I had heard that letting them soak in vinegar works to remove tarnish. It didn't work for me. A little came off, but definitely not enough to notice much shine.
This is what worked.
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It worked well, but it was not easy. I let the pulls soak in warm water mixed with BKF for over an hour in a plastic tub. Then I pulled out each one and scubbed each vigorously with a toothbrush and BKF paste I mixed together. Each pull took at least 5 minutes to clean, but the gunk came off.
This is what my work surface looked like when I was through. See all the dark tarnish that came off? Yuck!
I had 8 pulls to clean. Minus the soaking time, it took me at least 45 minutes of scrubbing to get all of them looking like this.
Real brass is actually quite pretty.