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.     

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.     

The psychological representation of musical pitch in a tonal context

In this series of experiments, evidence was found for a complex psychological representation of musical pitch. The results of a scaling study, in which subjects judged the similarities between pairs of tones presented in an explicitly tonal context, suggest that musical listeners extract a pattern of relationships among tones that is determined not only by pitch height and chroma, but also by membership in the major triad chord and the diatonic scale associated with the tonal system of the context. Multidimensional scaling of the similarity ratings gave a three-dimensional conical structure around which the tones were ordered according to pitch height. The major triad components formed a closely related cluster near the vertex of the cone; the remaining diatonic scale tones formed a less closely related subset farther from the vertex; and, the nondiatonic tones, still farther from the vertex, were widely dispersed. The results also suggest that, in the psychological representation, tones less closely related to the tonality are less stable than tones closely related to the tonality, and that the representation incorporates the tendency for unstable tones to move toward the more stable tones in time, reflecting the dynamic character of musical tones. In the similarity ratings of the scaling study, tones less related to the tonality were judged more similar to tones more related to the tonality than the reverse temporal order. Furthermore, in a delayed recognition task memory performance for nondiatonic tones was less accurate than for diatonic tones, and nondiatonic tones were more often confused with diatonic tones than diatonic tones were confused with nondiatonic tones. These results indicate the tonality-specific nature of the psychological representation and argue that the perception of music depends not only on psychoacoustic properties of the tones, but also on processes that relate the tones to one another through contact with a well-defined and complex psychological representation of musical pitch.     

Binaural summation of loudness: Noise and two-tone complexes

A series of six experiments used the method of magnitude estimation to assess how the two ears sum the loudness of stimuli with various spectra. The results showed that the binaural system sums loudnesses by at least two distinct sets of rules, one applicable to narrow-band stimuli (complete loudness summation), another to wide-band noises (partial summation, dependent on level). The main findings were: (1) Narrow-band noise (Vi-octave bands at 1,000 Hz) showed complete binaural loudness summation, like that previously reported for pure tones (Marks, 1978a). At all but low SPL, a monaural stimulus must be 10 dB greater than a binaural stimulus to be equally loud; a stimulus ratio of 10 dB corresponds to a loudness ratio of 2:1 on Stevens’ sone scale. (2) Wide-band noise (300-4,800 Hz) showed only partial summation, the subadditivity being confined largely to levels below about 60 dB SPL. This result obtained both with bands of white noise (flat spectrum) and pink noise (—3 dB/ octave). (3) Binaural summation of two-tone complexes depended slightly on frequency spacing. Narrow spacing (860 and 1,160 Hz) gave summation equal to about 10 dB, like that of narrowband noises and single tones, whereas wider spacing (675 and 1,475 Hz) gave less summation, equal to about 9 dB, and more like wide-band noise; however, a very wide spacing (300 and 4,800 Hz) gave summation like that of narrow-band noises and single pure tones.     

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.     

Effect of simultaneous auditory stimulation on vibrotactile thresholds

Vibrotactile thresholds were determined at 250 and 400 Hz in the presence of (1) the sounds emitted by the vibrator, (2) continuous tonal or narrow-band masking noise, or (3) a pulsed tone synchronized with the vibrator signal. The measure of a cross-modality effect was the threshold shift occurring between each condition and the control condition, in which earmuff silencers eliminated the vibrator sounds. Continuous tones or noise had no effect upon vibrotactile thresholds. However, auditory signals synchronized with the vibrator signals did significantly elevate vibrotactile thresholds.     

Loudness bisection and masking in the rat (Rattus norvegicus).

The bisection method of animal psychophysical scaling was examined as a measurement procedure. The critical assumptions of bisection scaling, as described by Pfanzagl (1968), were tested to determine if a valid equal-interval scale could be derived. A valid scale was derived in which loudness for the rat (Rattus norvegicus; n = 13) was a power function of sound pressure for 4-kHz tones. Masking noise reduced the discriminability of tonal stimuli but did not affect the bisection point. This result is consistent with an interval scale representation of loudness and demonstrates scale meaningfulness. Loudness bisection data that have been reported in the literature for 3 species (humans, rats, and pigeons) are in substantial agreement with our results.     

Interference in memory for tonal pitch: Implications for a working-memory model

The degree of interference caused by different kinds of stimuli on memory for tonal pitch was studied. Musically trained and untrained subjects heard a sequence of two tones separated by an interval of 5 sec. The tones were either identical in pitch or differed by a semitone. Subjects had to decide whether the tones were identical or not. The interval was filled with tonal, verbal, or visual material under attended and unattended conditions. The results revealed clear group differences. Musically trained subjects' retention of the first test tone was only affected by the interposition of other tones. In contrast, the performance of musically untrained subjects was also affected by verbal and visual items. The findings are discussed in the framework of Baddeley's (1986) working-memory model.     

Binding time: Evidence for integration of temporal stimulus features

Several lines of evidence suggest that during processing of events, the features of these events become connected via episodic bindings. Such bindings have been demonstrated for a large number of visual and auditory stimulus features, like color and orientation, or pitch and loudness. Importantly, most visual and auditory events typically also involve temporal features, like onset time or duration. So far, however, whether temporal stimulus features are also bound into event representations has never been tested directly. The aim of the present study was to investigate possible binding between stimulus duration and other features of auditory events. In Experiment 1, participants had to respond with two keys to a low or high pitch sinus tone. Critically, the tones were presented with two different presentation durations. Sequential analysis of RT data indicated binding of stimulus duration into the event representation: at pitch repetitions, performance was better when both pitch and duration repeated, relative to when only pitch repeated and duration switched. This finding was replicated with loudness as relevant stimulus feature in Experiment 2. In sum, the results demonstrate that temporal features are bound into auditory event representations. This finding is an important advancement for binding theory in general, and raises several new questions for future research.     

Perceptual hysteresis in the judgment of auditory pitch shift

Perceptual hysteresis can be defined as the enduring influence of the recent past on current perception. Here, hysteresis was investigated in a basic auditory task: pitch comparisons between successive tones. On each trial, listeners were presented with pairs of tones and asked to report the direction of subjective pitch shift, as either “up” or “down.” All tones were complexes known as Shepard tones (Shepard, 1964), which comprise several frequency components at octave multiples of a base frequency. The results showed that perceptual judgments were determined both by stimulus-related factors (the interval ratio between the base frequencies within a pair) and by recent context (the intervals in the two previous trials). When tones were presented in ordered sequences, for which the frequency interval between tones was varied in a progressive manner, strong hysteresis was found. In particular, ambiguous stimuli that led to equal probabilities of “up” and “down” responses within a randomized context were almost fully determined within an ordered context. Moreover, hysteresis did not act on the direction of the reported pitch shift, but rather on the perceptual representation of each tone. Thus, hysteresis could be observed within sequences in which listeners varied between “up” and “down” responses, enabling us to largely rule out confounds related to response bias. The strength of the perceptual hysteresis observed suggests that the ongoing context may have a substantial influence on fundamental aspects of auditory perception, such as how we perceive the changes in pitch between successive sounds.     

Impaired categorical perception of lexical tones in Mandarin-speaking congenital amusics

The degree to which cognitive resources are shared in the processing of musical pitch and lexical tones remains uncertain. Testing Mandarin amusics on their categorical perception of Mandarin lexical tones may provide insight into this issue. In the present study, a group of 15 amusic Mandarin speakers identified and discriminated Mandarin tones presented as continua in separate blocks. The tonal continua employed were from a high-level tone to a mid-rising tone and from a high-level tone to a high-falling tone. The two tonal continua were made in the contexts of natural speech and of nonlinguistic analogues. In contrast to the controls, the participants with amusia showed no improvement for discrimination pairs that crossed the classification boundary for either speech or nonlinguistic analogues, indicating a lack of categorical perception. The lack of categorical perception of Mandarin tones in the amusic group shows that the pitch deficits in amusics may be domain-general, and this suggests that the processing of musical pitch and lexical tones may share certain cognitive resources and/or processes (Patel 2003, 2008, 2012).     

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.     

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).     

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).     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equa Is k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equals k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

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 enhancement and summation in pairs or short sound bursts

When a pair of short, temporally spaced sound bursts is presented and the listeners are requested to match the loudness of a third, comparison burst to the overall loudness of the pair, a fundamentally different result is obtained than when they are instructed to match the loudness of the comparison burst to that of the second burst in the pair. Loudness-level changes occurring in the first situation are designated as loudness summation; those occurring in the second situation, as loudness enhancement. Some parameters of both phenomena are studied. The results lead to the suggestion of a principle of maximum similarity in stimulus matching and to a reinterpretation of some earlier data.