Critical bands and mixed-frequency scaling: Sequential dependencies, equal-loudness contours, and power function exponents

Abstract

Stimuli of random intensities and various but predictable frequencies were presented for repeated magnitude estimations on the same scale (mixed-frequency scaling). The frequencies for a particular judgment session were selected so that they lay either inside each other's critical bands or outside them. Contrastive dependencies of current magnitude estimation responses on previous stimuli of a different frequency were significantly affected by whether the two frequencies were inside or outside each other's critical bands, while assimilative dependencies were not. This reinforces the idea that such dependencies are sensory in nature and arise from a different mechanism than do the assimilative dependencies. Mixed-frequency scaling of loudness also gives rise to cross-frequency matching functions from which equal-loudness contours can be calculated. These contours calculated from the present judgments are similar to those produced from other methods, even when they are extrapolated to untested intensities. Power function exponents for loudness scaled in this way are larger for lower frequencies, as has been found in previous studies, and are consistent with the flattening of the calculated equal-loudness contours for low frequencies as intensity increases.

Constrained scaling: The effect of learned psychophysical scales on idiosyncratic response bias

“…West and Ward trained subjects to respond to lOOO-Hz tones according to a power function with an exponent of 0.60, then removed the feedback and randomly presented 65-, 100-, 1000-, and 8000-Hz tones. Subjects, responding according to the learned scale, produced results consistent with the research on equal loudness contours (e.g., see Marks, 1974b;Ward, 1990). Specifically, subjects' responses indicated that they found the 65-, 100-, and 8000-Hz tones to be significantly less loud than the lOOO-Hz tones at equal sound pressures.…”

“…The purpose of this was to provide subjects with an environment that promoted to the maximum extent their use of the learned scale. We expected, on the basis of wellestablished psychoacoustical results, that power function exponents for the 65-Hz tones would be larger than those for the IOOO-Hz tones (see Marks, 1974b, andWard, 1990, for reviews). This would reflect the fact that the rate of increase in loudness, relative to sound intensity, is greater for 65-Hz tones than for 1000-Hz tones.…”

“…Ward ( 1990) found a value for G equal to 0.0004. Using the average exponent found for the no-feedback 1000-Hz trials (0.54), it was determined that G was equal to 0.0003 when the mean 65-Hz exponent was 0.77 (the Equation 6 analysis) and 0.0002 when the mean 65-Hz exponent was 0.70 (the Equation 5 analysis).…”

“…In terms of intersubject variability, the lower variability for the exponent ratios suggests that the subjects maintained some idiosyncratic biases during the test phase, which were subsequently removed by taking ratios of the exponents. Following Marks (1974b) and Ward (1990), the exponents for different sound frequencies can be approximated by the following equations:…”

The slippery context effect in psychophysics: Intensive, extensive, and qualitative continua

“…They based this conjecture on the well-known finding that magnitude judgments of all sorts are susceptible to sequential dependencies: The response to the current stimulus depends not only on the physical characteristics of that stimulus but also on the stimuli and responses in earlier trials. In particular, Ward (1979Ward ( , 1982Ward ( , 1990) has uncovered two kinds of sequential processes. One, assimilation of the current response to prior responses, occurs independently of the quality or modality of the stimuli, whereas the sec-EXPERIMENT 4 Length at Two Colors Experiment 4 asked how changes in stimulus context might differentially affect judgments of length.…”