Papers there might not be, but the research has been attempted before. Notably by one Greg Crockett, who over 25 years ago programmed a major computer ( a Cray, I believe) with all the variables he could think of pertaining to banjos and the differing sounds resulting from those variables. His motive, of course, was to build a scientifically perfect banjo.

He never did, because aside from some very basic stuff that we already knew, such as "tighter heads favor higher frequencies", the computer basically said "GIGO" (garbage in, garbage out). According to the machine, there were simply too many unknowns and variables to derive any useful information.

I know not what variables the computer was asked to make sense of, but Greg was (and probably still is) a PhD in nuclear physics who had built several banjos by that time, so he had a pretty decent understanding of the mechanics involved and certainly knew more about computers than I ever will.

With the advent of chaos theory and fuzzy logic, you might be able to derive something today that simply couldn't be done 25 years ago, but until I see some solid proof of that (which corresponds with the things that we all know to be true from observation), I shall remain skeptical and shall simply continue to use my ears; seemingly the only parts of my body that remain in good working condition now that I've turned 60...

P.