22 tet guitar

Having recently read Paul Erlich's excellent paper on 22 tet I have
decided to refret a guitar. I have a question regarding the maths of
this operation. The programme JI Calc gives the ratio 977/942 for 19
tet, and the ratio 4233/4178 for 53 tet. I would be grateful if anyone
could tell me how these are derived and how I could work out the ratio
needed to generate 22 tet. I would like to make sure that the luthier
and I agree on figures as the luthiers I know in Edinburgh rarely if
ever do unconventional jobs. I would be extremely grateful for help on
this point.