There is no way a single pendant can provide adequate task lighting for a 12-ft. island. You need to do some investigating of light spread, lumens, etc.

But I can light an entire room with a single fixture; what makes kitchens so different? I've never had a kitchen with a bunch of pendants before. I guess I don't get it.

I think the idea is to have focused task lighting if you are planning to do prep or cleanup work on the island (as opposed to just ambient light). What about a single linear fixture with multiple bulbs? Or you always could just use cans.

I'd planned on cans but they'd look weird with the ceiling angles. (I'm not really fond of obvious cans.) One end of the island will be covered by cans somewhat though. Do you think a multi-bulb fixture with, say, a 4 ft. spread would be enough? It works for pool tables...

Something like this which is available with a 52" spread (and title 24 sockets as a bonus):

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I don't understand lighting enough to tell you if that fixture will give enough light for tasks but I think it's quite attractive and should look lovely over your island.

I'd definitely want lights spread out over a 12 ft island.

I think multiple pendants have been fashionable for many years, as I know I put them over my island in 2000. I've actually noticed recently a trend towards fewer larger pendants/fixtures. At the end of the day, it's really whatever you like. But, you do need more than one light fixture in that large a space. Lighting standards recommend MUCH more lighting in a kitchen than a living area, since a kitchen is a working space.

I'd really look for at least two large pendants, and more likely three. If you only do two, I think they really need to be BIG -- 12" or more in diameter, for sure. If you go with 3, you could get away with smaller ones. I did three 8" diameter simple pendants over my 7 ft island . . . My ceilings are 10 ft, and the larger pendants look balanced with the space, whereas I think the smaller more common pendants would look a little silly with those huge ceilings. Assuming you have tall ceilings since they are sloped . . . and knowing you have a gigantic island, I'd lean toward either two large (14-18" diameter multi-bulb) fixtures or three medium sized (8-12 inch, with one or two high watt bulbs).

That fixture linked above is only a bit over 4 ft wide, still leaving about 4 feet on each end, which seems a bit much to me to leave without an overhead light (since presumably each of the bulbs will just be 60 watt or equivalent). I'd want two fixtures, about 6 feet apart . . . or better yet, I'd really want three fixtures, each about 4 feet apart (i.e., end of island - 2 ft - light - 4 feet - light - 4 feet - light -2 feet -opposite end). That's what I'd do anyway.

I found this information to be very helpful when determining what I needed for lighting in my kitchen:
1.Room Foot Candles Needed
Living Room 10-20
Kitchen General 30-40
Kitchen Stove 70-80
Kitchen Sink 70-80

2.A lumen is a unit of measurement of light. A lumen is a way of measuring how much light gets to what you want to light. To determine the needed lumens, you will need to multiply your room square footage by your room foot-candle requirement.
For example, a 100 square foot living room, which needs 10-20 foot-candles, will need 1,000-2,000 lumens.
A 100 square foot dining room, which needs 30-40 foot-candles, will need 3,000-4,000 lumens.

3.You can find the rated lumen output under "Rated Lumens" on most products. Also if you are shopping on a website that doesn't list the lumen output there are calculators online that will help you convert the wattage to lumens.

As an example and an assumption that your island is 12x3 (36 sq feet): depending on what your are doing at your island you may need anywhere from 1440 lumens to 2880 lumens if you have a sink or stove on your island. If you have both a sink and stove you may need double the 2880.

Thanks all. I guess I'll multipendant it.

The kitchen is in the back of a greatroom which WILL have large pendants (we used to call 'em ceiling lights) in lieu of recessed lighting so I don't want to get too much stuff up there. But I guess we must be functional.

The island isn't symmetrical; the sink is not quite in the middle but almost. The island isn't supposed to be a focal point or anything. It's just there because I ran out of useable wall space.

For sink function, how about a pendant above the sink and one on each side, evenly spaced? Like SZruns suggests, but centered over the sink instead of the island ends? The end that gets the short end of the light stick will be in the can light area. Or for appearance's sake, do they need to be arranged centered over the island as a whole?

(The other cabinet runs are pretty well lit.)

Thanks again!

large pendants (we used to call 'em ceiling lights) in lieu of recessed lighting

"Ceiling lights" is a broad category that includes pendants, flush mounts, semi-flush mounts, chandeliers, and possibly even fans and recessed lights.

It's differentiated from table lamps, wall sconces, under cabinet lights, etc.

Gee thanks. I had no idea.

I too am in the same boat. I have a drop ceiling right in the middle of my 81” island. I might put one pendant light over the sink but I am not sure yet. Might look weird. Thanks for your help!