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 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.     

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.     

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.     

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.     

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.     

Factors producing and factors not producing time errors: An experiment with loudness comparisons

Pairs of 1-sec, 1,000-Hz tones, with interstimulus intervals of 1.5 sec, were judged by 60 subjects in categories of “louder,” “softer,” and “equal.” The judgments referred to the first tone in the pair for half of the subjects and to the second tone for the other half. Perceived loudness differences were scaled by a Thurstonian method. The SPL of the standard tone alternated between 50 and 70 dB in one experimental series and between 30 and 50 dB in the other. Time errors (TEs) were consistently positive (first tone overestimated relative to second) at the lower SPL and negative at the higher SPL. This “classical” effect of stimulus level on TE was thus shown to depend upon the relative, rather than the absolute, level of stimulation. The judgment mode was of very little consequence, which strongly contradicts TE theories that emphasize response-bias effects. The quantitative results are interpreted in terms of a general successive-comparison model employing the concepts of adaptation and differential weighting of sensation magnitudes.     

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.     

Aptitude-related differences in auditory recognition masking

An auditory backward recognition masking task (Massaro, 1970) was administered to undergraduates selected for extreme scores on the Scholastic Aptitude Test and the Cattell Culture Fair Intelligence Test. In two experiments, significant group differences were found in threshold interstimulus intervals (ISIs) required for 75% correct tone recognition. High-aptitude subjects required less time for correct identification of target tones as “high” or “low”. They were more able to overcome the constraints imposed on time-dependent information processing by a masking tone. These group differences were interpreted as indicating better information processing efficiency (h (higher signal-to-noise ratio) in the high-aptitude subjects.     

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).     

Perceptual organization of acoustic stimuli by budgerigars (Melopsittacus undulatus): I. Pure tones

A new combination of operant conditioning and psychophysical scaling procedures was used to study auditory perception in a small bird. In a same-different discrimination task, budgerigars learned to discriminate among pure tones that varied along one or more acoustic dimensions. Response latencies were used to generate a matrix of interstimulus similarities. Multidimensional scaling procedures were used to arrange these acoustic stimuli in a multidimensional space that supposedly reflects the bird's perceptual organization. For tones that varied in intensity, duration, and frequency simultaneously, budgerigars were much more sensitive to frequency changes. From a set of tones that varied only in intensity, it was possible to calculate the growth of loudness with intensity for the budgerigar. For tones that varied only in frequency, budgerigars showed evidence of an "acoustic fovea" for frequency change in the spectral region of 2-4 kHz. Budgerigars and humans also differed in their perceptual grouping of tone sequences that rise, fall, or remain constant in pitch. Surprisingly, budgerigars were much less responsive to pitch contour than were humans.     

Loudness effects in pairs of tone bursts

The loudness of dichotic and monotic pairs of short tone bursts was investigated as a function of the interburst time interval. For short intervals, the loudness was increased relative ty the loudness of a single burst. However, the loudness of a burst pair was equal to the loudness of the second burst in the pair and, therefore, no loudness summation but only a loudness enhancement took place. In dichotic bursts, the loudness enhancement decayed monotonically as the time interval increased, and the rate of decay increased with sound intensity. In monotic bursts, the loudness enhancement decayed to a minimum at about 40 msec, independent of sound intensity. It had a tendency to rebound at longer time intervals and go through a relative maximum in the vicinity of 200 msec. The results are interpreted in terms of an interaction of peripheral and central poststimulatory inhibition with temporal 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.     

Auditory change detection: simple sounds are not memorized better than complex sounds

Previous research has shown that the detectability of a local change in a visual image is essentially independent of the complexity of the image when the interstimulus interval (ISI) is very short, but is limited by a low-capacity memory system when the ISI exceeds 100 ms. In the study reported here, listeners made same/different judgments on pairs of successive "chords" (sums of pure tones with random frequencies). The change to be detected was always a frequency shift in one of the tones, and which tone would change was unpredictable. Performance worsened as the number of tones increased, but this effect was not larger for 2-s ISIs than for 0-ms ISIs. Similar results were obtained when a chord was followed by a single tone that had to be judged as higher or lower than the closest component of the chord. Overall, our data suggest that change detection is based on different mechanisms in audition and vision.     

NATURAL MUSICAL INTERVALS:

Abstract— Ancient and medieval scholars considered tones related by simple (small-integer) ratios to be naturally pleasing, but contemporary scholars attribute the special perceptual status of such sounds to exposure. We investigated the possibility of processing predispositions for some tone combinations by evaluating infants' ability to detect subtle changes to patterns of simultaneous and sequential tones Infants detected such changes to pairs of pure tones (intervals) only when the tones were related by simple frequency ratios. This was the case for 9-month-old infants tested with harmonic (simultaneous) intervals and for 6-tnonth-old infants tested with melodic (sequential) intervals. These results are consistent with a biological basis for the prevalence of particular intervals historically and cross-culturally.     

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.     

Proactive interference of a sequence of tones in a two-tone pitch comparison task

Subjects compared pitches of a standard tone and a comparison tone separated by 1,300–3,000 msec and responded according to whether the comparison tone sounded higher or lower in pitch than the standard tone. Three interfering tones at 300-msec intervals were presented before each pair of tones. Their pitch range varied, being either below or above the pitch of the standard tone; in some of the trials, their pitches were identical to the pitch of the standard tone (no interference). The highest error rate in performance was found when the interfering tones and the comparison tone deviated in the same direction in pitch from the standard tone. In turn, their deviations in the opposite directions resulted in the lowest error rate. This effect was not found to be dependent on whether the interfering tones were randomly ordered or monotonically ordered, together with the standard tone, into melodically ascending/descending sequences. An intermediate error rate in performance was found when the interfering tones and the standard tone were identical. The results support earlier hypotheses, presented in the context of retroactive interference, by demonstrating proactive interference of a tone sequence at the level of representations of individual tones.     

Hear it playing low and slow: How pitch level differentially influences time perception

Variations in both pitch and time are important in conveying meaning through speech and music, however, research is scant on perceptual interactions between these two domains. Using an ordinal comparison procedure, we explored how different pitch levels of flanker tones influenced the perceived duration of empty interstimulus intervals (ISIs). Participants heard monotonic, isochronous tone sequences (ISIs of 300, 600, or 1200 ms) composed of either one or five standard ISIs flanked by 500 Hz tones, followed by a final interval (FI) flanked by tones of either the same (500 Hz), higher (625 Hz), or lower (400 Hz) pitch. The FI varied in duration around the standard ISI duration. Participants were asked to determine if the FI was longer or shorter in duration than the preceding intervals. We found that an increase in FI flanker tone pitch level led to the underestimation of FI durations while a decrease in FI flanker tone pitch led to the overestimation of FI durations. The magnitude of these pitch-level effects decreased as the duration of the standard interval was increased, suggesting that the effect was driven by differences in mode-switch latencies to start/stop timing. Temporal context (One vs. Five Standard ISIs) did not have a consistent effect on performance. We propose that the interaction between pitch and time may have important consequences in understanding the ways in which meaning and emotion are communicated.     

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.