I used to use brown noise, but I find that rain/ thunderstorm sounds are better. It's a noise that your brain is used to ignoring, and other sounds blend into it - even if they are almost as loud -while with the more homogeneous brown and white noise, it has to be louder than the sounds it's trying to mask.

Having said that, I'm not sure how well it would do for high pitched tinnitus.

Edited to add - now listened to the neuro modulator, nice one.