n-Variable Bisection

This paper deals with the measurement problem of deriving an overall evaluation of stimuli by n-component bisection. Reflexivity and a generalised form of bisymmetry for two variables will be shown to characterise n-component bisection in terms of quasilinear means, unique up to linear transformations of their generating functions. Copyright 2000 Academic Press.     

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).     

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.     

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.     

Vibrotactile loudness addition

Os adjusted the intensity of vibration at a single locus on the right hand to a value equal in vibratory loudness to various patterns of vibration on the left hand. The patterns were created by 1 to 5 equated vibration generators, varied with respect to sensation level and distances among the vibrators. The results were: (a) increasing from 1 to 5 vibrators produced a doubling in vibratory loudness, (b) neither loudness level of the components nor distance among vibrators had any effect on the slope of the overall loudness growth function. Os also adjusted the intensity of a white noise to equal in magnitude the patterns of vibration presented (a) to the left hand as before and(b) to loci distributed over the surface of the body. The results were the same as those obtained using a single vibrator as standard. The specific loci stimulated did not appear to have any effect on vibrotactile loudness addition.     

Vibrotactile loudness addition

Os adjusted the intensity of vibration at a single locus on the right hand to a value equal in vibratory loudness to various patterns of vibration on the left hand. The patterns were created by 1 to 5 equated vibration generators, varied with respect to sensation level and distances among the vibrators. The results were: (a) increasing from 1 to 5 vibrators produced a doubling in vibratory loudness, (b) neither loudness level of the components nor distance among vibrators had any effect on the slope of the overall loudness growth function. as also adjusted the intensity of a white noise to equal in magnitude the patterns of vibration presented (a) to the left hand as before and (b) to loci distributed over the surface of the body. The results were the same as those obtained using a single vibrator as standard. The specific loci stimulated did not appear to have any effect on vibrotactile loudness addition.     

Discrimination of loudness similarity

Interval and ratio scale values were derived from measures of variability in the discrimination of loudness similarity. The interval values are linearly related to interval values based on equisection judgments (Garner, 1954), cumulating jnds (Riesz, 1933), and the dispersion of absolute judgments (Gamer, 1952). Scale values based on three diverse discriminability procedures and on the method of equisection are thus in good agreement. The ratio lvalues, however, are at variance with ratio values determined by direct ratio estimations (Stevens, 1955).     

Continuous judgment of level-fluctuating sounds and the relationship between overall loudness and instantaneous loudness

Summary The present investigation was designed to examine the most appropriate duration of instantaneous loudness and to find out the relationship between overall loudness and instantaneous loudness using 20-min road traffic noise. Instantaneous loudness was judged using the method of continuous judgment by category. The results suggest that instantaneous loudness is determined by the sound energy averaged during the 2.5-s period preceding each judgment, the duration of which seems to reflect the psychological present. It was also found that overall loudess is not an average of the instantaneous loudness of every moment, but that it is based on the instantaneous loudness above a certain level.     

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.     

A dynamic model of loudness adaptation

Previous research on loudness adaptation has provided heterogeneous and partly contradictory results. One major reason seems to be the inconsistent use of the term 'adaptation', which is due to differing operational definitions. Here, a measurement-theoretic definition of loudness adaptation is introduced, which also comprises a new method for the identification of certain linear dynamic systems. This is of particular interest, since there is a lack of dynamic models describing loudness adaptation. An experiment with sinusoidal sound stimuli (3000 Hz) was performed to test whether loudness adaptation can be modeled by such a linear system. The results of the system identification indicate that this is possible. Therefore, it can be concluded that the given definition of loudness adaptation might be appropriate and that the method of system identification is an applicable research tool.     

The anchor effects on the judgment of loudness using reaction time as an index of loudness

The present study was designed to investigate anchor effects on loudness judgments, using reaction time (RT) as an index of loudness. In Experiment 1, anchor effects were reexamined using verbal categories. Two kinds of anchor stimuli, 60- and 90-dB SPL 1,000-Hz pure tones, and four kinds of series stimuli, 60-, 70-, 80-, and 90-dB tones, were used. In this experiment, clear anchor effects were found just the same as in our previous experiment. Experiment 2 was conducted using RT as an index of loudness with stimulus conditions similar to those in Experiment 1. The same anchor effects could be seen in this experiment too. As RT is quite free from the limitations inevitably accompanying the verbal responses, it may be concluded that the anchor effects reflect the shift in perception.     

Temporal Bisection in Humans with Longer Stimulus Durations

Normal adults were tested in eight temporal bisection conditions, using 500-Hz tones as stimuli. Stimulus lengths matched, or overlapped with, durations normally used in bisection experiments with animals, and chronometric counting was prevented by using a concurrent digit-shadowing task. Four experimental groups were used to investigate any effects of stimulus spacing, and stimuli were logarithmically or linearly spaced between standard 'short' and 'long' durations of 1 and 4, or 2 and 8 sec. A slight leftward shift of the psychophysical function was found in the logarithmic spacing condition, relative to linear spacing. Four other groups tested the conjecture that the ratio of the short and long standards might play some role in determining the location of the bisection point, and conditions with long/short ratios of 2: 1 and 5: 1 were used. In all cases the bisection point was close to the arithmetic mean of the short and long standards, rather than the geometric mean, as in animal studies. Overall, however, smaller long/short ratios (which may indicate more difficult temporal discriminations) produced more sensitive timing. When the long/short ratio was held constant, however, data showed nearly perfect superimposition, indicating conformity to scalar timing. In general, results were similar to those from experiments with humans that used much shorter durations, indicating the animal/human differences in bisection do not depend on the absolute lengths of the stimuli used.     

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.     

The role of loudness in auditory imagery

Four experiments studied characteristics of auditory images initiated by named but unheard sounds. The sounds varied in their loudness ratings. As the difference between the loudness ratings of the two sound phrases increased, the times to mentally equate the loudness of the two images increased, whereas the times to identify the louder (or softer) of the images decreased. Moreover, congruity effects were found in the comparative judgment task: Times were faster to identify the louder of two loud-rated stimuli than to judge the softer of the same two stimuli, and times were faster to identify the softer of the two soft-rated than two loud-rated stimuli. The loudness ratings did not always influence performance, however, for neither an image generation nor a reading task showed response times that varied with loudness ratings. These results suggest that sensory/perceptual components are optionally represented in auditory images. These components are included when appropriate to a given task. A control experiment showed that the results cannot be considered epiphenomenal.     

Sequential effects in absolute judgments of loudness

The effects of preceding stimuli on the judgments of current stimuli were examined in a study using absolute judgments of loudness with feedback. It was found that the response on a given trial was dependent on the stimuli in the preceding sequence of at least five trials. Both assimilation and contrast effects were observed. The form of the dependency of a response on a prior stimulus was a function of the ordinal position of the stimulus in the preceding sequence of trials. The stimulus on the immediately preceding trial had an assimilative effect on the response and preceding stimuli two to five trials removed all showed a contrast effect on a given response. The extent to which these preceding stimuli contributed to the contrast effect was an increasing function of their recency. The reversal of the dependency of the response, from assimilation to the stimulus one trial back, to contrast with the stimuli two and more trials back, indicates a unique function of the immediately preceding stimulus in this task. Since there was a reduction in the variance of responses to those stimuli similar in value to the immediately preceding stimulus, it is proposed that the stimulus and feedback on the last trial were remembered and used asa standardin judging the presented stimulus. A model is presented in which it is assumed that the memory of the magnitude of the immediately preceding stimulus is contaminated in specified ways by prior stimuli in the series. The empirical findings of assimilation and contrastare expected consequences of the proposed memorial processes.