I understand that now, thanks.
Seems odd that the manufacturer would have chosen a non standard taper rather than use one that matched a readily available chuck arbor. As the taper socket is blind they would have to use purpose made short taper reamer unless they cut down a 1:48 or 1:50 taper pin reamer.
I tend to think of taper fits in terms of angles rather than ratios, although when driving I regards hills as 1:20 say rather than the percentage we see on road signs!
Out of interest, before I dismantled the tapers I machined a bit of scrap in the lathe and gripped it, a stub Mandrel, with a drill chuck in one of the turret positions. I then checked the MT3 taper for run-out (the small end so quite a long way from the chuck jaws) and was surprised that it was less than 0.1mm. Changing the turret position and re-gripping the mandrel showed consistent readings and I hope my home made adapter works as well.
Ian P