Following the work of Stanley Stevens, psychophysical functions of stimulus intensity are commonly assumed to follow power laws, as illustrated below:
This appears to be true for a wide variety of different types of stimuli and sensations. A table that is often presented to illustrate this generality is from Stevens, 1975:
However, it is not obvious from perusing this table what kinds of stimuli tend to be associated with what kinds of power exponents -- in particular, what kinds of stimuli tend to be associated with positively accelerated psychophysical functions of intensity vs. negatively accelerated psychophysical functions of intensity. Indeed, the exponents in the table above appear to be distributed rather haphazardly to me, and I have not seen any mention of work suggesting it is otherwise in my admittedly limited literature search.
So my question is: Is anyone aware of research that attempts to characterize what kinds of stimuli tend to be associated with what kinds of psychophysical functions of stimulus intensity? If so, what is the basic summary from this research, and what are some suggested readings? As hinted above, I am particularly interested in stimulus features that predict positively vs. negatively accelerated psychophysical functions of stimulus intensity, but references to and descriptions of more specific research questions are also quite welcome.
Update: I thought it might help to say just a little bit more about exactly what I'm interested in finding out here, in as clear and concise a way as I know how. What I am looking for are any references to review papers and/or research articles that are about (or even that just mention) predicting the form of the psychophysical power law across a range of different stimuli, using stimulus-level predictors. It is hard to extract any general conclusions about this from Stevens's table above, given that the power law exponent appears to vary widely, sometimes being >1 and sometimes <1, even for stimuli on the same psychological continuum, as in the cases of "Taste" and "Warmth." The point of the table (and indeed the body of research that it is based on) is just to show that these functions follow power laws of some kind or other -- while this is mildly interesting, what I really want to know is how well we can predict what kinds of power laws different stimuli will follow. Please let me know if I can offer any additional clarification.