Unit testing considerations and examples

So in your opinion unit tests are not required in this firmware module? I was expecting to test that the melody plays each note for the right amount of time, completes properly, etc. I thought it was a good thing to write unit tests for all code modules I would design in the future. When would firmware modules be pertinent vs when would they be useless?

I seem to be able to find articles on designing state machine unit tests, so I would guess this practice may be a good thing?