[peterle]

..same as yours mac (4.1 , 8 core) and all runs smooth with PT HDX 12.71
on Sierra.
You have to make a EFI-update for your 4.1 mac pro to become a
5.1 which then runs Sierra well.

> search for "EFI-upgrade 4.1 5.1 mac pro " or similar on google.
install the EFI update on your mac pro (can be a bit tricky)
and he becomes (depending on compatible Hardware) a 5.1.
> important point here: Graphics card !(ati 5870 works here)

The 4.1 (2009)and 5.1 macpro (2010-2012)
are nearly identically regarding the Hardware,
so its possible to upgrade an 4.1 to an 5.1 with the EFI ,
which Sierra needs as minimum.