https://www.youtube.com/watch?v=2yDCox-qKbk
Thump the back of your head like that with your ears covered well about 40 times and enjoy the silence.
Thankfully that's what it's always been to me. The ringing is the meaning of silence and the notes are not at odds with each other.
When I realised that other people didn't hear the ringing when it was silent, I was a fair bit shocked.
I'm exactly the same, although I do know what caused it for me. My mother's then-boyfriend was an abusive piece of crap who used to haul me around by my ears whenever he felt angry. Sometimes he would throw me head first into the wall by pulling my ears hard in that direction, then use the back of my head for subsequent blows, so it could be neurological rather than an audiological phenomenon. (You'd think she would've put a stop to that, but you would be wrong - she stayed with him for a few more years.)
Normally the ringing would stop after a few hours, but I remember the day that it never stopped. I got so used to it that I tuned it out and completely forgot that the world was ever silent.