The most common and most likely answer to this crossword clue is the 3 letter word EMO
E
M
O
Buddy explains!

The straight part
We know that "Music" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case music = emo.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 EMO mean?
EMO noun- (early 1990s) A particular style of hardcore punk rock
- (early 1990s) An individual or group of people associated with that subculture and musical style.
- (late 1990s-current) Any form of guitar-driven alternative rock that is particularly or notably emotional
- (late 1990s-current) An individual or group of people associated with a fashion or stereotype of that style of rock.
- (2000s) A young person who is considered to be over-emotional or stereotypically emo.
- Emotional; sensitive.
- Depressed.
- Associated with youth subcultures embodying emotional sensitivity.