The most common and most likely answer to this crossword clue is the 8 letter word FOLKSONG
I've seen this crossword clue in Independent
F
O
L
K
S
O
N
G
More clues leading to the result FOLKSONG
Buddy explains!

The straight part
We know that "traditional music" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case traditional music = folksong.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.
What does FOLKSONG mean?
FOLKSONG noun- A song, in any folk style, originating among ordinary people, usually non-professional musicians, and handed down by oral tradition.
- A song in the style of folk music, a modern genre of popular music.