After creating a make recover tape on a TAC-4 9000/770, the system lost three of five volume groups from the /etc/lvmtab. What would be the best way to recreate the volume groups in the lvmtab?

I do not understand how simply making a recovery tape could cause such a disaster. Did you try to run that tape? If you simply were running make_recovery and this happened I think that it was coincidence and you actually have some other problem.

But in any event, after a disaster like this, vgscan is the way I would proceed. First I would "cp /etc/lvmtab /etc/lvmtab.save". Then I would run "vgscan -pv" and see if it looks reasonable. As long as you use -p nothing will actually change. If it looks good (or at least better than the current state), I would run "pvscan -v". It may tell you to run other programs next like vgchange. Follow the instructions the vgscan gives you. Good luck.