I watched a set of Rechnagel mounts fitted, not Mannlicher ones, (though they do make them), but the top rings were more than a half circle. To spring them, the installer placed an allen key in each of the 2 grub screws on both sides and simply tensioned them backwards to open the ring up. No scratches that way. A trick worth knowing.

Some of the oldest factory-made rings, such as the Akah rings I had on a 1935 Mauser 9x57, can't be separated in the usual way and the Landlicht scope needed to be dismantled to slide them onto the centre tube. They had enough adjustment then to be nipped up to tighten.