The Slope of the Loudness Function: A Puzzle

Abstract

This paper deals with the slope of the loudness function considered as a sensory parameter. Shapes of individual loudness functions are examined in a measurement situation in which loudness is estimated by marking a point on a line. It is shown that such personalized loudness functions can be converted to power functions by computing zero points differing widely from listener to listener. The slopes of the computed loudness functions also differ markedly.

It is then shown that the slopes and zero points are closely related. All are simple transformations of a single loudness function with a slope of 0.30. The transformation is that of an elastic scale with a fixed unit system stretched between the righthand margin (maximum loudness) and the estimated zero point. This interpretation seems to be consistent with a single (sensory) loudness function reported through an elastic transformation (judgmental anchoring) reflecting the range of loudnesses the listener expects to hear.

The author begins by arguing with Stevens’s conclusions on the slope of the loudness function, ends by conceding reluctantly that Stevens was correct, and rediscovers the anchoring phenomenon along the way.

Reprinted from Messick, S. & Gulliksen, H. (Eds.), Psychological scaling, New York: Wiley, 1960. Abstract to this article added by the author.

This research was supported by The United States Air Force under Contract No. AF 41(657)-126, monitored by Aero Medical Laboratory, Directorate of Research, Wright Air Development Center, Wright-Patterson Air Force Base, Ohio.

The assistance of J. Howett and G. Yonemura in carrying out this study is gratefully acknowledged.