There is some relation between frequency of tinnitus and frequency hearing loss, but not enough to be clinically useful.

I have no high tone hearing in my left ear thanks to rifle shooting, yet have never had tinnitus in my life.  So clearly there can be no necessary connection between deafness and tinnitus.

It is difficult to prove a correlation between the frequency affected and tinnitus. 

From  a clinical point of view there is  a correlation of tinnitus frequency and hearing loss which can be observes quite regularly. Usually the maximum hearing loss corresponds with the hearing loss frequency (see Schecklmann et al "Relationship between Audiometric slope and tinnitus pitch in tinnitus patients: insights into the mechanisms of tinnitus generation.", PLoS One. 2012;7(4):e34878.). This is mostly the case in patients where hearing loss reflects the most importatn trigger for tinnitus perception. In patients with other features of tinnitus generation (e.g. somatonsensory aspects) there might be no such correlation. In these cases the tinnitus frequency tends to be in the low frequency range.

there may be a relationship between tinnitus and hearing loss and tinnitus. However, do not forget that many patients with tinnitus also have normal hearing and many causes of tinnitus are not related to otologic pathology

In my clinical work with patients with tinnitus and hearing loss, with tinnitus and normal hearing, and hearing loss without tinnitus, I gave up on trying to determine an association. I did know that in most cases of tinnitus with hearing loss, the tinnitus was often resolved when hearing aids were worn. For those with tinnitus and normal hearing, hearing aids were inappropriate and tinnitus maskers were as often ineffective as effective. Of course, for those with hearing loss and no tinnitus, I often worried that hearing aids might be the trigger for tinnitus and in one case  I came in late (a hearing aid fit by  another practitioner had triggered tinnitus). 

So, in answer to your question, there may be a relation between tinnitus and hearing loss such that the tinnitus might be at the same frequency as the frequency of maximum hearing loss (assuming a NI notch). But, there is no relation for those with normal hearing (such as myself - I am listening to a 6400 Hz , or so, tone in my right ear while typing this and listening to television). 

As to research,, there is insufficient research to provide anything other than a vague answer to your question. It remains a patient-by-patient issue.

it is very difficult to find meaningful correlation between exact Frequency and intensity of hearing loss and Tinnitus but there is relation between hearing loss type and intensity and tinnitus frequency response. on the other hand we should attend to tinnitus duration because more duration can change in tonotopic map and central frequency of viii auditory neuron cells.

in general we accordance to neurofunctional tinnitus model we can say decreasing in hearing ability results in decrease of related spontaneous activity of outer hair cells which leads to increase of midbrain and high brain spontaneous activities to compensate its consequences.

later this abnormal activities can origin the neutral sound perception in brain which may attended or not. during conscious perception of phantom sound via  evaluative learning process it may lead to clinical distress tinnitus.

furthermore, in one research on healthy volunteers in UK (2014) by blocking special frequency band of input sound to ear continuously  in two week, they reported correlated phantom sound perception with blocked Frequency band but not exactly match.

Eventually we can say there is correlation between hearing loss type and specification but not exactly match.

I hope it is being useful. feel free to contact if you think I can help more.

Exact relation between tinnitus and hearing loss level  cannot be proved clinically since perceptual nature for tinnitus is highly variable within in subject and across subjects. 

Please see 

http://bit.ly/2eJ252H

and

http://bit.ly/1OHNSKd