Speaker wire construction and sound quality

I'm not new to mid to high end stereo listening but have concentrated, over the years, mostly on the obvious equipment choices such as amplifiers, CD players, loudspeakers, etc. Most recent decisions regarding these have been based on information and advice found through forums such as this and, for the most part, have worked out well.

In the old days (50+ years ago) when monaural was king and high volume strong bass reproduction was the goal of most young pursuers of high fidelity, speaker wire construction and quality were not common subjects of conversation. Everyday electrical extension cord in those days was the cable of choice. In the past twenty or thirty years my approach has not been that much different in that I have simply chosen specialized and relatively expensive heavy gauge wire and left it at that.

Things have changed. The choice of speaker conductor has become a big deal and I simply don't understand the technical arguments supporting one type or another of the available choices. For the most part I'm pretty happy with my system but am always looking for ways to reduce brilliance/shrillness which I am very sensitive to because of a hearing condition called hyperacusis.

I've tried some of the more obvious fixes such as tube based DAC's and they definitely have helped. FYI, my basic system consists of the following: Rogue Audio Sphinx integrated hybrid amp, Shanling solid state CD player, California Audio tube DAC and Martin Logan Odyssey speakers. This was not a ground up designed system, just what it has ended up being as a process of piecemeal evolution.

Getting back to speaker wire, is there really that much difference in sonic quality related to a choice of the many that are available? I've read many articles on the subject and the opinions vary greatly to the extent of being totally contradictory to one another. I don't have a super audiophile system, I know, but are there some basic considerations that one should take into account in making a choice, and is there any advantage to bi-wiring?

I'm not that good at describing sound character because I don't have a good handle on the terminology but I do know brilliance when I hear it. It was suggested by someone whose knowledge I respect, that speaker wire could have a positive effect in resolving the brilliance issue while maintaining detail. As an experiment, he loaned me a pair of cables that are highly reviewed and cost over $5000. I can't afford something like this but was curious to see if I could tell the difference; I couldn't. I even tried the same experiment with my pair of Jamo Concert 8 bookshelf speakers using the same music ( Jazz at the Pawnshop) thinking they might be more sensitive to subtle changes, and still could not discern a difference. I realize that this could be as a result of my own observation deficiencies but would very much like to hear what you all have to say about this issue.