A drum chandy would be a great improvement. To calculate for yourself, measure the room and add the two numbers together (10+12 = 22.) That would be 22 inches. Measure your table width. Chandy should be half that width. Five foot wide table can take a 30" fixture. Then you have to find something in between but closer to the 30." You want 1/4 of the table out from under the fixture so it doesn't feel like diners have something hanging over their heads. Take the visual "weightiness" of the fixture into account. The beautiful drum Sweetlake posted will feel heavier because it looks solid. A more airy fixture will appear to be lighter. Also, hang it no higher than 36" above the table. You can hang it lower, but the only time you'd go higher is if the tallest person in your household would be standing by the table and looking down into the fixture. Keep it even with eye level of the tallest member of the household.

I think something with a rectangular shape might play up the interesting window shape.

What kind of a thing are you looking for? Do you want something modern, traditional, exotic?
It looks like you could use something with more width than length, but it's difficult to make suggestions without knowing "your taste."
Perhaps something like these:

Whatever you go for, it should be lower (so that when you are seated you can see each other, but not so high you see the light bulbs if it is a drum shade or like those suggested here.
Your table looks square so rectangular would be off-kilter. Try a round or square pendant light.
You have red in your room and something like this might give a little kick in red
Failing that a red drum shade

I rather like the existing bowl pendant with your casual Shaker style dining set although I agree with ASVInt that it should be lowered.

I like this centerpiece for its sparkle and the contrast it would bring to the dark table. http://houzz.com/photos/330457

Sorry... Posted this in wrong site.

I, too, like the shape of what you currently have. Here's another, but with detailing that mimics the knife strokes of your painting. As noted by others, hanging it lower would be a good call.