For the very small amount of ringing that I sometimes detect, likely the result of playing in rock bands and attending concerts long ago (6 dB dip shelf from about 4500 to 5500 Hz), I have found that listening to very low levels of music, either on the system or via headphones, has improved the ringing (meaning reduced it) considerably. Perhaps it is the brain’s desire to hear detail at low levels that partially compensates so as to improve perceived signal to noise. Anyway, give it a try, it might help.
Tinnitus worries...
I have had on and off periodic ringing in the ears for 30 years, (lots of live music) and back in March I decided to invest in a new home audio system, speakers, amp preamp CD player and cables costing about 7k, I have almost constant low level tinnitus now, my doctor says it's a cumulative thing and there is little that can be done. I hardly listen to music beyond normal talking decibels, and am very careful about any other loud DB exposure. Odd how the tinnitus became constant the minute I got my new system set up. I guess this is more of a warning than anything else, so be careful!