Let's say you want to divide a smooth cylinder--say hard maple -- that's about 3 inches in diameter using a parting tool -- or any other way -- so as to leave the smallest possible gap. ( I am thinking about grain match.) What's the least gap that you have ever gotten, approximately? I have used an old kitchen knife and gotten good results; but I am thinking that people here have some better thoughts.
I often use my Veritas hard backed cross cut saw to parts projects, some to conserve grain, others because I find this easier than a parting tool.
I get about 1/16in kerf with this saw. If the project is bigger diameter than twice this saw blade depth, I used a brass backed tenon saw which has a deeper blade. About the same kerf, perhaps a bit thicker.
I make a v-groove with a skew and then use my hacksaw to cut through the blank. I do this by running the lathe at a relatively slow speed. It's something I saw Alan Lacer do in a demo.
I have a parting tool I made out of a piece of bandsaw blade from a Wood Miser blade. Ground the teeth off and put a handle on it. Sharpened it so the cutting tip was slightly below center and thinned the blade top and bottom. The blade is about an inch wide and well under a 1/16" thick. About three inches long with a sort of fat handle. Be careful, its sort of flimsy and would twist if allowed. Keep it short.
They are already ground thinner on the back edge, so when I ground the teeth off, which would be the top of the bevel. It is mounted in rectangular Wenge handle glued together with it sticking out. Obviously they use great steel in those blades, and so far it hasn't failed, even being only about 1/16" kerf.
Even if you can't part all the way off, just starting with it will guide a thin saw to finish by hand.