Ahmedito:
If you cannot make a living as a pianist, you certainly have a future as a cryptologist.
The piece is the transcription for left hand of Bach's D minor Chaconne for violin - a piece that German musicologist Helga Thoene claims it was composed as a funeral hommage to Maria Barbara, Bach's first wife.
So the man Brahms had great admiration for was J. S. Bach. The dead spouse who was also a relative is his cousin Maria Barbara.
I rest my case.
(And if I'm wrong, I still have one more chance, right?

)
Best wishes,
Bernhard.