Ratio-Estimations of Loudness-Intervals

By using a ratio-method to study the apparent magnitude of loudness-intervals, the present experiment unties the property scaled from the method of scaling.

Abstract

Two loudness-scales have been published: (a) the sone scale,1 and (b) the lambda scale.2 These two scales, based on different scaling procedures, are quite divers. The sone scale, based on direct estimates of the apparent ratios of loudnesses, is a power function of sound-intensity with an exponent of 0.3. The lambda scale, based on both estimates of equalappearing intervals and the apparent ratios of loudnesses, is much less steep and may be approximated by either a logarithmic function or a power function with an exponent of 0.13. Though the lambda scale, founded on both equisectional and fractionational judgments, is a hybrid scale, the form of the scale based primarily on equisectional data is in general agreement with both discriminability and interval scales.3 The present experiment deals with the adequacy of the sone and the lambda scales to predict ratio-estimations of loudness-intervals. Ordinarily, the apparent magnitude of loudness-ratios is studied by ratio-scaling methods, and the apparent magnitude of loudness-intervals by interval scaling-methods.4 That is, the scalings of ratios and of intervals are coupled to two different scaling tasks: that of making ratio-estimations and that of partitioning a segment into equal intervals. By using a ratio-method to study the apparent magnitude of loudness-intervals, the present experiment unties the property scaled from the method of scaling.