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.     

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.     

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).     

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.     

Prepulse effects on magnitude estimation of startle-eliciting stimuli and startle responses

The present studies investigated the relationship between prepulse effects on the modification of the brainstem startle reflex and magnitude estimates of startle-eliciting stimuli. In Experiment 1, startle eyeblink responses were elicited in 24 students, half of whom were instructed to estimate the loudness of the startle stimulus (actual intensities of 80, 90, and 100 dB) and half of whom were instructed to estimate the magnitude of their eyeblink. When weak acoustic prepulses preceded the startle-eliciting stimulus, eyeblink amplitude was inhibited, and estimates of response magnitude decreased, but estimates of startle stimulus magnitude decreased only when 100-dB startle stimuli were presented. In Experiment 2, the same startle stimuli were preceded on some trials by a vibrotactile prepulse to the hand. In conditions in which startle amplitude was inhibited, startle stimulus magnitude estimates were not affected. This suggests that the effect of acoustic prepulses on 100-dB startle stimuli in Experiment 1 may have been due to loudness assimilation, an effect independent of the prepulse inhibition of startle responding.     

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.     

Power functions of loudness magnitude estimations and auditory brainstem evoked responses

The correspondence between subjective and neural response to change in acoustic intensity was considered by deriving power functions from subjective loudness estimations and from the amplitude and latency of auditory brainstem evoked response components (BER). Thirty-six subjects provided loudness magnitude estimations of 2-sec trains of positive polarity click stimuli, 20/sec, at intensity levels ranging from 55 to 90 dB in 5-dB steps. The loudness power function yielded an exponent of .48. With longer trains of the same click stimuli, the exponents of BER latency measures ranged from -.14 for wave I to -.03 for later waves. The exponents of BER amplitude-intensity functions ranged from .40 to .19. Although these exponents tended to be larger than exponents previously reported, they were all lower than the exponent derived from the subjective loudness estimates, and a clear correspondence between the exponents of the loudness and BER component intensity functions was not found.     

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.     

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.     

Effect of loudness on reaction time and response force in different motor tasks

Van der Molen and Keuss, in 1979 and 1981, showed that paradoxically long reaction times occur with extremely strong auditory stimuli when the task is difficult, e.g., choice-by-location or Simon paradigm. It was argued that this paradoxical behavior of RT is due to active inhibition of an arousal-dependent bypassing mechanism to prevent false responses. As the peak force, i.e., maximal force exerted by participants on a response key, is considered to be related to immediate arousal, we predicted that for extremely loud stimuli and for difficult tasks, lengthening of RT should be associated with reduction of peak force. Moreover, these effects should be enhanced when emphasis is on accuracy rather than speed. Although the relation between RT and intensity depended on task difficulty, no increase in RT was found for the loudest tones. Moreover, peak force increased monotonically with loudness, showing no tendency to be suppressed for loudest tones and difficult tasks.     

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.     

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.     

Loudness and reaction time: I

It is widely assumed, based on Chocholle’s (1940) research, that stimuli that appear equal in loudness will generate the same reaction times. In Experiment 1, we first obtained equal-loudness functions for five stimulus frequencies at four different intensity levels. It was found that equal loudness produced equal RT at 80 phons and 60 phons, but not at 40 phons and 20 phons. It is likely that Chocholle obtained equivalence between loudness and RT at all intensity levels because of relay-click transients in his RT signals. One main conclusion drawn from Experiment 1 is that signal detection (in reaction time) and stimulus discrimination (in loudness estimation) require different perceptual processes. In the second phase of this investigation, the RT-intensity functions from six different experiments were used to generate scales of auditory intensity. Our analyses indicate that when the nonsensory or “residual” component is removed from auditory RT measures, the remaining sensory-detection component is inversely related to sound pressure according to a power function whose exponent is about — 3. The absolute value of this exponent is the same as the .3 exponent for loudness when interval-scaling procedures are used, and is one-half the size of the .6 exponent which is commonly assumed for loudness scaling.     

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.     

Stimulus sequence and the exponent of the power function for loudness

In two experiments, 15 and 13 subjects estimated the loudness of 12 sound-pressure levels (38-104 dB; 6-dB intervals) of a 1000-Hz tone by the method of magnitude estimation with a modulus assigned to the first stimulus presented. The tone duration was 1 sec. and the interstimulus interval was 6 sec. The presentation order was systematically ascending-descending in one experiment and balanced-irregular in the other. The results indicate that (1) loudness is a power function of sound pressure with an exponent of 0.60 for the systematic order and 0.29 for the irregular order. (2) For both the irregular and systematic orders, a large step-size (12 or 18 dB) between the stimulus on Trial n and on Trial n-1 (or n-3) results in a slight assimilation effect. This also occurs for the small step-size (6 dB) in the irregular order. (3) The size of momentary exponents (based on two points, Trials n and n-1 or n-3) depends on the sound pressures of successive stimuli, whether the steps are positive or negative, and whether the stimuli have been presented in systematic or irregular order. For positive steps, the momentary exponent is lower for a soft tone (Trial n) than for a loud tone, whereas for negative steps the momentary exponent is lower for a loud tone than for a soft tone. These effects ar more pronounced when these stimuli are presented in an irregular order. A relative judgment model is offered for magnitude estimation. It assumes that subjects judge the loudness of a stimulus in terms of three reference markers: the minimum and maximum sound pressures as well as the sound pressure of the previous stimulus.     

Shift in stimulus range and the exponent of the power function for loudness

The exponent of the power function for loudness was tracked over the course of 60 trials with one stimulus range and compared to the exponent over the course of 60 subsequent trials with a different stimulus range. Three stimulus sets were used: (1) weak, a short range of relatively soft tones (45-55 dBA); (2) strong, a short range of relatively loud tones (64-74 dBA); and (3) complete, a longer range of soft to loud tones (40-90 dBA). All pairs of stimulus sets were tested, together with three control conditions in which no shift in range occurred. Ten subjects were run in each of the nine groups. For preshift trials, the mean exponent was lowest for the strong stimulus series, highest for the weak series, and at an intermediate value for the complete series. These differences were all significant. Following a shift in stimulus range, the weak series still yielded the highest exponent, but the exponents were not reliably different for the complete and strong series. Postshift exponents also depended significantly on the preshift range experienced by the subjects. These effects were not confined to the period immediately following the shift in range, but persisted for up to 60 trials.     

Magnitude judgments of loudness change for discrete, dynamic, and hybrid stimuli

Recent investigations of loudness change within stimuli have identified differences as a function of direction of change and power range (e.g., Canévet, Acustica, 62, 2136–2142, 1986; Neuhoff, Nature, 395, 123–124, 1998), with claims of differences between dynamic and static stimuli. Experiment 1 provides the needed direct empirical evaluation of loudness change across static, dynamic, and hybrid stimuli. Consistent with recent findings for dynamic stimuli, quantitative and qualitative differences in pattern of loudness change were found as a function of power change direction. With identical patterns of loudness change, only quantitative differences were found across stimulus type. In Experiment 2, Points of Subjective loudness Equality (PSE) provided additional information about loudness judgments for the static and dynamic stimuli. Because the quantitative differences across stimulus type exceed the magnitude that could be expected based upon temporal integration by the auditory system, other factors need to be, and are, considered.     

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.     

Perceived vibration and the loudness of low-frequency tones

Vibration and low-frequency tones were scaled for loudness by two numerical estimation procedures and by cross-modality matching. The same ranges of frequencies, from 30 to 250 Hz, were delivered to the ear and to the fingertip. For vibratory loudness, two sets of power functions were obtained, of which the low-frequency set was somewhat steeper. Tonal loudness gave a family of power functions of approximately the same slope at all the frequencies tested. For frequencies above 100 Hz, the growth of loudness is about the same for both modalities. Below this frequency, vibratory loudness grows more rapidly than tonal loudness.