Thanks for all the replies! I will contact Neumann support and post the results.
I would take them to various spots in the apartment just to rule out local interference or something.
I walked around the apartment holding them and could not hear any obvious changes. Also, turning various other devices (LED driver, chargers) on and off does not affect the hiss. Wrapping one of them up in aluminum foil, leaving a small hole for the tweeter also does not make a noticable change.
Why is 0 gain the "favorable setting"? I use -15dB input gain and 94dB output level and that is more than enough for nearfield desktop use. No hiss detected unless I put my ear next to the tweeter. Also I just tried the 0dB & 114dB settings and the hiss is still not bad. Maybe there is an issue with the electricity at your apartment, or you are getting group loop somehow? You might want to check whether the noise is coming from the midwoofer or the tweeter. If it is from the midwoofer then this is not hiss.
Oops, I didn't notice the minus sign in the gain control! Switching to -15dB reduces the hiss a little but, but it's still noticeable at 1m. I don't have anything that could measure the quality of the electricity in the apartment. I'll read up about ground loops, but for all tests the only thing connected to the was the power cord, and I tried different power outlets throughout the apartment.
The hiss comes almost entirely from the tweeter, but there's a weak lower hiss from the midwoofer if i put my ear ~2cm from the midwoofer grill. At ~15cm the midwoofer hiss is not audible anymore.
I did some more thorough testing, by putting a speaker in a random on/off state and then trying to guess the state. Single speaker at 94dB, -15dB gain, no input connected and the light covered. Speaker was set in a random on/off state by balancing the on/off rocker switch on a power strip in a middle position, covering it with a towel, then dropping (with eyes closed) a heavy object onto the rocker, and then covering the whole thing up with another towel so I couldn't see how the object fell (randomization was therefore not the best). All of this listening to loud brown noise with headphones so that the pop when the light on the KH80 changes from red to white isn't audible. Distance to speaker marked with a microphone stand, so that I never get closer to the speaker than the given distance. Table was covered with a towel so that there is no tabletop reflection from the speaker. Don't know the ambient noise in my apartment, but I've been in libraries that were quieter.
Null hypothesis: the hiss is not audible at the given distance.
At 220cm:
| Actually on | Actually off |
| Guessed on | 11 | 9 |
| Guessed off | 6 | 8 |
p-value: 0.36: with a certainty of 95%, the null hypothesis cannot be rejected.
At 120cm:
| Actually on | Actually off |
| Guessed on | 11 | 9 |
| Guessed off | 3 | 24 |
p-value: 0.0015: with a certainty of >99%, the null hypothesis can be rejected.
At 100cm:
| Actually on | Actually off |
| Guessed on | 6 | 0 |
| Guessed off | 0 | 11 |
p-value 0.00008: with a certainty of >99.99%, the null hypothesis can be rejected.