I've heard something similar for the past two years, except mine is at 78 Hz, and only in my left ear. As with you, I hear it only when it is extremely quiet. When the room ambient noise is above about 35 dBA, I never hear it.

Also, oddly, it comes and goes over a scale of months, seemingly at random. One day, I'll wake up in my quiet bedroom and hear it, and I'll continue to hear it in quiet environments for a month or two. Then, after those several months, I'll wake up again and find it gone.

I notice a very loose correlation to it abating after a loud weekend, like a weekend spent driving my race car or doing metal fabrication, but otherwise it seems random.

A while back I ran it down with medical professionals, but the gist of that expensive adventure was that it was likely idiopathic. It appears to be of the subjective type rather than objective, but -- long story short -- that's not definitive.

My "solution" for now is to run the ceiling fan at night during the months it's present.