The most common and most likely answer to this crossword clue is the 6 plus 5 letter word PLAYED FALSE
I've seen this crossword clue in The Times
P
L
A
Y
E
D
F
A
L
S
E
Buddy explains!
The straight part
We know that "What traitor did/struck the wrong note" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what traitor did/struck the wrong note = played false.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.