Center them on the beam and range/stove -- as those are more visually impactful elements of the view than the sink. People can ignore a sink faucet visually but not pendants that don't line up with island, beam, and range.

My two cents. (I am not a designer)

The sink faucet is centered with beam and stove behind it

I would center from the width of the island. You will have chairs on that side and will notice their spacing more than the faucet spacing.

Can I ask why the island wasn't centered to the beam?

I’m not a designer, my eye goes to the cabinets behind the the sink. I generally have a pretty good eye for symmetry. Usually hang pics without measuring. When looking at your photos, my eye naturally goes to the lines of the cabinets behind the island. In both instances the pendants seem to line up at about the same spot on the cabinets, about the third line or a bit more than the third line on the wall cabinets, given my rough use of measuring stick overlaid on your photos. However measuring in your first photo, off the side off the island, the lights may seem off to anyone seated there. In the second photo centered off the sink, they will be centered to those sitting there and to anyone looking in that direction. Keep in mind, not all views into your kitchen area will be straight on as we are looking at it. You have a lovely kitchen there!

debra

I would use the outside edges of the island rather than the off-center sink to determine the pendant placement.

Try using balloons tied to strings thumbtacked into the ceiling as faux light fixtures to help to decide on the placement.

You received some feedback about this in your thread from two days ago:

https://www.houzz.com/discussions/6410768/asymmetrical-island-and-pendant-placement

I think it would look best to have the pendants hung equal distances from the center of the beam. That way the chains will be the same length coming from the angled ceiling. I would just ignore the sink and the extra inches of island on the left.

I am really bad at math, so I just eyeballed it. But something like this?

I think they need to be closer together then you showed. Maybe centered to the 3 door wall uppers flanking the range hood?