The noise is completely independent of settings on the interface. It is constant even with the interface's main volume control and all input gains all the way down. It is there even with the Mute button pushed in. The noise is definitely originating in the interface, because it stops when I unplug the speaker cable.
I have not made an actual measurement yet, though. I'll do that today. I'm wondering if my expectations are just unrealistic. I'm accustomed to no perceptible noise, but perhaps the MOTU was just very quiet.
Part of the problem, I think, is that I've always felt the gain was too high on my ADAMs. With both the current and previous interfaces I've had to turn the output down to -30 dB.
So another question for Focusrite users, please: what do you have your main volume set to? (Your speaker type and whether or not you're K-system calibrated would be helpful information, too.)