Individual differences in power functions for a 1-week intersession interval

Two experiments examined correlations of the power function exponents of individual Ss obtained in each of two sessions. Half the Ss for any task performed second sessions immediately after the first, the other half after a week’s delay. In Experiment I, groups of 16 Ss gave magnitude estimations of apparent area, or else of area and loudness. In Experiment II, groups of 16 Ss made cross-modality matches of apparent time duration to area. Significant correlations in all cases indicated consistent and persisting S differences in exponents. The results are related to the findings of other studies of such individual differences.     

Synesthetic perception and poetic metaphor

To explore the role of cross-modal perception in the apprehension of synesthetic metaphors, subjects read 15 short lines from poetry, each of which contained a metaphor relating visual and auditory qualities; the subjects' task was to set the loudness of a 1000-Hz tone and the brightness of a white light to match the levels implied by each metaphor. The sound settings and light settings suggest that a cross-modal equivalence between loudness and brightness largely underlay the responses to the metaphors. This general cross-modal equivalence was characterized by some notable intersubject differences and was modified, in part, by certain metaphors that resisted complete equivalence. Even so, the metaphorically induced settings of loudness and brightness are mainly governed by a cross-modality matching function that is qualitatively like the relation found in people with visual-auditory synesthesia, and that is quantitatively like the function obtained in more traditional psychophysical studies.     

Cross-modality matching of brightness to loudness by 5-year-olds

The purpose was to determine whether 5-year-old children could match the brightness of a light to the loudness of a sound, and whether the resulting cross-modality function resembled the power function produced by adults. Each of five children adjusted the voltage on a 15D-W lamp to make the apparent brightness appear equal to the loudness of a 500-Hz tone, which the E set to eight different levels. The results resembled those of five adults who performed the same task.     

Apparent warmth as a function of thermal irradiation

The skin of the back was periodically exposed to a source of radiant heat. In Experiment 1, 20 Ss matched numbers to the apparent warmth aroused by various levels of irradiant flux (method of magnitude estimation). In Experiment 2, 15 Ss matched the loudness of a white noise to the apparent uwmth aroused by the same levels used in Experiment I (method of cross-modality matching). Both experiments showed that apparent warmth is related to absorbed irradiance by a power function whose exponent is approximately 0.7.     

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.     

On predicting exponents for cross-modality matches

Mashhour and Hosman used magnitude estimations to scale seven continua: line length, time duration, finger span, loudness of noise, weight, gray reflectance, and surface area. The first four continua also served as the adjusted stimuli in 17 cross-modality matches among the various continua. Contrary to the view expressed by Mashhour and Hosman, the results appear to support the psychophysical power law. A reanalysis of the data shows that the exponents of the power functions obtained in cross-modality matches agree with the exponents of the power functions produced by magnitude estimations, provided correction is made for the regression effect. The measured discrepancies between the exponents predicted and those actually obtained show scatter that is consistent with that of other experiments. In particular, the scatter accords well with the distribution of 68 exponents predicted by Moskowitz from experiments in which Os matched both number and loudness to various taste concentrations.     

Cross-modality matching functions generated by magnitude estimation

It is possible to generate cross-modality matching functions by having subjects make magnitude estimates of sets of stimuli appropriate to different modalities. The sets are interspersed among each other in the same test session and judged on a common absolute scale of sensory magnitude. An appropriate statistical device locates stimulus levels that appear, on the average, to match. The method is fast, efficient, circumvents the need for continuous stimulus adjustment, and holds promise for the study of the individual as well as the average psychophysical function. To illustrate its potential uses, advantages, and limitations, we used the method to generate cross-modality matching functions relating loudness and brightness. Compared to the scales of loudness and brightness generated by the magnitude estimations of the same stimuli, the matching functions (1) conform better to power functions, (2) may show less variation in slope (exponent), and (3) show far less variation in absolute magnitude (position).     

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.     

Sequential dependencies and response range in cross-modality matches of duration to loudness

Subjects matched durations of keypresses to loudnesses of pure tones. Resulting duration responses were found to be assimilated to the value of the immediately preceding stimulus and responses from one to at least six trials back in the sequence of loudness stimuli. Responses were contrasted with the values of stimuli two through six trials back in the sequence. These sequential dependencies and other properties of the data were predicted by a cognitive model in which cross-modality matches are mediated by category judgments of stimuli on both continua, and subjects use heuristic strategies to reduce response uncertainty.     

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.     

Individual brightness functions

A total of 34 individual brightness functions were measured for 18 observers by two different methods. In one method the observer set various luminance levels of a white target and assigned numbers proportional to the apparent brightness of the levels set. In the other method the observer adjusted the loudness of a white noise and the luminance of a white target in order to achieve a series of cross-modality matches between loudness and brightness. Both methods gave good approximations to power functions, showing that the psychophysical power law holds for the individual perceiver.     

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 PROPERTIES OF DISTRIBUTIONS OF MAGNITUDE ESTIMATES OF LOUDNESS AND SOFTNESS

JOHN, I. D. The properties of distributions of magnitude estimates of loudness and softness. Scand. J. Psychol. 1971, 12, 261–270.–Distributions of magnitude estimations (MEs) of loudness and softness made by ten Ss to ten repetitions of ten stimuli were examined. Skew and relative variability of the distributions of MEs of individuals Ss was inconsistent with hypotheses advanced by Stevens & Guirao (1962) and Eisler (1962). The results were interpreted as consisted with Eriksen & Hake's (1957) subjective standard hypothesis, and a tendency to use large numbers with relatively greater consistency than smaller numbers. A reciprocal relationship was not found between MEs of loudness and softness.     

Cross-modality matching of muscular tension to loudness

In a single session, Ss produced and estimated a series of electromyographically measured tensions, estimated the loudness of pure tones, and then matched muscular tension to tonal loudness. In all cases, power functions adequately represented the estimation and matching data. For two Ss, who scaled tension in the abductor of the little finger, the slopes of the estimation functions successfully predicted the slopes of the matching functions. For the other Ss the prediction from estimation to matching data was fair, but not good; these Ss scaled adductor tension, for which the electromyographic measurements were methodologically questionable. The data suggest that a consistent scale of muscular tension can be constructed, and that the scale can be validated by crossmodal comparison.     

Tactile vibration: Change of exponent with frequency

When cross-modality matches were made between a 60-Hz vibration and such other continua as electric current through the finger, number, force of handgrip, and both binaural and monaural loudness, the exponent of the power function for vibration was found to be about 1.0 at 60 Hz. The dependence of the exponent on frequency has been studied in a series of intramodality matching experiments. The exponent appears to reach its largest value in the vicinity of 30 Hz and its lowest value in the vicinity of 250 Hz. The highest value is roughly twice the lowest value. Over the low-frequency range, there is a suggestive similarity between the power functions for vibration and those for auditory loudness. As a vibration sensor, the ear may behave much like the finger.     

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.     

Subject differences in cross-modality matching

Forty-eight Ss performed four tasks each: (1) magnitude estimation of area, (2) magnitude estimation of numerousness, (3) cross-modality matching of force of handgrip to area, and (4) cross-modality matching of force of handgrip to numerousness. An additional 48 Ss performed Tasks 2 and 4. Psychophysical power functions were fitted to the data of each S for each condition. Higher correlations between individual exponents were found for conditions employing a common response (i.e., estimating or squeezing) than were found for conditions with the same set of stimuli. Individual differences among exponents stem more from the idiosyncratic use of the dependent variable than from different sensory characteristics.     

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.     

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.     

Saturation of red: A prothetic continuum

A battery of procedures was used to scale the saturation of colors produced by mixtures of red and gray papers. By direct magnitude estimation, the apparent saturation was found to grow as the1.7 power of the percentage of red in the mixture. The power law was confirmed by the cross-modality matching of loudness to saturation. The inverse continuum, paleness, was also scaled. Saturation appears to be a prothetic continuum because the category scale is curved and the subjective size of the jnd increases as saturation increases.