I don't know much about plumbing, but I'm wondering what kinds of vents that a plumbing system might have. The only kinds I can think of are the ones that vent pressure from water heaters, and the vent tubes from the sewer pipes that stick out the top of the roof. The latter is just a tube as far as I know, there is no valve associated with it that might make a whining sound.

But yeah, it sure sounds like some kind of pressure release/build cycle through some kind of...

OH HEY. You said it was in the master bath. Is the sound coming from the toilet flush mechanism in the toilet tank? I have, on more than one occasion in the past, had to replace toilet flush mechanisms because they would make intermittent noises.

Although yours seems to be occurring in much faster cycles than I've ever heard before, I could see how it might happen this way. Here's how the cycle worked in the ones I had to replace:

- Flapper drain seal is not particularly good. Old flapper or some such. Or perhaps the chain that attaches to the flapper is loose enough to have folded and lodged partly under the flapper, causing a continuous leak.
- Tiny amount of water leaks past the flapper slowly.
- Water level lowers slightly over time.
- Floater sinks slightly and barely engages the flush valve. Not enough for a full flush, but just enough for a tiny amount of water to come out (here's where the noise is).
- Water level rises a bit and lifts the floater, closing the valve.

A combination of old flapper which leaks water, and an old flush mechanism with old seals on the valve that allow small amounts of water to leak out without fully flushing, can cause this.

I've also had the floater in one system be made of styrofoam, which got old and no longer stayed dry, it started to waterlog, which made the mechanism be "twitchy" where it sort of was on the edge of flushing constantly, thus making nearly continuous noises.