Oofta
Legend
Yeah, I got that. I'd probably just let the other two make checks as normal, and then say that the person who was proficient in both the Perform skill and the Harp did slightly better than both of the others. (Unless there was a compelling reason not to. Maybe one of the others is using a magical instrument? Maybe one of them rolled a nat-20? Maybe the double-proficient harpist has a hangover, or is playing someone else's instrument? I can think of a dozen reasons off the top of my head.)
I should clarify. A swing of +1d20 will most likely govern any skill check or proficiency bonus, and it seems weird to nullify the specialist's proficiencies with a bad roll. ("Specialist" being someone who is skilled in both Perform and the harp.) Even with Advantage, the odds of the specialist getting out-performed by a lucky roll seems unfairly high. And playing a harp isn't really a test of luck....it's almost purely a test of skill.
Maybe allow a roll with a minimum of 10 for the specialist? Or 15 because they have advantage? I think the person who has just proficiency in the tool should have a chance to win, but I agree a single roll even with advantage can be quite the swing. But that's true of a lot of things D&D.
Like I said before, the person who has never picked up a harp before doesn't stand a chance winning a contest for playing the harp IMHO.