I prefer to give you my reasons for which stones would be set first, and what tools would be used.
1) From my perspective, there are 4 sizes of smaller diamonds in this ring. (This does not include the main larger diamond.)
2) The side stones are in two sizes; the centre of the '3 rows' seems to be slightly larger.
3) The sequence of setting these stones is determined by their close proximity to each other. We should keep these claws in good condition while we are using our gem-setting tools.
4) What tools should be used to tighten each stone? From my own experience, I'd use the finest pointed tools; the question is, why? The closeness of each claw prevents the use of wide-nosed pliers.
5) I would use a 'bead burnisher' to move the claws toward each other. The tip of this tool would grasp the claw, allowing for clean movement. Any damage to the claws will be a major repair problem. (See the photo below showing how this tool is used.)
You can see how these 'recess-tipped' burnishers come in different sizes. Each has its own purpose.
6) The 'bead burnisher' should have a recess at the tip, where the claw will temporarily fit against. DON'T PUSH THE CLAW, BUT ONLY MOVE IT.
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(These diagrams might not be what an artist would draw, I'm a gemstone setter, not an artist :>)
1) The middle (red coloured stones) row of stones should be set first! Be careful with your burnishers at this stage of setting.
2) The two outside rows (blue colour) should be set last.
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This next diagram is the 'visual extension' to the centre stone.1) These mini-claws are really tight against each other. OUCH!
You should pick the most desirable-sized 'burnisher' you can find to fit each small claw.
2) I would 'pre-polish' all of the claws. NOW. When the stones go in, it will be too late!
3) The gemstones in this diagram at #4 are next.
4) This 'group of tight-fitting stones' is last to be set. These stones should be well-fitting with limited space in between each of them.
5) After this stone setting process, a complete 'light rouge' will suffice.
6) After the large centre stone is set, I would use a "77B, Cup Bur" to round the claws. AVOID USING A FILE, AS THESE CLAWS ARE QUITE SMALL & EXTREMELY DELICATE.
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WE'VE JUST COMPLETED THIS "CLUSTER RING". As always, there are no short-cuts in this 'Intermediate Level' of stone setting.