Pro taper
Rat, you always are very helpful so I will give you my solution (hope it helps). Whatever someone call a "taper" really doesn't matter except to describe a very general shape. I assume you are trying to create something that someone wants or are trying to figure out what they are really describing. I have heard people describe the same shaft with a different name. Just about everyone has a shaft that they are trying to describe and words never convey the specifics, so have them bring the shaft. Take the shaft and chuck it up, measuring every .020 at the front (gradual taper) and every .050 when it starts to grow more rapidly. Mark the dimensions on your lathe and you can give them a very close identical taper. Make sure that you sand both directions to blend in the shaft, and never stop in any one place while the shaft is spinning. Leave the shaft about .010 large and look down the shaft. You will see all the spots that are sanded unevenly. Sand the spots and the shaft front to back evenly (rotating the chuck by hand) until the shaft looks smooth. The tricky part is starting with a shaft that is close to the original without making it too small or wavy (if you take off too much at one time, chances are the shaft will warp). After this is accomplished, you will probably find out that no two shafts play exactly the same, even with the same taper. Best of luck, Kent