We haven’t seen that violin since Sherlock left it at John’s wedding. Not since Sherlock poured his heart and soul into that piece. Only in Sherlock’s mind when he played again as John and Mary fought, on their last chance at reconciliation.
That violin is Sherlock’s soul. A window to that great heart. It always has been. It speaks for him when he cannot. He doesn’t play like a scientist, he plays like a lover, with emotion, with sentiment.
That broken string on the beautiful instrument is that final snap, the climax to the story arc. He’s been pulled and played for far too long. His heart, his soul, is on the line now more than it ever has been.