He was French. His name was Monsieur Bergeron and he was skinny, tall man with a black pony tail (which Sherlock’s mother found outrageous but since he was one of the best violin teachers, she complied).
He loved to use great gestures and waved his hands about when he explained things, so he looked like he was trying to dance while chasing away a swarm of bees.
He cherished Sherlock’s intellect instead of being frightened like most people and challenged him with pleasure. They clashed constantly.
Sherlock liked him a lot and treasures the violin Monsieur gave him.
John taught Sherlock to shoot and how to handle a gun in various situations (which led to some of the most spectacular sex they ever had), so Sherlock decided that it might be a nice thing to teach John how to play the violin.
He played different scenarios with various outcomes in his mind, all started by the physical closeness of the situation and was very much looking forward to these lessons.
Compared to John (and probably everybody else on this planet) Sherlock is not a good teacher. He is way too impatient and criticising.
And John, as skilful as he can be with his surgeon’s hands, does not have a violinist’s hands.
Therefore the project died pretty much before it even began.