I've found a solution that offers me considerable relief, but only on a temporary/sometimes quite brief basis.
But, then, there were plenty of times in the past when I desperately wished I could make a bout of particularly intense tinnitus go away, even for a few minutes. (And sometimes just getting rid of it, even briefly, allows me to get back to work -- or may be just reading the news -- my tinnitus can be quite distracting at times.)
First, my clumsy and probably far-too-facile hypothesis: the sort of whining, 'feedback'-like tinnitus that too often intrudes on my life IS the result of a neural/muscle feedback loop in my auditory system normally used to suppress or accentuate certain frequencies. (There's some science to support this, per my not necessarily recent reading.) But -- much like the rather different scenario of a public address/sound reinforcement system -- if the attempt to accentuate certain frequencies goes 'too far,' the frequencies are too elevated and (somehow) excite more compensation, causing greater difficulty (and, so, perhaps even greater attempt to accentuate the problem frequency?)
In order to break this increasingly problematic feedback loop, I 'intervene' by holding one or both fingers over the 'tabs' (tragus) of the ear, blocking the entrance to the ear canal -- and then humming at the problem frequency -- or a lower octave representation of it) for a few seconds or more until I sense a diminution of the unwanted 'ringing.' It took me a while to 'perfect' my technique. Since it's hard to target particular frequencies (especially an octave or two down from the ringing pitch), I frequently 'slide' (glissando) the pitch up to more or less the target range and then slide back down when I'm done. This seems to maximize the benefit.
Now -- as noted, the relief (for me) is temporary and sometimes tantalizingly brief. But even a half minute or so without that blasted ringing is worth the trouble for me.
I've shared this a number of times over the years -- but only a handful of folks have reported trying it and getting any benefit. But, honestly, my tinnitus can be so annoying that if my suggestion can even temporarily help some other sufferer, I'm happy to share.
(If you try it and get any relief, please let me know.)