This is the phenomenon of diplacusis.

If one ear has normal thresholds and one has SNHL (a unilateral loss), there is a lot of diplacusis.

Bilateral SNHL gives less diplacusis, but there are probably pitch distortions because both ears are "messed up" the same way.

The newspaper said a report from the Association of British Orchestras showed that besides deafness, musicians could suffer damaged frequency discrimination, tinnitus (ringing or buzzing) and diplacusis (in which the pitch of a single tone is heard differently by each ear).

Diplacusis, also known as diplacusis binauralis or interaural pitch difference (IPD) is a type of tinnitus that is the perception of a single auditory stimulus as two separate sounds which may differ in pitch or in time.