The most common and most likely answer to this crossword clue is the 3 plus 3 letter word TIN EAR
I've seen this crossword clue in The Times
T
I
N
E
A
R
More clues leading to the result TIN EAR
Buddy explains!

The straight part
We know that "an unmusical attribute" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an unmusical attribute = tin ear.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.