-A Bard can get a +1d4 to a d20 roll, usable 1/day, to indicate he intently concentrates listening to his naturally musical ear. The circumstances of the roll must have something to do with music to be eligible. Think of this as using Bardic Inspiration on yourself.
-Anybody can get Advantage on a Perception check that has to do with hearing or sound. Maybe 1/day or repeatedly during 1 encounter per day.
-Anybody can add their Proficiency bonus to an appropriate Knowledge skill to indicate that you have studied (or at least heard about) famous musicians, performers, &c. Does Bardic Lore still exist?
-Your character gets a cantrip (Thunderwave?), usable 1/Short Rest. This could be another cantrip modified to do Thunder damage. You must have a musical instrument of some sort in your hand. (In effect, you screech a note. Later you have to re-tune the instrument so it sounds good again.)
-If you have the 'sing for your supper' background ability, you live one lifestyle higher than it indicates - because you are THAT good with music, and people leave bigger tips for you.