Dear Colleagues –
For those interested in psychophysical “laws”, the following two papers are now available freely online at Academia.edu and at ResearchGate and are available, on request, directly from me.
The first paper is::
“Sensation-growth equations for non-zero threshold sensation, evaluated using non-traditional, bounded Fechnerian integration, for Fechner’s Law and for Ekman’s Law, using 12 different Weber Fractions” Proceedings of InterNoise e-Congress 2020, Seoul, S. Korea
Let me explain the point of this paper. Traditionally, when deriving sensation-growth equations, lower bounds such as the stimulus-detection threshold and the corresponding sensation are ignored. That tradition of unbounded integration is replaced here by non-traditional, bounded integration, in which sensation at the stimulus-detection threshold is nonzero. Twelve Weber Fractions were chosen, all having historical utility. The Weber Fractions were combined with either Fechner’s Law or with Ekman’s Law to derive the sensation growth. The result is 24 reimagined sensation-growth equations as alternatives to the status quo. The equations have unique features; notably, the threshold sensation is always additive for sensation-growth derived using Fechner’s Law, and is always multiplicative for sensation-growth derived using Ekman’s Law.
The second papers is
“Non-classical, bounded Fechnerian integration for loudness: contrary to Luce and Edwards, initial loudness-difference-size stipulations are only recouped for linear loudness growth” Audio Engineering Society Convention Paper, The 149th Convention of the Audio Engineering Society, New York, NY, USA
The latter paper examines the limits of the equations introduced in the first paper, particularly, whether they return some simplifying assumptions made in their derivations. The same is then done for the sensation-growth equations introduced by Luce and Edwards (Psychological Review, 1958), thereby revealing a substantial error that has propagated throughout the literature to the present day: namely, that three popular forms of the Weber Fraction, when combined with Fechner’s Law, do not produce sensation-growth equations that subsequently return the selfsame Fechner’s Law (contrary to Luce & Edwards).
Thanks very much for your attention, and Happy New Year -
Lance Nizami, PhD
Bedford, MA 01730