I'm impressed by Sherlock's ability to play that quartet alone, which I suspect means he's memorized everyone's part and simply adds his V1 part to those he "hears". What is the "morbid connection" Sherlock is thinking John won't recognize?

"Lieder" is plural, but it looks like Sherlock only plays a single Lied? Which one was it? So many good ones to choose from.

Oooh! Sherlock should compose something for John. I agree that it must illuminate his complexity as a character, both the light and shade, and all that's between. I wonder if other modes would work, or if a microtonal scale might be appropriate. And yes to either a suite of songs, or some other type of multi-sectional work.

And is the next phase of the experiment what happens in the minutes following this scene?

Fascinating how John keeps returning to John in his thoughts after he thinks through his relationship to others (Moriarty, Mycroft, and Irene). Does that mean this part of the series is deliberately structured as a rondo?

I'll end these music-related comments by adding that I love the counterpoint you weave here: Sherlock's seemingly cool deliberations against the physicality of John (his fingers, the way he holds and moves his body, his facial expressions, and breathing).

*applause for your work*