YASID

Anyone have a reference for a short story in which a famous composer is "brought back from the dead"
by giving a completely nonmusical person a "personality transplant" (my term, I'm not sure what it
was called in the story)? The twist is that the "revived composer" realizes just before they take
away the personality transplant is that he is the critics' version of the composer, a complete hack
with no actual original ability.

I read this in a short story collection. It might be James Blish or Arthur C. Clarke but I haven't
seen any titles that ring a bell in their bibliographies.