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.