NOW the rumble has progressed to a high-pitched whistle, almost like a sustained smoke alarm beep. It's no longer rumbling, just whistling. We shut off the steam boiler for 4 hours, no change. We shut off the water and drained some out, no change. We cut the electricity, no change. We checked all 6 apartments and found no source for the noise. What the heck is this??? Our next step is an exorcist!

1) wind: is the sound any better or worse on windy days?

2) air movement inside the walls, such as when the unit is heated and air is escaping

3) sounds made by the building heating and cooling at different times in the day: we had this with a skylight, made a whistling sound in the morning as the air in the partially sealed skylight warmed and escaped. It can also be wood creaking.

4) something outside: sound can carry in funny ways, sometimes from surprisingly far away

my guess is either wind, or heating/cooling of the building