Thanks for all the help. The likely answer is Kona, but I'm not even going to run to HoAnne's to confirm it. I couldn't afford it in the first place and happily I just found a good two yards of undyed cotton that will do very nicely, a bit softer hand, but that's a good thing since it's going to be bedware. When I can get around to it. More about that in the next post.
I've come up with a plan for this cloth, but I have a problem. I need more of the same fabric and, although it's a type of high-end cotton used by dyers, I cannot remember what the brand might be.
So, I'm asking all the fiber folk who may be reading to see if you can name what I will describe.
It's 100% cotton, very fine threads, tightly woven, with a smooth hand - if a little "hard". Even after dyeing and several washer/dryer trips it's still crisp and has held the dye like Alcatraz. It cracks when you snap it and will probably be hell to hand quilt, hence my decision to use it in a machine pieced design.
A long time ago I bought a few yards from TestFabric, but I don't recall the hand of that cloth being this fine. Any guesses?