It's based on the premise that it is simplest to cut gears using an integer value of DP. Given that the circumference of a circle involves pi, which is irrational, and that useful gears have an integer number of teeth, it follows that the circular pitch of a gear with integer DP will be irrational. For a worm to mate with an integer DP gear the pitch of the 'thread' on the worm, to match the circular pitch of the gear, will also be irrational. So in essence you need to screwcut a thread with an irrational value for the TPI.
Of course since the 'TPI' will involve pi as a factor it is impossible to cut an exact thread, no matter how long the gear train. However, worms are fairly short, so an approximation is fine. My lathe uses 88/56, which is pi/2 to within 0.04%.
Andrew
Edited By Andrew Johnston on 17/11/2015 13:18:09
Edited By Andrew Johnston on 17/11/2015 13:18:56