Most tinnitus pitches sit between 3 kHz and 8 kHz, which is exactly the region where hearing damage tends to start. That is not a coincidence. The leading model — central gain — says that when the cochlea stops sending input at a particular frequency, the corresponding part of the auditory cortex turns up its internal volume to compensate. With nothing real to amplify it ends up amplifying spontaneous neural firing, and you hear a phantom tone pitched to the missing input.
This explains a lot. It explains why the pitch usually matches the high-frequency dip on the audiogram. It explains why people with severe hearing loss in the high frequencies have higher-pitched tinnitus than people with hearing loss in the speech range. It explains why hearing aids — which restore the missing input — quiet tinnitus in roughly two thirds of people with hearing loss.
So a high-pitched tone is the most common presentation. Lower hums, hisses and clickings exist too, often pointing to slightly different mechanisms.