations with a variable standard: Sequential effects and other properties

Twelve Ss made magnitude estimations of the loudness of each one of a sequence of pure tones according to the rule R(N) = R(N - 1) · [S(N)/S(N - 1)], where R(N) is the response on Trial N, R(N - 1) is the response on Trial N - 1, and S(N)/S(N - 1) is the judged ratio of the “loudness” of the pure tone presented on Trial N to that of the pure tone presented on Trial N - 1. It was found that these magnitude estimations were assimilated toward the immediately preceding stimuli as far as five trials back in the sequence of stimuli. In addition, ratio judgments were consistently asymmetric and the data displayed a form of “time order error.” In all cases, there are similar effects displayed in category judgment data. These and other data imply that at least some kinds of magnitude estimations may involve a judgment of the “difference” or “distance” between pairs of stimuli as a first step in the production of the response required by the judgment situation.     

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.     

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.     

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.     

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.     

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.     

Vibrotactile--auditory interactions are post-perceptual

Vibrotactile stimuli can elicit compelling auditory sensations, even when sound energy levels are minimal and undetectable. It has previously been shown that subjects judge auditory tones embedded in white noise to be louder when they are accompanied by a vibrotactile stimulus of the same frequency. A first experiment replicated this result at four different levels of auditory stimulation (no tone, tone at detection threshold, tone at 5 dB above threshold, and tone at 10 dB above threshold). The presence of a vibrotactile stimulus induced an increase in the perceived loudness of auditory tones at three of the four values in this range. In two further experiments, a 2-interval forced-choice procedure was used to assess the nature of this cross-modal interaction. Subjects were biased when vibrotaction was applied in one interval, but applying vibrotaction in both intervals produced performance comparable to conditions without vibrotactile stimuli. This demonstrates that vibrotaction is sometimes ignored when judging the presence of an auditory tone. Hence the interaction between vibrotaction and audition does not appear to occur at an early perceptual level.     

Evaluating frequency proximity in stream segregation

Consecutive sounds of similar structure that are close in frequency or pitch are more likely to be perceived as part of the same sequence than those at greater frequency separations. The principle of grouping into such perceptual sequences, or auditory streams, is known as frequency proximity. However, the metric by which one frequency difference is judged to be greater or less than another in complex auditory scenes is not yet known. Two experiments explored the metric for frequency proximity. We presented repeating three-tone stimulus patterns at a rate where they are normally heard as two streams, one containing the highest tone and one containing the lowest. The middle tone joined one stream or the other depending on its frequency. Subjects reported the perceived allocation of the variable tone by responding on a 5-point scale. The frequency at which either of these two percepts was equally probable was found to be lower than a logarithmic midpoint or the midpoints on a cochlear map or the Mel scale; that is, it was unlike metrics arrived at by direct comparisons of tones. Further, the midpoint for high and low tones presented synchronously was lower than that for the same tones presented sequentially, demonstrating that in addition to a proximity factor, some additional factor or factors must operate differently when the lower and upper fixed tones are, or are not, presented simultaneously.     

Confrontation naming impairment in dementia

In tone languages pitch variations (tones) serve to distinguish the lexical meanings of words. This study was conducted to examine the extent and nature of impairment in the perception of tones by aphasic patients who were monolingual speakers of Thai, a tone language which has five contrastive tones (mid, low, falling, high, rising). Six subjects participated in the study: two Broca aphasics, one transcortical motor aphasic, one conduction aphasic, one right brain-damaged nonaphasic, and one normal control. Three sets of stimuli (two real-speech, one synthetic-speech) were presented for identification, each set containing five Thai words minimally distinguished by tone. Results of the perception tests indicated that the performance of all four left brain-damaged aphasics differed significantly from that of the normal control, while the performance of the right brain-damaged nonaphasic did not. The normal performance of the right brain-damaged nonaphasic patient on this tone identification task suggests that deficits in the perception of tone exhibited by left brain-damaged patients can be attributed specifically to pathology in the language dominant hemisphere rather than to a general brain-damage effect. No difference in performance among the left brain-damaged patients could be attributed to a specific type of aphasic syndrome. The pattern of tonal confusions of the aphasics in comparison to that of normals suggests that their deficit is primarily quantitative rather than qualitative. Although two (mid, low) of the five tones accounted for a large percentage of the aphasics' errors, no uniform rank order of tones in terms of identifiability could be established across aphasic subjects, which suggests that their deficit is general to all five tones rather than selective to individual tones.     

Intramodal and crossmodal pairing and anchoring in comparisons of successive stimuli

Two experiments were conducted to study effects of modality, temporal position, and their interaction on comparisons of successive stimuli. In Experiment 1, intramodal (tone–tone and line–line) and crossmodal (tone–line and line–tone) stimulus pairs, with two interstimulus intervals (ISIs), 400 and 2,000 ms, were presented. Participants indicated which stimulus was the “stronger.” Time-order errors (TOEs) were assessed using the D% measure and were found in all types of pairs. Variation in TOEs across conditions was well accounted for by changes in parameters (stimulus weights, reference levels) in an extended version of Hellström’s sensation weighting (SW) model. With an ISI of 2,000 ms, the first stimulus had a lower weight (less impact on the response) than did the second stimulus. More negative TOEs were found with the longer ISI in all pair types except tone–line. In Experiment 2, participants indicated which of two lines was the longer or which of two tones was the louder. An intra- or crossmodal anchor, or no anchor, was interpolated between the stimuli. Anchoring tended to reduce the weight of the first stimulus, suggesting interference with memory, and to yield negative TOEs. Intramodal anchors yielded reduced weights of both stimuli, most dramatically for tones, suggesting an additional effect of stimulus interference. Response times decreased with crossmodal anchors. For line–line pairs, strong negative TOEs were found. In both experiments, the variation in TOE across conditions was well accounted for by the SW model.