Critical fusion frequency as a function of stimulus intensity: and wavelength composition

Six Ss made judgments of equal loudness by adjusting the intensity of comparison tones of 10 different frequencies. The comparison tones were presented diotically alternately with standaxd tones. Each standard tone remained fixed at one frequency (125, 1,000, or 8,000 Hz) and one intensity (10, 20, 40, or 70 dB sensation level)while collecting the data for any single equal-loudness contour. In this manner, families of equal-loudness contours were generated for each of the three standard frequencies. The contours for the 1,000-Hz standard were compared with those in the literature. The families of contours for the 125- and 8,000-Hz standards, determined by the same algorithm, differed in the spacing of the contours from the 1,000-Hz standard family as well as from each other. Implications for the reflexive, symmetric, and transitive properties of the equal-loudness relation axe discussed.     

Auditory sensitivity and equal loudness in the squirrel monkey (Saimiri sciureus).

The effects of the type of reinforcer on auditory sensitivity and equal-loudness data were determined in the squirrel monkey. The monkeys, restrained and provided with earphones, were conditioned to depress and hold a bar down in the presence of a stimulus light and then to terminate the holding response after onset of a tone. In Experiment 1, the specified behavior sequence postponed electric shock; in Experiment 2, a food reinforcer was dependent on bar release during the tone. The shape of the auditory sensitivity function and the acuity level at each frequency were the same for the two procedures. The audible frequency range extended from below 0.125 kHz (lowest frequency used) to 46 kHz. Sensitivity was maximum at 8 kHz. Latency of bar release following tone onset served as the basic data for constructing a family of equal-loudness contours. The type of reinforcer appeared not to be a determinant of either the shape of individual loudness contours or the pattern of family of equal-loudness functions. At the lower sound-pressure levels, the equal-loudness contours closely paralleled the threshold curves. At more-intense levels, the contours tended to flatten and depend less on frequency.     

Context effects,reliability, and internal consistency of intermodal joint scaling

Context effects, intraindividual variability, and internal consistency of intermodal joint scaling with magnitude estimation (“magnitude matching”) were studied by instructing 12 subjects to judge the three pairs of odor intensity, loudness, and brightness on a common scale of perceived intensity as well as to judge odor intensity separately (unimodal magnitude estimation). Significant context effects were found by comparing odor intensity judgments obtained by separate versus intermodal joint scaling as well as across different modalities (loudness vs. brightness) in joint scaling. But no such effects were found for loudness or brightness when compared across modality of joint scaling. Intraindividual variability in the estimates imply about equal reliability in intermodal joint scaling and separate scaling. Good internal consistency was found, indicating that subjects are successful in expressing perceived intensities of different modalities on a common scale.     

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.     

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.     

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.     

Mixed-modality psychophysical scaling: Sequential dependencies and other properties

J. C. Stevens and Marks’s (1980) method of magnitude matching and a derivative, category matching, are examined in two experiments. Category matching produces highly similar matching functions to those of magnitude matching. The two methods are both subject to significant sequential dependencies, which, however, should not affect exponents of matching functions. Such mixed-modality scaling methods are also useful for theory testing. In the present case, responses were assimilated to the immediately previous response (different modality stimulus) but contrasted with the stimulus (same modality) two trials back in the sequence. The dependency of the response-response dependency on Sn-S_n-k was independent of stimulus modality. However, the usual dependency of the coefficient of variation of ratios of successive responses on Sn-S_n-k was not found. These results support the class of theories in which assimilative response-response dependencies and contrastive response-stimulus dependencies arise from different mechanisms, and disconfirm those in which both effects arise in a linked fashion from a single mechanism.     

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.     

Remembrance of sounds past: memory and psychophysical scaling

What is the role of long-term memories of previous stimulus-response mappings, and of previous sensory and perceptual experiences generally, in psychophysical scaling judgments? I conducted four experiments in an attempt to provide some preliminary answers to this question. In each experiment, subjects made judgments of the loudness of sounds on 3 successive days. Stimulus intensities were drawn randomly from the same set on Days 1 and 3 but from a different set, either all 12 dB higher or all 12 dB lower, on Day 2. Four different types of psychophysical scaling judgments were studied: category judgment without an experimenter-induced identification function, ratio magnitude estimation with a variable standard, absolute magnitude estimation, and cross-modality matching. The first two methods required completely relative judgment, the last two completely absolute judgment. Data from all methods reveal profound effects of stimulus-response mappings experienced on previous days (long-term memory) and immediately previous stimuli and responses (short-term memory) on responses to current stimuli. Responses were typically a compromise between absolute and relative judgment. Individual differences were dramatic.     

Unmasking the magnitude estimation response

The fuzzy judgement model of Ward (1979) predicts an inverse relation between the amount of stimulus information available to subjects and the magnitude of sequential dependencies on previous stimuli and responses in psychophysical scaling tasks. Ward confirmed this prediction for magnitude estimations of interdot distance for previous responses but not for previous stimuli, although the inverse relation has been repeatedly reported for both the previous stimuli and responses in absolute identification (e.g., Mori, 1989). This paper further explores this seemingly puzzling contradiction. A magnitude estimation of loudness experiment was conducted in which the amount of stimulus information available to subjects was manipulated by a modified version of informational masking (Watson, 1987). An absolute-identification-with-feedback experiment was also conducted to check the effectiveness of the informational masking in reducing the amount of stimulus information. The results of the magnitude estimation experiment show a striking similarity with those of Ward and generalize the failure of sequential dependencies on previous stimuli to vary inversely with stimulus information. An additional assumption that judgement strategies are altered under low-information conditions is necessary to explain this result.     

Mixed-modality psychophysical scaling: Double cross-modality matching for “difficult” continua

In mixed-modality psychophysical scaling, stimuli from different modalities are presented alternately for judgment on the same scale. The usual purpose is to produce cross-modality matching functions without actually doing cross-modality matches. This paper reports the results of two experiments that extend the method to situations in which the responses, themselves crossmodality matches on an easy-to-control continuum (duration), are used to derive matching functions for two difficult-to-control continua (here loudness and brightness). Derived cross-modality matching functions are highly similar to those obtained from magnitude estimation or category judgment responses. First- and second-order sequential dependencies also closely resemble those found in data from the methods that employ numerical response scales, with one exception. For the first time in these studies of mixed-modality scaling, current responses sometimes were found to be weakly contrasted to the values of previous stimuli of different modality from the current stimulus. The various sequential dependencies found may arise from different levels of processing, with intramodal response-stimulus contrast arising from sensory differentiation, inter- and intramodality response-response assimilation from perceptual categorization processes, and intermodality response-stimulus contrast from cognitive expectancies.     

Comparison of magnitude estimation and interval scaling of loudness

To identify whether equal-appearing interval or magnitude estimation scaling resulted in a data set with a closer correlation to the physical stimuli involved 20 young adults completing two tasks. In Task 1 subjects used a 7-point equal-appearing interval loudness of 18 10-sec. samples of babble speech, presented randomly at intensities of 5 to 90 dB SPL. In Task 2 subjects used magnitude estimation scaling to rate these stimuli, presented in a randomized order. Analysis showed significantly high correlations for both scaling methods and the stimuli (Spearman rho = 1.00 and .99, respectively). Subjects can use either form of scaling to rate changes in loudness.     

On the cross-modal perception of intensity

Are cross-modality matches based on absolute equivalences between the intensities of perceptual experiences in different senses, or are they based on relative positions within the respective sets of stimuli? To help answer this question, we conducted a series of three experiments; in each the levels of stimulus magnitude in one modality stayed constant while the levels in the other changed from session to session. Results obtained by two methods--magnitude matching and cross-modal difference estimation--agreed in revealing the following: First, the cross-modality matches seem to represent in all cases a compromise between absolute equivalence and relative (contextual) comparison, the compromise being about 50-50 for both auditory loudness versus vibratory loudness and auditory loudness versus visual brightness, but more nearly, though not wholly, absolute for perceived auditory duration versus visual duration. Second, individual variations abounded, with some subjects evidencing totally absolute matching, others totally relative matching (with little consistency, however, between tasks or between comparisons of different pairs of modalities). Third, the judgments of cross-modal difference were consistent with a model of linear subtraction, and in the case of loudness, the underlying scale was roughly compatible with Stevens's sone scale. Finally, a model designed to describe sequential dependencies in response can account for at least part of the context-induced changes in cross-modal equivalence.     

The listener's temperament and perceived tempo and loudness of music

The relationship between the listener's temperament and perceived magnitude of tempo and loudness of music was studied using the techniques of magnitude production, magnitude estimation scaling and cross‐modal matching. Four piano pieces were presented at several levels of tempo and loudness. In Study 1, participants adjusted tempo and loudness of music to their subjective level of comfort. In Study 2, participants estimated these parameters on a numerical scale and matched the length of a line segment to the estimates of these musical features. The results showed significant correlations of selected aspects of perceived tempo with perseveration and endurance as well as of selected aspects of perceived loudness with endurance and emotional reactivity. Perceived tempo and loudness, as measured by magnitude production and cross‐modal matching tasks, do not seem to systematically correlate with the six formal characteristics of behaviour distinguished in the most recent version of the Regulative Theory of Temperament (RTT). Additionally, there is some evidence that they are selectively associated with reactivity and activity, the dimensions of a previous version of the RTT. The study extends the methodology of research on music preferences and the stimulatory value of music. Copyright © 2009 John Wiley & Sons, Ltd.     

Reliability of magnitude matching

In each of four experimental sessions, each of 16 subjects gave magnitude estimates of the taste intensities of NaCl and the loudness of noise on a single, common scale--the method of magnitude matching. In all sessions, the intensity levels of the noises were identical; but in two sessions, the concentrations of NaCl were low, and in two they were high. Cross-modality matches (magnitude matches) between NaCl and noise were derived from the judgments, revealing two main findings: First, given constant NaCl concentrations, individual subjects showed reliably different magnitude matches. Second, changing the NaCl concentrations (context) strongly affected the magnitude matches. These findings suggest that magnitude matching may be useful in assessing interindividual as well as intergroup differences, though caution must be taken to minimize effects of context: Context effects are pervasive; they suggest the presence of a complex relativistic process operating when people judge the intensities of qualitatively different stimuli.     

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.     

Variability and sequential effects in cross-modality matching of area and loudness

Individual subjects' performance was examined for cross-modality matching (CMM) of loudness to visual area, as well as for magnitude estimation (ME) of the component continua. Average exponents of power functions relating response magnitude to stimulus intensity were .73 for area, .20 for loudness, and 2.44 for CMM. Predictions of the CMM exponent based on ME were higher than the empirical values, whereas more accurate predictions were made from magnitude production exponents obtained in a previous study. Sequential dependencies were assessed by comparing the response on trial n to the response on trial n--1. The coefficient of variation of the response ratio Rn/Rn-1 was systematically related to the stimulus ratio Sn/Sn-1 for both area and loudness. The coefficient was lowest for ratios near 1 and increased for larger or smaller values. For CMM, the coefficient of variation appeared to be independent of stimulus ratios. The correlation between log Rn and log Rn-1 was also related to Sn/Sn-1 for both ME and CMM. The correlation was highest when Sn/Sn-1 was 1 and dropped to 0 with increasing stimulus separation, but CMM yielded a shallower function than ME.     

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.     

Auditory reaction time and the derivation of equal loudness contours for the monkey

Monkeys were trained to release a telegraph key at the onset of a pure tone. Latency of the response was measured over a 70-db range of sound pressure (re 0.0002 dyn/cm(2)) at six frequencies (250 to 15,000 cps). Latency was found to be an inverse exponential function of intensity at all frequencies. Equal loudness was inferred from the equal latency contours which were constructed from the latency-intensity functions at each frequency. These data indicate peak auditory sensitivity for the monkey near 1000 cps. At the frequencies above and below 1000 cps consistently more sound energy was required for equal latency.     

Additivity of loudness across critical bands: A critical test

The use of magnitude estimation as well as axiomatic measurement theory has led to the suggestion that loudness adds across critical bands. In the present paper, we challenge this postulate by applying a more sensitive methodology, based on Falmagne’s (1976) random conjoint measurement procedure. A necessary condition for additivity of loudness was investigated in tone complexes consisting of 2-kHz and 5-kHz (resp. 3-kHz) components; the results showed systematic deviations from additivity. We argue that these deviations are due to asymmetric masking of the higher component by the lower one, and we propose a tentative quantitative model to account for the data. Such a model is in line with results from tone-on-tone masking, which show masking to be effective over a range of several critical bands.